diff --git a/src/Sift/Proof/Drat.hs b/src/Sift/Proof/Drat.hs
new file mode 100644
index 0000000..847e8e0
--- /dev/null
+++ b/src/Sift/Proof/Drat.hs
@@ -0,0 +1,166 @@
+{-# LANGUAGE FlexibleContexts #-}
+module Sift.Proof.Drat
+  ( ProofResult(..)
+  , solveProof
+  , verifyProof
+  , isRup
+  , renderProof
+  ) where
+
+import Control.Monad (forM_)
+import Control.Monad.ST (ST, runST)
+import Data.STRef
+import Data.Array.ST (readArray)
+import Data.List (nub)
+import qualified Data.Map.Strict as Map
+import Sift.Types
+import qualified Sift.Cdcl.State as St
+import Sift.Cdcl.Search
+  ( propagate, analyze, pickBranchVar, maybeReduce, installLearnt, luby )
+
+data ProofResult
+  = ProofSat Assignment
+  | ProofUnsat [Clause]
+  deriving (Eq, Show)
+
+solveProof :: CNF -> ProofResult
+solveProof (CNF cs) = runST $ do
+  let nv = maximum (0 : map varId (concatMap varsOfClause cs))
+  s <- St.newSolver nv
+  proofRef <- newSTRef []
+  forM_ cs (St.addClause s . map litToInt)
+  ok0 <- readSTRef (St.okFlag s)
+  if not ok0
+    then pure (ProofUnsat [[]])
+    else do
+      confl0 <- propagate s
+      if confl0 >= 0
+        then pure (ProofUnsat [[]])
+        else do
+          verdict <- runRestarts s proofRef 0
+          if verdict
+            then do
+              model <- extractAssignment s
+              pure (ProofSat model)
+            else do
+              recorded <- reverse <$> readSTRef proofRef
+              pure (ProofUnsat (map toClause recorded ++ [[]]))
+
+toClause :: [Int] -> Clause
+toClause = map (litFromInt . St.dimacsOfLit)
+
+runRestarts :: St.Solver s -> STRef s [[Int]] -> Int -> ST s Bool
+runRestarts s proofRef restartNo = do
+  let budget = luby restartNo * 100
+  outcome <- proofSearch s proofRef budget
+  case outcome of
+    Just verdict -> pure verdict
+    Nothing -> do
+      modifySTRef' (St.statRest s) (+ 1)
+      runRestarts s proofRef (restartNo + 1)
+
+proofSearch :: St.Solver s -> STRef s [[Int]] -> Int -> ST s (Maybe Bool)
+proofSearch s proofRef confBudget = loop 0
+  where
+    loop confSoFar = do
+      confl <- propagate s
+      if confl >= 0
+        then do
+          modifySTRef' (St.statConf s) (+ 1)
+          lvl <- St.currentLevel s
+          if lvl == 0
+            then pure (Just False)
+            else do
+              (learnt, btLevel, lbd) <- analyze s confl
+              modifySTRef' proofRef (learnt :)
+              St.cancelUntil s btLevel
+              installLearnt s learnt lbd
+              loop (confSoFar + 1)
+        else
+          if confSoFar >= confBudget
+            then do St.cancelUntil s 0; pure Nothing
+            else do
+              maybeReduce s
+              v <- pickBranchVar s
+              if v < 0
+                then pure (Just True)
+                else do
+                  modifySTRef' (St.statDec s) (+ 1)
+                  pol <- readArray (St.polarity s) v
+                  let l = if pol then St.posLit v else St.negLit v
+                  St.newDecisionLevel s
+                  _ <- St.enqueue s l (-1)
+                  loop confSoFar
+
+extractAssignment :: St.Solver s -> ST s Assignment
+extractAssignment s = do
+  pairs <- mapM (\v -> do
+                    vv <- St.varValue s v
+                    pure (Var (v + 1), vv /= -1)) [0 .. St.numVars s - 1]
+  pure (Map.fromList pairs)
+
+verifyProof :: CNF -> [Clause] -> Bool
+verifyProof (CNF orig) = go orig
+  where
+    go _ [] = False
+    go formula (c : rest)
+      | not (isRup formula c) = False
+      | null c                = True
+      | otherwise             = go (c : formula) rest
+
+isRup :: [Clause] -> Clause -> Bool
+isRup formula lemma =
+  propagatesToConflict formula (map neg lemma)
+
+propagatesToConflict :: [Clause] -> [Lit] -> Bool
+propagatesToConflict clauses0 assumed =
+  case assignAll Map.empty assumed of
+    Nothing -> True
+    Just a0 -> loop a0
+  where
+    clauses = normalizeClauses clauses0
+    assignAll a []       = Just a
+    assignAll a (l : ls) = case extend a l of
+      Nothing -> Nothing
+      Just a' -> assignAll a' ls
+    extend a l = case Map.lookup (litVar l) a of
+      Just b
+        | b == litSign l -> Just a
+        | otherwise      -> Nothing
+      Nothing -> Just (Map.insert (litVar l) (litSign l) a)
+    loop a
+      | any (falsifiedBy a) clauses = True
+      | otherwise =
+          case pickUnit a clauses of
+            Nothing -> False
+            Just l  -> case extend a l of
+              Nothing -> True
+              Just a' -> loop a'
+
+normalizeClauses :: [Clause] -> [Clause]
+normalizeClauses = concatMap norm
+  where
+    norm c =
+      let deduped = nub c
+      in if any (\l -> neg l `elem` deduped) deduped then [] else [deduped]
+
+falsifiedBy :: Assignment -> Clause -> Bool
+falsifiedBy a c = all (\l -> litValue a l == Just False) c
+
+pickUnit :: Assignment -> [Clause] -> Maybe Lit
+pickUnit a = firstJust . map (unitLiteral a)
+  where
+    firstJust []             = Nothing
+    firstJust (Just l : _)   = Just l
+    firstJust (Nothing : xs) = firstJust xs
+
+unitLiteral :: Assignment -> Clause -> Maybe Lit
+unitLiteral a c =
+  case [ l | l <- c, litValue a l == Nothing ] of
+    [l] | not (any (\k -> litValue a k == Just True) c) -> Just l
+    _   -> Nothing
+
+renderProof :: [Clause] -> String
+renderProof = unlines . map renderClause
+  where
+    renderClause c = unwords (map (show . litToInt) c ++ ["0"])