diff --git a/app/toysat/toysat.hs b/app/toysat/toysat.hs
index 49104806..9b090b14 100644
--- a/app/toysat/toysat.hs
+++ b/app/toysat/toysat.hs
@@ -853,7 +853,7 @@ solvePB opt solver formula = do
             where
               -- Use BOXED array to tie the knot
               a :: Array SAT.Var Bool
-              a = array (1,nv') $ assocs m ++ [(v, Tseitin.evalFormula a phi) | (v,phi) <- defs]
+              a = array (1,nv') $ assocs m ++ [(v, Tseitin.evalFormula a phi) | (v,phi) <- IntMap.toList defs]
 
       pbo <- PBO.newOptimizer2 solver obj'' (\m -> SAT.evalPBSum m obj')
       setupOptimizer pbo opt
@@ -960,8 +960,8 @@ solveWBO' opt solver isMaxSat formula (wcnf, wbo2maxsat_info) wcnfFileName = do
           a :: Array SAT.Var Bool
           a = array (1,nv') $
                 assocs m ++
-                [(v, Tseitin.evalFormula a phi) | (v, phi) <- defsTseitin] ++
-                [(v, SAT.evalPBConstraint a constr) | (v, constr) <- defsPB]
+                [(v, Tseitin.evalFormula a phi) | (v, phi) <- IntMap.toList defsTseitin] ++
+                [(v, SAT.evalPBConstraint a constr) | (v, constr) <- IntMap.toList defsPB]
 
   let softConstrs = [(c, constr) | (Just c, constr) <- PBFile.wboConstraints formula]
 
diff --git a/src/ToySolver/Converter/PB.hs b/src/ToySolver/Converter/PB.hs
index 3d2e3077..228d4718 100644
--- a/src/ToySolver/Converter/PB.hs
+++ b/src/ToySolver/Converter/PB.hs
@@ -216,7 +216,7 @@ quadratizePB' (formula, maxObj) =
       }
     , maxObj
     )
-  , PBQuadratizeInfo $ TseitinInfo nv1 nv2 [(v, And [atom l1, atom l2]) | (v, (l1,l2)) <- prodDefs]
+  , PBQuadratizeInfo $ TseitinInfo nv1 nv2 (IntMap.fromList [(v, And [atom l1, atom l2]) | (v, (l1,l2)) <- prodDefs])
   )
   where
     nv1 = PBFile.pbNumVars formula
@@ -556,13 +556,8 @@ wbo2pb wbo = runST $ do
     , WBO2PBInfo nv (PBFile.pbNumVars formula) defs
     )
 
-data WBO2PBInfo = WBO2PBInfo !Int !Int [(SAT.Var, PBFile.Constraint)]
-  deriving (Show)
-
--- TODO: change defs representation to SAT.VarMap
-instance Eq WBO2PBInfo where
-  WBO2PBInfo nv1 nv2 defs == WBO2PBInfo nv1' nv2' defs' =
-    nv1 == nv1' && nv2 == nv2' && sortOn fst defs == sortOn fst defs'  
+data WBO2PBInfo = WBO2PBInfo !Int !Int (SAT.VarMap PBFile.Constraint)
+  deriving (Show, Eq)
 
 instance Transformer WBO2PBInfo where
   type Source WBO2PBInfo = SAT.Model
@@ -570,7 +565,7 @@ instance Transformer WBO2PBInfo where
 
 instance ForwardTransformer WBO2PBInfo where
   transformForward (WBO2PBInfo _nv1 nv2 defs) m =
-    array (1, nv2) $ assocs m ++ [(v, SAT.evalPBConstraint m constr) | (v, constr) <- defs]
+    array (1, nv2) $ assocs m ++ [(v, SAT.evalPBConstraint m constr) | (v, constr) <- IntMap.toList defs]
 
 instance BackwardTransformer WBO2PBInfo where
   transformBackward (WBO2PBInfo nv1 _nv2 _defs) = SAT.restrictModel nv1
@@ -583,7 +578,7 @@ instance J.ToJSON WBO2PBInfo where
     , "num_transformed_variables" .= nv2
     , "definitions" .= J.object
         [ fromString ("x" ++ show v) .= jPBConstraint constr
-        | (v, constr) <- defs
+        | (v, constr) <- IntMap.toList defs
         ]
     ]
 
@@ -593,14 +588,14 @@ instance J.FromJSON WBO2PBInfo where
     WBO2PBInfo
       <$> obj .: "num_original_variables"
       <*> obj .: "num_transformed_variables"
-      <*> mapM f (Map.toList defs)
+      <*> (IntMap.fromList <$> mapM f (Map.toList defs))
     where
       f (name, constr) = do
         v <- parseVarNameText name
         constr' <- parsePBConstraint constr
         return (v, constr')
 
