satInterP.c

/**CFile****************************************************************

  FileName    [satInter.c]

  SystemName  [ABC: Logic synthesis and verification system.]

  PackageName [SAT sat_solver.]

  Synopsis    [Interpolation package.]

  Author      [Alan Mishchenko]
  
  Affiliation [UC Berkeley]

  Date        [Ver. 1.0. Started - June 20, 2005.]

  Revision    [$Id: satInter.c,v 1.4 2005/09/16 22:55:03 casem Exp $]

***********************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>

#include "satStore.h"
#include "misc/vec/vec.h"

ABC_NAMESPACE_IMPL_START


////////////////////////////////////////////////////////////////////////
///                        DECLARATIONS                              ///
////////////////////////////////////////////////////////////////////////

// variable assignments 
static const lit    LIT_UNDEF = 0xffffffff;

// interpolation manager
struct Intp_Man_t_
{
    // clauses of the problems
    Sto_Man_t *     pCnf;         // the set of CNF clauses for A and B
    // various parameters
    int             fVerbose;     // verbosiness flag
    int             fProofVerif;  // verifies the proof
    int             fProofWrite;  // writes the proof file
    int             nVarsAlloc;   // the allocated size of var arrays
    int             nClosAlloc;   // the allocated size of clause arrays
    // internal BCP
    int             nRootSize;    // the number of root level assignments
    int             nTrailSize;   // the number of assignments made 
    lit *           pTrail;       // chronological order of assignments (size nVars)
    lit *           pAssigns;     // assignments by variable (size nVars) 
    char *          pSeens;       // temporary mark (size nVars)
    Sto_Cls_t **    pReasons;     // reasons for each assignment (size nVars)          
    Sto_Cls_t **    pWatches;     // watched clauses for each literal (size 2*nVars)          
    // proof data
//    Vec_Int_t *     vAnties;      // anticedents for all clauses
//    Vec_Int_t *     vBreaks;      // beginnings of anticedents for each clause
    Vec_Ptr_t *     vAntClas;     // anticedant clauses
    int             nAntStart;    // starting antecedant clause
    // proof recording
    int             Counter;      // counter of resolved clauses
    int *           pProofNums;   // the proof numbers for each clause (size nClauses)
    FILE *          pFile;        // the file for proof recording
    // internal verification
    lit *           pResLits;     // the literals of the resolvent   
    int             nResLits;     // the number of literals of the resolvent
    int             nResLitsAlloc;// the number of literals of the resolvent
    // runtime stats
    abctime         timeBcp;      // the runtime for BCP
    abctime         timeTrace;    // the runtime of trace construction
    abctime         timeTotal;    // the total runtime of interpolation
};

// reading/writing the proof for a clause
static inline int          Intp_ManProofGet( Intp_Man_t * p, Sto_Cls_t * pCls )                  { return p->pProofNums[pCls->Id];           }
static inline void         Intp_ManProofSet( Intp_Man_t * p, Sto_Cls_t * pCls, int n )           { p->pProofNums[pCls->Id] = n;              }

////////////////////////////////////////////////////////////////////////
///                     FUNCTION DEFINITIONS                         ///
////////////////////////////////////////////////////////////////////////

/**Function*************************************************************

  Synopsis    [Allocate proof manager.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
Intp_Man_t * Intp_ManAlloc()
{
    Intp_Man_t * p;
    // allocate the manager
    p = (Intp_Man_t *)ABC_ALLOC( char, sizeof(Intp_Man_t) );
    memset( p, 0, sizeof(Intp_Man_t) );
    // verification
    p->nResLitsAlloc = (1<<16);
    p->pResLits = ABC_ALLOC( lit, p->nResLitsAlloc );
    // proof recording
//    p->vAnties = Vec_IntAlloc( 1000 );
//    p->vBreaks = Vec_IntAlloc( 1000 );
    p->vAntClas = Vec_PtrAlloc( 1000 );
    p->nAntStart = 0;
    // parameters
    p->fProofWrite = 0;
    p->fProofVerif = 1;
    return p;    
}

