diff --git a/src/Sift/Theory/DiffLogic.hs b/src/Sift/Theory/DiffLogic.hs
new file mode 100644
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--- /dev/null
+++ b/src/Sift/Theory/DiffLogic.hs
@@ -0,0 +1,132 @@
+module Sift.Theory.DiffLogic
+  ( DiffAtom(..)
+  , DlProblem(..)
+  , DlResult(..)
+  , solveDl
+  , feasible
+  , evalAtom
+  , dlModelSatisfies
+  ) where
+
+import Sift.Types
+import Sift.Verify (satisfies)
+import Sift.Cdcl (CdclResult(..), solveCdcl)
+import Data.List (foldl')
+import Data.Map.Strict (Map)
+import qualified Data.Map.Strict as Map
+import qualified Data.Set as Set
+
+data DiffAtom = DiffAtom
+  { dlLhs   :: Int
+  , dlRhs   :: Int
+  , dlBound :: Int
+  } deriving (Eq, Show)
+
+data DlProblem = DlProblem
+  { dlAtoms :: [DiffAtom]
+  , dlCnf   :: CNF
+  } deriving (Eq, Show)
+
+data DlResult
+  = DlSat (Map Int Int)
+  | DlUnsat
+  deriving (Eq, Show)
+
+data Asserted = Asserted
+  { acBlock :: Lit
+  , acFrom  :: Int
+  , acTo    :: Int
+  , acW     :: Int
+  } deriving (Eq, Show)
+
+solveDl :: DlProblem -> DlResult
+solveDl prob = loop iterLimit (dlCnf prob)
+  where
+    atoms = dlAtoms prob
+    numAtoms = length atoms
+    iterLimit :: Int
+    iterLimit = if numAtoms >= 20 then 1000000 else 2 ^ numAtoms + 1
+    loop budget cnf
+      | budget <= 0 = DlUnsat
+      | otherwise =
+      case solveCdcl cnf of
+        CdclUnsat -> DlUnsat
+        CdclSat model ->
+          let asserted =
+                [ assertionOf i atom model | (i, atom) <- zip [1 ..] atoms ]
+          in case feasible asserted of
+               Right potentials -> DlSat potentials
+               Left core ->
+                 let blocking = map acBlock core
+                 in loop (budget - 1) (CNF (blocking : clauses cnf))
+
+assertionOf :: Int -> DiffAtom -> Assignment -> Asserted
+assertionOf i (DiffAtom lhs rhs bound) model =
+  if Map.findWithDefault True (Var i) model
+    then Asserted (negLit (Var i)) rhs lhs bound
+    else Asserted (posLit (Var i)) lhs rhs (negate bound - 1)
+
+feasible :: [Asserted] -> Either [Asserted] (Map Int Int)
+feasible asserted =
+  case changed of
+    [] -> Right distV
+    (x : _) ->
+      let onCycle = walkBack (length nodes) x
+      in Left (traceCycle onCycle)
+  where
+    nodes = Set.toList (Set.fromList (concatMap (\a -> [acFrom a, acTo a]) asserted))
+    dist0 = Map.fromList [ (nd, 0) | nd <- nodes ]
+    (distV, predsV) = iterateRelax (length nodes) asserted dist0 Map.empty
+    (distV1, predsV1) = relaxRound asserted distV predsV
+    changed = [ nd | nd <- nodes, Map.findWithDefault 0 nd distV1 < Map.findWithDefault 0 nd distV ]
+
+    walkBack :: Int -> Int -> Int
+    walkBack 0 node = node
+    walkBack k node =
+      case Map.lookup node predsV1 of
+        Just e  -> walkBack (k - 1) (acFrom e)
+        Nothing -> node
+
+    traceCycle :: Int -> [Asserted]
+    traceCycle startNode =
+      case go (length nodes + 1) startNode [] of
+        Just cyc -> cyc
+        Nothing  -> asserted
+      where
+        go steps cur acc
+          | steps < 0 = Nothing
+          | otherwise =
+              case Map.lookup cur predsV1 of
+                Nothing   -> Nothing
+                Just edge ->
+                  let prev = acFrom edge
+                  in if prev == startNode
+                       then Just (edge : acc)
+                       else go (steps - 1) prev (edge : acc)
+
+iterateRelax :: Int -> [Asserted] -> Map Int Int -> Map Int Asserted -> (Map Int Int, Map Int Asserted)
+iterateRelax 0 _ dist preds = (dist, preds)
+iterateRelax k edges dist preds =
+  let (dist', preds') = relaxRound edges dist preds
+  in iterateRelax (k - 1) edges dist' preds'
+
+relaxRound :: [Asserted] -> Map Int Int -> Map Int Asserted -> (Map Int Int, Map Int Asserted)
+relaxRound edges dist preds = foldl' relax (dist, preds) edges
+  where
+    relax (d, p) a =
+      let du = Map.findWithDefault 0 (acFrom a) d
+          dv = Map.findWithDefault 0 (acTo a) d
+      in if du + acW a < dv
+           then (Map.insert (acTo a) (du + acW a) d, Map.insert (acTo a) a p)
+           else (d, p)
+
+evalAtom :: Map Int Int -> DiffAtom -> Bool
+evalAtom assignment (DiffAtom lhs rhs bound) =
+  Map.findWithDefault 0 lhs assignment - Map.findWithDefault 0 rhs assignment <= bound
+
+dlModelSatisfies :: DlProblem -> Map Int Int -> Bool
+dlModelSatisfies prob assignment =
+  satisfies atomTruth (dlCnf prob)
+  where
+    atomTruth = Map.fromList
+      [ (Var i, evalAtom assignment atom) | (i, atom) <- zip [1 ..] (dlAtoms prob) ]