-addWBO :: (PrimMonad m, SAT.AddPBNL m enc) => enc -> PBFile.SoftFormula -> m (SAT.PBSum, [(SAT.Var, PBFile.Constraint)])
+addWBO :: (PrimMonad m, SAT.AddPBNL m enc) => enc -> PBFile.SoftFormula -> m (SAT.PBSum, (SAT.VarMap PBFile.Constraint))
 addWBO db wbo = do
   SAT.newVars_ db $ PBFile.wboNumVars wbo
 
@@ -671,7 +666,7 @@ addWBO db wbo = do
     modifyMutVar objRef ((offset,[trueLit]) :)
 
   obj <- liftM reverse $ readMutVar objRef
-  defs <- liftM reverse $ readMutVar defsRef
+  defs <- liftM IntMap.fromList $ readMutVar defsRef
 
   case PBFile.wboTopCost wbo of
     Nothing -> return ()
diff --git a/src/ToySolver/Converter/SAT2KSAT.hs b/src/ToySolver/Converter/SAT2KSAT.hs
index 69b23aa0..12c51af5 100644
--- a/src/ToySolver/Converter/SAT2KSAT.hs
+++ b/src/ToySolver/Converter/SAT2KSAT.hs
@@ -22,6 +22,7 @@ module ToySolver.Converter.SAT2KSAT
 import Control.Monad
 import Control.Monad.ST
 import Data.Foldable (toList)
+import qualified Data.IntMap.Lazy as IntMap
 import Data.Sequence ((<|), (|>))
 import qualified Data.Sequence as Seq
 import Data.STRef
@@ -38,7 +39,7 @@ sat2ksat k _ | k < 3 = error "ToySolver.Converter.SAT2KSAT.sat2ksat: k must be >
 sat2ksat k cnf = runST $ do
   let nv1 = CNF.cnfNumVars cnf
   db <- newCNFStore
-  defsRef <- newSTRef Seq.empty
+  defsRef <- newSTRef IntMap.empty
   SAT.newVars_ db nv1
   forM_ (CNF.cnfClauses cnf) $ \clause -> do
     let loop lits = do
@@ -49,12 +50,12 @@ sat2ksat k cnf = runST $ do
             case Seq.splitAt (k-1) lits of
               (lits1, lits2) -> do
                 SAT.addClause db (toList (lits1 |> (-v)))
-                modifySTRef' defsRef (|> (v, toList lits1))
+                modifySTRef' defsRef (IntMap.insert v (toList lits1))
                 loop (v <| lits2)
     loop $ Seq.fromList $ SAT.unpackClause clause
   cnf2 <- getCNFFormula db
   defs <- readSTRef defsRef
-  return (cnf2, TseitinInfo nv1 (CNF.cnfNumVars cnf2) [(v, Or [atom lit | lit <- clause]) | (v, clause) <- toList defs])
+  return (cnf2, TseitinInfo nv1 (CNF.cnfNumVars cnf2) (fmap (\clause -> Or [atom lit | lit <- clause]) defs))
   where
     atom l
       | l < 0 = Not (Atom (- l))
diff --git a/src/ToySolver/Converter/SAT2MaxSAT.hs b/src/ToySolver/Converter/SAT2MaxSAT.hs
index 300fda2d..0f077eaf 100644
--- a/src/ToySolver/Converter/SAT2MaxSAT.hs
+++ b/src/ToySolver/Converter/SAT2MaxSAT.hs
@@ -94,7 +94,7 @@ sat3ToMaxSAT2 cnf =
           }
         , t
         )
-      , TseitinInfo (CNF.cnfNumVars cnf) nv
+      , TseitinInfo (CNF.cnfNumVars cnf) nv $ IntMap.fromList
           [ (d, SAT.And [atom a, atom b, atom c])
             -- we define d as "a && b && c", but "a + b + c >= 2" is also fine.
           | (d, (a,b,c)) <- ds
@@ -142,7 +142,7 @@ simplifyMaxSAT2 (wcnf, threshold) =
   case foldl' f (nv1, Set.empty, IntMap.empty, threshold) (CNF.wcnfClauses wcnf) of
     (nv2, cs, defs, threshold2) ->
       ( (nv2, cs, threshold2)
-      , TseitinInfo nv1 nv2 [(v, atom (- a)) | (v, (a, _b)) <- IntMap.toList defs]
+      , TseitinInfo nv1 nv2 (fmap (\(a, _b) -> atom (- a)) defs)
         -- we deine v as "~a" but "~b" is also fine.
       )
   where
diff --git a/src/ToySolver/Converter/Tseitin.hs b/src/ToySolver/Converter/Tseitin.hs
index 58af9fef..f0812d90 100644
--- a/src/ToySolver/Converter/Tseitin.hs
+++ b/src/ToySolver/Converter/Tseitin.hs
@@ -21,7 +21,7 @@ import qualified Data.Aeson as J
 import qualified Data.Aeson.Types as J
 import Data.Aeson ((.=), (.:))
 import Data.Array.IArray
-import Data.List (sortOn)
+import qualified Data.IntMap.Strict as IntMap
 import qualified Data.Map.Lazy as Map
 import Data.String
 import qualified Data.Text as T
@@ -32,13 +32,8 @@ import ToySolver.SAT.Internal.JSON
 import qualified ToySolver.SAT.Types as SAT
 import qualified ToySolver.SAT.Encoder.Tseitin as Tseitin
 