/**Function*************************************************************

  Synopsis    [Resize proof manager.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManResize( Intp_Man_t * p )
{
    // check if resizing is needed
    if ( p->nVarsAlloc < p->pCnf->nVars )
    {
        // find the new size
        if ( p->nVarsAlloc == 0 )
            p->nVarsAlloc = 1;
        while ( p->nVarsAlloc < p->pCnf->nVars ) 
            p->nVarsAlloc *= 2;
        // resize the arrays
        p->pTrail    = ABC_REALLOC(lit,         p->pTrail,    p->nVarsAlloc );
        p->pAssigns  = ABC_REALLOC(lit,         p->pAssigns,  p->nVarsAlloc );
        p->pSeens    = ABC_REALLOC(char,        p->pSeens,    p->nVarsAlloc );
//        p->pVarTypes = ABC_REALLOC(int,         p->pVarTypes, p->nVarsAlloc );
        p->pReasons  = ABC_REALLOC(Sto_Cls_t *, p->pReasons,  p->nVarsAlloc );
        p->pWatches  = ABC_REALLOC(Sto_Cls_t *, p->pWatches,  p->nVarsAlloc*2 );
    }

    // clean the free space
    memset( p->pAssigns , 0xff, sizeof(lit) * p->pCnf->nVars );
    memset( p->pSeens   , 0,    sizeof(char) * p->pCnf->nVars );
//    memset( p->pVarTypes, 0,    sizeof(int) * p->pCnf->nVars );
    memset( p->pReasons , 0,    sizeof(Sto_Cls_t *) * p->pCnf->nVars );
    memset( p->pWatches , 0,    sizeof(Sto_Cls_t *) * p->pCnf->nVars*2 );

    // check if resizing of clauses is needed
    if ( p->nClosAlloc < p->pCnf->nClauses )
    {
        // find the new size
        if ( p->nClosAlloc == 0 )
            p->nClosAlloc = 1;
        while ( p->nClosAlloc < p->pCnf->nClauses ) 
            p->nClosAlloc *= 2;
        // resize the arrays
        p->pProofNums = ABC_REALLOC( int, p->pProofNums,  p->nClosAlloc );
    }
    memset( p->pProofNums, 0, sizeof(int) * p->pCnf->nClauses );
}

/**Function*************************************************************

  Synopsis    [Deallocate proof manager.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManFree( Intp_Man_t * p )
{
/*
    printf( "Runtime stats:\n" );
ABC_PRT( "BCP     ", p->timeBcp   );
ABC_PRT( "Trace   ", p->timeTrace );
ABC_PRT( "TOTAL   ", p->timeTotal );
*/
//    Vec_IntFree( p->vAnties );
//    Vec_IntFree( p->vBreaks );
    Vec_VecFree( (Vec_Vec_t *)p->vAntClas );
//    ABC_FREE( p->pInters );
    ABC_FREE( p->pProofNums );
    ABC_FREE( p->pTrail );
    ABC_FREE( p->pAssigns );
    ABC_FREE( p->pSeens );
//    ABC_FREE( p->pVarTypes );
    ABC_FREE( p->pReasons );
    ABC_FREE( p->pWatches );
    ABC_FREE( p->pResLits );
    ABC_FREE( p );
}




/**Function*************************************************************

  Synopsis    [Prints the clause.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManPrintClause( Intp_Man_t * p, Sto_Cls_t * pClause )
{
    int i;
    printf( "Clause ID = %d. Proof = %d. {", pClause->Id, Intp_ManProofGet(p, pClause) );
    for ( i = 0; i < (int)pClause->nLits; i++ )
        printf( " %d", pClause->pLits[i] );
    printf( " }\n" );
}

/**Function*************************************************************

  Synopsis    [Prints the resolvent.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManPrintResolvent( lit * pResLits, int nResLits )
{
    int i;
    printf( "Resolvent: {" );
    for ( i = 0; i < nResLits; i++ )
        printf( " %d", pResLits[i] );
    printf( " }\n" );
}

