diff --git a/abclib.dsp b/abclib.dsp
index 6bc62da16..d91c22e98 100644
--- a/abclib.dsp
+++ b/abclib.dsp
@@ -1267,6 +1267,10 @@ SOURCE=.\src\sat\bsat\satMem.h
 # End Source File
 # Begin Source File
 
+SOURCE=.\src\sat\bsat\satProof.c
+# End Source File
+# Begin Source File
+
 SOURCE=.\src\sat\bsat\satSolver.c
 # End Source File
 # Begin Source File
diff --git a/src/misc/vec/vecInt.h b/src/misc/vec/vecInt.h
index 59c91e535..0d0c24a8f 100644
--- a/src/misc/vec/vecInt.h
+++ b/src/misc/vec/vecInt.h
@@ -316,6 +316,22 @@ static inline int * Vec_IntArray( Vec_Int_t * p )
     return p->pArray;
 }
 
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline int * Vec_IntLimit( Vec_Int_t * p )
+{
+    return p->pArray + p->nSize;
+}
+
 /**Function*************************************************************
 
   Synopsis    []
diff --git a/src/sat/bsat/module.make b/src/sat/bsat/module.make
index 4f633df4d..d04abc2af 100644
--- a/src/sat/bsat/module.make
+++ b/src/sat/bsat/module.make
@@ -3,6 +3,7 @@ SRC +=  src/sat/bsat/satMem.c \
     src/sat/bsat/satInterA.c \
     src/sat/bsat/satInterB.c \
     src/sat/bsat/satInterP.c \
+    src/sat/bsat/satProof.c \
     src/sat/bsat/satSolver.c \
     src/sat/bsat/satSolver2.c \
     src/sat/bsat/satStore.c \
diff --git a/src/sat/bsat/satProof.c b/src/sat/bsat/satProof.c
new file mode 100644
index 000000000..b3cf2b6ce
--- /dev/null
+++ b/src/sat/bsat/satProof.c
@@ -0,0 +1,476 @@
+/**CFile****************************************************************
+
+  FileName    [satProof.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [SAT solver.]
+
+  Synopsis    [Proof manipulation procedures.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: satProof.c,v 1.4 2005/09/16 22:55:03 casem Exp $]
+
+***********************************************************************/
+
+#include "satSolver.h"
+#include "vec.h"
+#include "aig.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+/*
+    Proof is represented as a vector of integers.
+    The first entry is -1.
+    The clause is represented as an offset in this array.
+    One clause's entry is <size><label><ant1><ant2>...<antN>
+    Label is initialized to 0.
+    Root clauses are 1-based. They are marked by prepending bit 1;
+*/
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+typedef struct Sat_Set_t_ Sat_Set_t;
+struct Sat_Set_t_
+{
+    int nEnts;
+    int Label;
+    int pEnts[0];
+};
+
+static inline int          Sat_SetCheck( Vec_Int_t * p, Sat_Set_t * pNode ) { return (int *)pNode > Vec_IntArray(p) && (int *)pNode < Vec_IntLimit(p); }
+static inline int          Sat_SetId( Vec_Int_t * p, Sat_Set_t * pNode )    { return (int *)pNode - Vec_IntArray(p);                                   }
+static inline Sat_Set_t *  Sat_SetFromId( Vec_Int_t * p, int i )             { return (Sat_Set_t *)(Vec_IntArray(p) + i);                              }
+static inline int          Sat_SetSize( Sat_Set_t * pNode )                 { return pNode->nEnts + 2;          }
+
+#define Sat_PoolForEachSet( p, pNode, i )  \
+    for ( i = 1; (i < Vec_IntSize(p)) && ((pNode) = Sat_SetFromId(p, Vec_IntEntry(p,i))); i += Sat_SetSize(pNode) )
+#define Sat_SetForEachSet( p, pSet, pNode, i )  \
+    for ( i = 0; (i < pSet->nEnts) && (((pNode) = ((pSet->pEnts[i] & 1) ? NULL : Sat_SetFromId(p, pSet->pEnts[i]))), 1); i++ )
+#define Sat_VecForEachSet( pVec, p, pNode, i )  \
+    for ( i = 0; (i < Vec_IntSize(pVec)) && ((pNode) = Sat_SetFromId(p, Vec_IntEntry(pVec,i))); i++ )
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Recursively visits useful proof nodes.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Sat_ProofReduceOne( Vec_Int_t * p, Sat_Set_t * pNode, int * pnSize, Vec_Int_t * vStack )
+{
+    Sat_Set_t * pNext;
+    int i, NodeId;
+    if ( pNode->Label )
+        return pNode->Label;
+    // start with node
+    pNode->Label = 1;
+    Vec_IntPush( vStack, Sat_SetId(p, pNode) );
+    // perform DFS search
+    while ( Vec_IntSize(vStack) )
+    {