-data TseitinInfo = TseitinInfo !Int !Int [(SAT.Var, Tseitin.Formula)]
-  deriving (Show, Read)
-
--- TODO: change defs representation to SAT.VarMap
-instance Eq TseitinInfo where
-  TseitinInfo nv1 nv2 defs == TseitinInfo nv1' nv2' defs' =
-    nv1 == nv1' && nv2 == nv2' && sortOn fst defs == sortOn fst defs'
+data TseitinInfo = TseitinInfo !Int !Int (SAT.VarMap Tseitin.Formula)
+  deriving (Show, Read, Eq)
 
 instance Transformer TseitinInfo where
   type Source TseitinInfo = SAT.Model
@@ -50,7 +45,7 @@ instance ForwardTransformer TseitinInfo where
       -- Use BOXED array to tie the knot
       a :: Array SAT.Var Bool
       a = array (1, nv2) $
-            assocs m ++ [(v, Tseitin.evalFormula a phi) | (v, phi) <- defs]
+            assocs m ++ [(v, Tseitin.evalFormula a phi) | (v, phi) <- IntMap.toList defs]
 
 instance BackwardTransformer TseitinInfo where
   transformBackward (TseitinInfo nv1 _nv2 _defs) = SAT.restrictModel nv1
@@ -63,7 +58,7 @@ instance J.ToJSON TseitinInfo where
     , "num_transformed_variables" .= nv2
     , "definitions" .= J.object
         [ fromString ("x" ++ show v) .= formula
-        | (v, formula) <- defs
+        | (v, formula) <- IntMap.toList defs
         ]
     ]
 
@@ -73,7 +68,7 @@ instance J.FromJSON TseitinInfo where
     TseitinInfo
       <$> obj .: "num_original_variables"
       <*> obj .: "num_transformed_variables"
-      <*> mapM f (Map.toList defs)
+      <*> (IntMap.fromList <$> mapM f (Map.toList defs))
     where
       f :: (T.Text, SAT.Formula) -> J.Parser (SAT.Var, SAT.Formula)
       f (name, formula) = do
diff --git a/src/ToySolver/SAT/Encoder/Tseitin.hs b/src/ToySolver/SAT/Encoder/Tseitin.hs
index ea25ced2..58435548 100644
--- a/src/ToySolver/SAT/Encoder/Tseitin.hs
+++ b/src/ToySolver/SAT/Encoder/Tseitin.hs
@@ -89,6 +89,7 @@ module ToySolver.SAT.Encoder.Tseitin
 import Control.Monad
 import Control.Monad.Primitive
 import Data.Primitive.MutVar
+import qualified Data.IntMap.Lazy as IntMap
 import Data.Map (Map)
 import qualified Data.Map as Map
 import qualified Data.IntSet as IntSet
@@ -429,7 +430,7 @@ encodeFACarryWithPolarity encoder polarity a b c = do
   encodeWithPolarityHelper encoder (encFACarryTable encoder) definePos defineNeg polarity (a,b,c)
 