/**Function*************************************************************

  Synopsis    [Prints the interpolant for one clause.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManPrintInterOne( Intp_Man_t * p, Sto_Cls_t * pClause )
{
    printf( "Clause %2d :  ", pClause->Id );
//    Extra_PrintBinary___( stdout, Intp_ManAigRead(p, pClause), (1 << p->nVarsAB) );
    printf( "\n" );
}



/**Function*************************************************************

  Synopsis    [Adds one clause to the watcher list.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline void Intp_ManWatchClause( Intp_Man_t * p, Sto_Cls_t * pClause, lit Lit )
{
    assert( lit_check(Lit, p->pCnf->nVars) );
    if ( pClause->pLits[0] == Lit )
        pClause->pNext0 = p->pWatches[lit_neg(Lit)];  
    else
    {
        assert( pClause->pLits[1] == Lit );
        pClause->pNext1 = p->pWatches[lit_neg(Lit)];  
    }
    p->pWatches[lit_neg(Lit)] = pClause;
}


/**Function*************************************************************

  Synopsis    [Records implication.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline int Intp_ManEnqueue( Intp_Man_t * p, lit Lit, Sto_Cls_t * pReason )
{
    int Var = lit_var(Lit);
    if ( p->pAssigns[Var] != LIT_UNDEF )
        return p->pAssigns[Var] == Lit;
    p->pAssigns[Var] = Lit;
    p->pReasons[Var] = pReason;
    p->pTrail[p->nTrailSize++] = Lit;
//printf( "assigning var %d value %d\n", Var, !lit_sign(Lit) );
    return 1;
}

/**Function*************************************************************

  Synopsis    [Records implication.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline void Intp_ManCancelUntil( Intp_Man_t * p, int Level )
{
    lit Lit;
    int i, Var;
    for ( i = p->nTrailSize - 1; i >= Level; i-- )
    {
        Lit = p->pTrail[i];
        Var = lit_var( Lit );
        p->pReasons[Var] = NULL;
        p->pAssigns[Var] = LIT_UNDEF;
//printf( "cancelling var %d\n", Var );
    }
    p->nTrailSize = Level;
}

/**Function*************************************************************

  Synopsis    [Propagate one assignment.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
static inline Sto_Cls_t * Intp_ManPropagateOne( Intp_Man_t * p, lit Lit )
{
    Sto_Cls_t ** ppPrev, * pCur, * pTemp;
    lit LitF = lit_neg(Lit);
    int i;
    // iterate through the literals
    ppPrev = p->pWatches + Lit;
    for ( pCur = p->pWatches[Lit]; pCur; pCur = *ppPrev )
    {
        // make sure the false literal is in the second literal of the clause
        if ( pCur->pLits[0] == LitF )
        {
            pCur->pLits[0] = pCur->pLits[1];
            pCur->pLits[1] = LitF;
            pTemp = pCur->pNext0;
            pCur->pNext0 = pCur->pNext1;
            pCur->pNext1 = pTemp;
        }
        assert( pCur->pLits[1] == LitF );

        // if the first literal is true, the clause is satisfied
        if ( pCur->pLits[0] == p->pAssigns[lit_var(pCur->pLits[0])] )
        {
            ppPrev = &pCur->pNext1;
            continue;
        }

        // look for a new literal to watch
        for ( i = 2; i < (int)pCur->nLits; i++ )
        {
            // skip the case when the literal is false
            if ( lit_neg(pCur->pLits[i]) == p->pAssigns[lit_var(pCur->pLits[i])] )
                continue;
            // the literal is either true or unassigned - watch it
            pCur->pLits[1] = pCur->pLits[i];
            pCur->pLits[i] = LitF;
            // remove this clause from the watch list of Lit
            *ppPrev = pCur->pNext1;
            // add this clause to the watch list of pCur->pLits[i] (now it is pCur->pLits[1])
            Intp_ManWatchClause( p, pCur, pCur->pLits[1] );
            break;
        }
        if ( i < (int)pCur->nLits ) // found new watch
            continue;