+        NodeId = Vec_IntPop( vStack );
+        if ( NodeId & 1 ) // extrated second time
+        {
+            pNode = Sat_SetFromId( p, NodeId ^ 1 );
+            pNode->Label = *pnSize;
+            *pnSize += Sat_SetSize(pNode);
+            // update fanins
+            Sat_SetForEachSet( p, pNode, pNext, i )
+                if ( pNext )
+                    pNode->pEnts[i] = pNext->Label;
+            continue;
+        }
+        // extracted first time
+        // add second time
+        Vec_IntPush( vStack, NodeId ^ 1 );
+        // add its anticedents
+        pNode = Sat_SetFromId( p, NodeId );
+        Sat_SetForEachSet( p, pNode, pNext, i )
+            if ( pNext && !pNext->Label )
+            {
+                pNext->Label = 1;
+                Vec_IntPush( vStack, Sat_SetId(p, pNode) ); // add first time
+            }
+    }
+    return pNode->Label;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Recursively visits useful proof nodes.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+/*
+int Sat_ProofReduce_rec( Vec_Int_t * p, Sat_Set_t * pNode, int * pnSize )
+{
+    int * pBeg;
+    assert( Sat_SetCheck(p, pNode) );
+    if ( pNode->Label )
+        return pNode->Label;
+    for ( pBeg = pNode->pEnts; pBeg < pNode->pEnts + pNode->nEnts; pBeg++ )
+        if ( !(*pBeg & 1) )
+            *pBeg = Sat_ProofReduce_rec( p, Sat_SetFromId(p, *pBeg), pnSize );
+    pNode->Label = *pnSize;
+    *pnSize += Sat_SetSize(pNode);
+    return pNode->Label;
+}
+*/
+
+/**Function*************************************************************
+
+  Synopsis    [Reduces the proof to contain only roots and their children.]
+
+  Description [The result is updated proof and updated roots.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Sat_ProofReduce( Vec_Int_t * p, Vec_Int_t * vRoots )
+{
+    int i, nSize = 1;
+    int * pBeg, * pEnd, * pNew;
+    Vec_Int_t * vStack;
+    Sat_Set_t * pNode;
+    // mark used nodes
+    vStack = Vec_IntAlloc( 1000 );
+    Sat_VecForEachSet( vRoots, p, pNode, i )
+        vRoots->pArray[i] = Sat_ProofReduceOne( p, pNode, &nSize, vStack );
+    Vec_IntFree( vStack );
+    // compact proof
+    pNew = Vec_IntArray(p) + 1;
+    Sat_PoolForEachSet( p, pNode, i )
+    {
+        if ( !pNode->Label )
+            continue;
+        assert( pNew - Vec_IntArray(p) == pNode->Label );
+        pNode->Label = 0;
+        pBeg = (int *)pNode;
+        pEnd = pBeg + Sat_SetSize(pNode);
+        while ( pBeg < pEnd )
+            *pNew++ = *pBeg++;
+    }
+    // report the result
+    printf( "The proof was reduced from %d to %d (by %6.2f %%)\n", 
+        Vec_IntSize(p), nSize, 100.0 * (Vec_IntSize(p) - nSize) / Vec_IntSize(p) );
+    assert( pNew - Vec_IntArray(p) == nSize );
+    Vec_IntShrink( p, nSize );
+}   
+
+/**Function*************************************************************
+
+  Synopsis    [Recursively visits useful proof nodes.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Sat_ProofLabel( Vec_Int_t * p, Sat_Set_t * pNode, Vec_Int_t * vUsed, Vec_Int_t * vStack )
+{
+    Sat_Set_t * pNext;
+    int i, NodeId;
+    if ( pNode->Label )
+        return;
+    // start with node
+    pNode->Label = 1;
+    Vec_IntPush( vStack, Sat_SetId(p, pNode) );
+    // perform DFS search
+    while ( Vec_IntSize(vStack) )
+    {
+        NodeId = Vec_IntPop( vStack );
+        if ( NodeId & 1 ) // extrated second time
+        {
+            Vec_IntPush( vUsed, NodeId ^ 1 );
+            continue;
+        }
+        // extracted first time
+        // add second time
+        Vec_IntPush( vStack, NodeId ^ 1 );
+        // add its anticedents
+        pNode = Sat_SetFromId( p, NodeId );
+        Sat_SetForEachSet( p, pNode, pNext, i )
+            if ( pNext && !pNext->Label )
+            {
+                pNext->Label = 1;
+                Vec_IntPush( vStack, Sat_SetId(p, pNode) ); // add first time
+            }
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes UNSAT core.]
