diff --git a/src/Sift/Cdcl/Incremental.hs b/src/Sift/Cdcl/Incremental.hs
new file mode 100644
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+++ b/src/Sift/Cdcl/Incremental.hs
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+{-# LANGUAGE FlexibleContexts #-}
+module Sift.Cdcl.Incremental
+  ( IncResult(..)
+  , solveAssuming
+  , solveManyAssuming
+  ) where
+
+import Control.Monad (forM, forM_)
+import Control.Monad.ST (ST, runST)
+import Data.STRef
+import Data.Array.ST
+import Data.List (nub)
+import qualified Data.Map.Strict as Map
+import Sift.Types (Var(..), Lit, CNF(..), Assignment, litToInt, litFromInt, varsOfClause, varId)
+import Sift.Cdcl.State
+import Sift.Cdcl.Search (propagate, analyze, analyzeFinal, pickBranchVar, maybeReduce, installLearnt, luby)
+
+data IncResult
+  = IncSat Assignment
+  | IncUnsat [Lit]
+  deriving (Eq, Show)
+
+data StepOutcome
+  = StepSat
+  | StepUnsat [Int]
+  | StepRestart
+
+data AssumeStep
+  = AssumeConflict [Int]
+  | AssumeLit Int
+  | AssumeDone
+
+solveAssuming :: CNF -> [Lit] -> IncResult
+solveAssuming cnf assumps =
+  case solveManyAssuming cnf [assumps] of
+    [r] -> r
+    _   -> IncUnsat []
+
+solveManyAssuming :: CNF -> [[Lit]] -> [IncResult]
+solveManyAssuming (CNF cs) queries = runST $ do
+  let clauseMax = maximum (0 : map varId (concatMap varsOfClause cs))
+      assumpMax = maximum (0 : [ abs (litToInt l) | q <- queries, l <- q ])
+      nv = max clauseMax assumpMax
+  s <- newSolver nv
+  forM_ cs (addClause s . map litToInt)
+  forM queries $ \assumps -> do
+    outcome <- solveOne s (map (litOfDimacs . litToInt) assumps)
+    case outcome of
+      Right () -> do
+        model <- extractAssignment s
+        pure (IncSat model)
+      Left core ->
+        pure (IncUnsat (nub (map (litFromInt . dimacsOfLit . litNeg) core)))
+
+solveOne :: Solver s -> [Int] -> ST s (Either [Int] ())
+solveOne s assumps = do
+  cancelUntil s 0
+  ok <- readSTRef (okFlag s)
+  if not ok
+    then pure (Left [])
+    else do
+      confl0 <- propagate s
+      if confl0 >= 0
+        then do writeSTRef (okFlag s) False; pure (Left [])
+        else runRestarts 0
+  where
+    runRestarts restartNo = do
+      let budget = lubyBudget restartNo
+      outcome <- searchAssuming s assumps budget
+      case outcome of
+        StepSat        -> pure (Right ())
+        StepUnsat core -> pure (Left core)
+        StepRestart    -> do
+          modifySTRef' (statRest s) (+ 1)
+          runRestarts (restartNo + 1)
+
+lubyBudget :: Int -> Int
+lubyBudget restartNo = luby restartNo * 100
+
+searchAssuming :: Solver s -> [Int] -> Int -> ST s StepOutcome
+searchAssuming s assumps confBudget = loop 0
+  where
+    loop confSoFar = do
+      confl <- propagate s
+      if confl >= 0
+        then do
+          modifySTRef' (statConf s) (+ 1)
+          lvl <- currentLevel s
+          if lvl == 0
+            then do writeSTRef (okFlag s) False; pure (StepUnsat [])
+            else do
+              (learnt, btLevel, lbd) <- analyze s confl
+              cancelUntil s btLevel
+              installLearnt s learnt lbd
+              loop (confSoFar + 1)
+        else
+          if confSoFar >= confBudget
+            then do cancelUntil s 0; pure StepRestart
+            else do
+              maybeReduce s
+              step <- nextAssumption s assumps
+              case step of
+                AssumeConflict core -> pure (StepUnsat core)
+                AssumeLit next -> do
+                  newDecisionLevel s
+                  _ <- enqueue s next (-1)
+                  loop confSoFar
+                AssumeDone -> do
+                  v <- pickBranchVar s
+                  if v < 0
+                    then pure StepSat
+                    else do
+                      modifySTRef' (statDec s) (+ 1)
+                      pol <- readArray (polarity s) v
+                      let l = if pol then posLit v else negLit v
+                      newDecisionLevel s
+                      _ <- enqueue s l (-1)
+                      loop confSoFar
+
+nextAssumption :: Solver s -> [Int] -> ST s AssumeStep
+nextAssumption s assumps = go
+  where
+    total = length assumps
+    go = do
+      dl <- currentLevel s
+      if dl >= total
+        then pure AssumeDone
+        else do
+          let p = assumps !! dl
+          v <- litValueInt s p
+          if v == 1
+            then do newDecisionLevel s; go
+            else if v == -1
+              then do
+                core <- analyzeFinal s (litNeg p)
+                pure (AssumeConflict core)
+              else pure (AssumeLit p)
+
+extractAssignment :: Solver s -> ST s Assignment
+extractAssignment s = do
+  pairs <- forM [0 .. numVars s - 1] $ \v -> do
+    vv <- varValue s v
+    pure (Var (v + 1), vv /= -1)
+  pure (Map.fromList pairs)