 
-getDefinitions :: PrimMonad m => Encoder m -> m [(SAT.Var, Formula)]
+getDefinitions :: PrimMonad m => Encoder m -> m (SAT.VarMap Formula)
 getDefinitions encoder = do
   tableConj <- readMutVar (encConjTable encoder)
   tableITE <- readMutVar (encITETable encoder)
@@ -439,14 +440,18 @@ getDefinitions encoder = do
   let atom l
         | l < 0 = Not (Atom (- l))
         | otherwise = Atom l
-      m1 = [(v, andB [atom l1 | l1 <- IntSet.toList ls]) | (ls, (v, _, _)) <- Map.toList tableConj]
-      m2 = [(v, ite (atom c) (atom t) (atom e)) | ((c,t,e), (v, _, _)) <- Map.toList tableITE]
-      m3 = [(v, (atom a .||. atom b) .&&. (atom (-a) .||. atom (-b))) | ((a,b), (v, _, _)) <- Map.toList tableXOR]
-      m4 = [(v, orB [andB [atom l | l <- ls] | ls <- [[a,b,c],[a,-b,-c],[-a,b,-c],[-a,-b,c]]])
-             | ((a,b,c), (v, _, _)) <- Map.toList tableFASum]
-      m5 = [(v, orB [andB [atom l | l <- ls] | ls <- [[a,b],[a,c],[b,c]]])
-             | ((a,b,c), (v, _, _)) <- Map.toList tableFACarry]
-  return $ concat [m1, m2, m3, m4, m5]
+      m1 = IntMap.fromList [(v, andB [atom l1 | l1 <- IntSet.toList ls]) | (ls, (v, _, _)) <- Map.toList tableConj]
+      m2 = IntMap.fromList [(v, ite (atom c) (atom t) (atom e)) | ((c,t,e), (v, _, _)) <- Map.toList tableITE]
+      m3 = IntMap.fromList [(v, (atom a .||. atom b) .&&. (atom (-a) .||. atom (-b))) | ((a,b), (v, _, _)) <- Map.toList tableXOR]
+      m4 = IntMap.fromList
+             [ (v, orB [andB [atom l | l <- ls] | ls <- [[a,b,c],[a,-b,-c],[-a,b,-c],[-a,-b,c]]])
+             | ((a,b,c), (v, _, _)) <- Map.toList tableFASum
+             ]
+      m5 = IntMap.fromList
+             [ (v, orB [andB [atom l | l <- ls] | ls <- [[a,b],[a,c],[b,c]]])
+             | ((a,b,c), (v, _, _)) <- Map.toList tableFACarry
+             ]
+  return $ IntMap.unions [m1, m2, m3, m4, m5]
 
 
 data Polarity
diff --git a/test/Test/SAT/Encoder.hs b/test/Test/SAT/Encoder.hs
index 7bcdf286..9c6e6b28 100644
--- a/test/Test/SAT/Encoder.hs
+++ b/test/Test/SAT/Encoder.hs
@@ -161,7 +161,7 @@ prop_PBEncoder_addPBAtLeast = QM.monadicIO $ do
     return (cnf, defs)
   forM_ (allAssignments 4) $ \m -> do
     let m2 :: Array SAT.Var Bool
-        m2 = array (1, CNF.cnfNumVars cnf) $ assocs m ++ [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- defs]
+        m2 = array (1, CNF.cnfNumVars cnf) $ assocs m ++ [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- IntMap.toList defs]
         b1 = SAT.evalPBLinAtLeast m (lhs,rhs)
         b2 = evalCNF (array (bounds m2) (assocs m2)) cnf
     QM.assert $ b1 == b2
@@ -189,7 +189,7 @@ prop_PBEncoder_encodePBLinAtLeastWithPolarity = QM.monadicIO $ do
     let m2 :: Array SAT.Var Bool
         m2 = array (1, CNF.cnfNumVars cnf) $
                assocs m ++
-               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- defs] ++
+               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- IntMap.toList defs] ++
                Cardinality.evalTotalizerDefinitions m2 defs2
         b1 = evalCNF (array (bounds m2) (assocs m2)) cnf
         cmp a b = isJust $ do
@@ -269,7 +269,7 @@ prop_CardinalityEncoder_addAtLeast = QM.monadicIO $ do
     let m2 :: Array SAT.Var Bool
         m2 = array (1, CNF.cnfNumVars cnf) $
                assocs m ++
-               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- defs] ++
+               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- IntMap.toList defs] ++
                Cardinality.evalTotalizerDefinitions m2 defs2
         b1 = SAT.evalAtLeast m (lhs,rhs)
         b2 = evalCNF (array (bounds m2) (assocs m2)) cnf
@@ -375,7 +375,7 @@ prop_encodeAtLeastWithPolarity = QM.monadicIO $ do
     let m2 :: Array SAT.Var Bool
         m2 = array (1, CNF.cnfNumVars cnf) $
                assocs m ++
-               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- defs] ++
+               [(v, Tseitin.evalFormula m2 phi) | (v,phi) <- IntMap.toList defs] ++
                Cardinality.evalTotalizerDefinitions m2 defs2
         b1 = evalCNF (array (bounds m2) (assocs m2)) cnf
         cmp a b = isJust $ do