+
+  Description [The result is the array of root clause indexes.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Sat_ProofCore( Vec_Int_t * p, int nRoots, int * pBeg, int * pEnd )
+{
+    unsigned * pSeen;
+    Vec_Int_t * vCore, * vUsed, * vStack;
+    Sat_Set_t * pNode;
+    int i;
+    // collect visited clauses
+    vUsed = Vec_IntAlloc( 1000 );
+    vStack = Vec_IntAlloc( 1000 );
+    while ( pBeg < pEnd )
+        Sat_ProofLabel( p, Sat_SetFromId(p, *pBeg++), vUsed, vStack );
+    Vec_IntFree( vStack );
+    // find the core
+    vCore = Vec_IntAlloc( 1000 );
+    pSeen = ABC_CALLOC( unsigned, Aig_BitWordNum(nRoots) );
+    Sat_VecForEachSet( vUsed, p, pNode, i )
+    {
+        pNode->Label = 0;
+        for ( pBeg = pNode->pEnts; pBeg < pNode->pEnts + pNode->nEnts; pBeg++ )
+            if ( (*pBeg & 1) && !Aig_InfoHasBit(pBeg, *pBeg>>1) )
+            {
+                Aig_InfoSetBit( pBeg, *pBeg>>1 );
+                Vec_IntPush( vCore, (*pBeg>>1)-1 );
+            }
+    }
+    Vec_IntFree( vUsed );
+    ABC_FREE( pSeen );
+    return vCore;
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Performs one resultion step.]
+
+  Description [Returns ID of the resolvent if success, and -1 if failure.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Sat_Set_t * Sat_ProofResolve( Vec_Int_t * p, Sat_Set_t * c1, Sat_Set_t * c2 )
+{
+    int i, k, Id, Var = -1, Count = 0;
+    // find resolution variable
+    for ( i = 0; i < c1->nEnts; i++ )
+    for ( k = 0; k < c2->nEnts; k++ )
+        if ( (c1->pEnts[i] ^ c2->pEnts[k]) == 1 )
+        {
+            Var = (c1->pEnts[i] >> 1);
+            Count++;
+        }
+    if ( Count == 0 )
+    {
+        printf( "Cannot find resolution variable\n" );
+        return NULL;
+    }
+    if ( Count > 1 )
+    {
+        printf( "Found more than 1 resolution variables\n" );
+        return NULL;
+    }
+    // perform resolution
+    Id = Vec_IntSize( p );
+    Vec_IntPush( p, 0 ); // placeholder
+    Vec_IntPush( p, 0 );
+    for ( i = 0; i < c1->nEnts; i++ )
+    {
+        if ( (c1->pEnts[i] >> 1) == Var )
+            continue;
+        for ( k = Id + 2; k < Vec_IntSize(p); k++ )
+            if ( p->pArray[k] == c1->pEnts[i] )
+                break;
+        if ( k == Vec_IntSize(p) )
+            Vec_IntPush( p, c1->pEnts[i] );
+    }
+    for ( i = 0; i < c2->nEnts; i++ )
+    {
+        if ( (c2->pEnts[i] >> 1) == Var )
+            continue;
+        for ( k = Id + 2; k < Vec_IntSize(p); k++ )
+            if ( p->pArray[k] == c2->pEnts[i] )
+                break;
+        if ( k == Vec_IntSize(p) )
+            Vec_IntPush( p, c2->pEnts[i] );
+    }
+    Vec_IntWriteEntry( p, Id, Vec_IntSize(p) - Id - 2 );
+    return Sat_SetFromId( p, Id );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks the proof for consitency.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Sat_Set_t * Sat_ProofCheckGetOne( Vec_Int_t * vClauses, Vec_Int_t * vProof, Vec_Int_t * vResolves, int iAnt )
+{
+    Sat_Set_t * pAnt;
+    if ( iAnt & 1 )
+        return Sat_SetFromId( vClauses, iAnt >> 1 );
+    pAnt = Sat_SetFromId( vProof, iAnt );
+    return Sat_SetFromId( vResolves, pAnt->Label );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks the proof for consitency.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Sat_ProofCheck( Vec_Int_t * vClauses, Vec_Int_t * vProof, int iRoot )
+{
+    Vec_Int_t * vOrigs, * vStack, * vUsed, * vResolves;
+    Sat_Set_t * pSet, * pSet0, * pSet1;
+    int i, k;
+    // collect original clauses
+    vOrigs = Vec_IntAlloc( 1000 );
+    Vec_IntPush( vOrigs, -1 );
+    Sat_PoolForEachSet( vClauses, pSet, i )
+        Vec_IntPush( vOrigs, Sat_SetId(vClauses, pSet) );
+    // collect visited clauses
+    vUsed = Vec_IntAlloc( 1000 );
+    vStack = Vec_IntAlloc( 1000 );
+    Sat_ProofLabel( vProof, Sat_SetFromId(vProof, iRoot), vUsed, vStack );
+    Vec_IntFree( vStack );
+    // perform resolution steps
+    vResolves = Vec_IntAlloc( 1000 );
+    Vec_IntPush( vResolves, -1 );
+    Sat_VecForEachSet( vUsed, vProof, pSet, i )
+    {
+        pSet0 = Sat_ProofCheckGetOne( vOrigs, vProof, vResolves, pSet->pEnts[0] );
+        for ( k = 1; k < pSet->nEnts; k++ )
+        {
+            pSet1 = Sat_ProofCheckGetOne( vOrigs, vProof, vResolves, pSet->pEnts[k] );
+            pSet0 = Sat_ProofResolve( vResolves, pSet0, pSet1 );
+        }
+        pSet->Label = Sat_SetId( vResolves, pSet0 );
+    }
+    // clean the proof
+    Sat_VecForEachSet( vUsed, vProof, pSet, i )
+        pSet->Label = 0;
+    // compare the final clause
+    if ( pSet0->nEnts > 0 )
+        printf( "Cound not derive the empty clause\n" );
+    Vec_IntFree( vResolves );
+    Vec_IntFree( vUsed );
+    Vec_IntFree( vOrigs );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Creates variable map.]
+
+  Description [1=A, 2=B, neg=global]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Sat_ProofVarMapCheck( Vec_Int_t * vClauses, Vec_Int_t * vVarMap )
+{
+    Sat_Set_t * pSet;
+    int i, k, fSeeA, fSeeB;
+    // make sure all clauses are either A or B
+    Sat_PoolForEachSet( vClauses, pSet, i )
+    {
+        fSeeA = fSeeB = 0;
+        for ( k = 0; k < pSet->nEnts; k++ )
+        {
+            fSeeA += (Vec_IntEntry(vVarMap, pSet->pEnts[k]) == 1);
+            fSeeB += (Vec_IntEntry(vVarMap, pSet->pEnts[k]) == 2);
+        }
+        if ( fSeeA && fSeeB )
+            printf( "VarMap error!\n" );
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes interpolant of the proof.]
+
+  Description [Assuming that res vars are recorded, too...]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Aig_Man_t * Sat_ProofInterpolant( Vec_Int_t * vProof, int iRoot, Vec_Int_t * vClauses, Vec_Int_t * vVarMap )
+{
+    Vec_Int_t * vOrigs, * vUsed, * vStack;
+    Aig_Man_t * pAig;
+    Sat_Set_t * pSet;
+    int i;
+
+    Sat_ProofVarMapCheck( vClauses, vVarMap );
+
+    // collect original clauses
+    vOrigs = Vec_IntAlloc( 1000 );
+    Vec_IntPush( vOrigs, -1 );
+    Sat_PoolForEachSet( vClauses, pSet, i )
+        Vec_IntPush( vOrigs, Sat_SetId(vClauses, pSet) );
+
+    // collect visited clauses
+    vUsed = Vec_IntAlloc( 1000 );
+    vStack = Vec_IntAlloc( 1000 );
+    Sat_ProofLabel( vProof, Sat_SetFromId(vProof, iRoot), vUsed, vStack );
+    Vec_IntFree( vStack );
+
+    // start the AIG
+    pAig = Aig_ManStart( 10000 );
+    pAig->pName = Aig_UtilStrsav( "interpol" );
+    for ( i = 0; i < Vec_IntSize(vVarMap); i++ )
+        if ( Vec_IntEntry(vVarMap, i) < 0 )
+            Aig_ObjCreatePi( pAig );
+ 
+    return pAig;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+ABC_NAMESPACE_IMPL_END
+