        // clause is unit - enqueue new implication
        if ( Intp_ManEnqueue(p, pCur->pLits[0], pCur) )
        {
            ppPrev = &pCur->pNext1;
            continue;
        }

        // conflict detected - return the conflict clause
        return pCur;
    }
    return NULL;
}

/**Function*************************************************************

  Synopsis    [Propagate the current assignments.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
Sto_Cls_t * Intp_ManPropagate( Intp_Man_t * p, int Start )
{
    Sto_Cls_t * pClause;
    int i;
    abctime clk = Abc_Clock();
    for ( i = Start; i < p->nTrailSize; i++ )
    {
        pClause = Intp_ManPropagateOne( p, p->pTrail[i] );
        if ( pClause )
        {
p->timeBcp += Abc_Clock() - clk;
            return pClause;
        }
    }
p->timeBcp += Abc_Clock() - clk;
    return NULL;
}


/**Function*************************************************************

  Synopsis    [Writes one root clause into a file.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManProofWriteOne( Intp_Man_t * p, Sto_Cls_t * pClause )
{
    Intp_ManProofSet( p, pClause, ++p->Counter );

    if ( p->fProofWrite )
    {
        int v;
        fprintf( p->pFile, "%d", Intp_ManProofGet(p, pClause) );
        for ( v = 0; v < (int)pClause->nLits; v++ )
            fprintf( p->pFile, " %d", lit_print(pClause->pLits[v]) );
        fprintf( p->pFile, " 0 0\n" );
    }
}

/**Function*************************************************************

  Synopsis    [Traces the proof for one clause.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int Intp_ManProofTraceOne( Intp_Man_t * p, Sto_Cls_t * pConflict, Sto_Cls_t * pFinal )
{
    Sto_Cls_t * pReason;
    int i, v, Var, PrevId;
    int fPrint = 0;
    abctime clk = Abc_Clock();

    // collect resolvent literals
    if ( p->fProofVerif )
    {
        assert( (int)pConflict->nLits <= p->nResLitsAlloc );
        memcpy( p->pResLits, pConflict->pLits, sizeof(lit) * pConflict->nLits );
        p->nResLits = pConflict->nLits;
    }

    // mark all the variables in the conflict as seen
    for ( v = 0; v < (int)pConflict->nLits; v++ )
        p->pSeens[lit_var(pConflict->pLits[v])] = 1;

    // start the anticedents
//    pFinal->pAntis = Vec_PtrAlloc( 32 );
//    Vec_PtrPush( pFinal->pAntis, pConflict );

//    assert( pFinal->Id == Vec_IntSize(p->vBreaks) );
//    Vec_IntPush( p->vBreaks, Vec_IntSize(p->vAnties) );
//    Vec_IntPush( p->vAnties, pConflict->Id );
    {
        Vec_Int_t * vAnts = Vec_IntAlloc( 16 );
        assert( Vec_PtrSize(p->vAntClas) == pFinal->Id - p->nAntStart );
        Vec_IntPush( vAnts, pConflict->Id );
        Vec_PtrPush( p->vAntClas, vAnts );
    }

//    if ( p->pCnf->nClausesA )
//        Intp_ManAigCopy( p, Intp_ManAigRead(p, pFinal), Intp_ManAigRead(p, pConflict) );

    // follow the trail backwards
    PrevId = Intp_ManProofGet(p, pConflict);
    for ( i = p->nTrailSize - 1; i >= 0; i-- )
    {
        // skip literals that are not involved
        Var = lit_var(p->pTrail[i]);
        if ( !p->pSeens[Var] )
            continue;
        p->pSeens[Var] = 0;

        // skip literals of the resulting clause
        pReason = p->pReasons[Var];
        if ( pReason == NULL )
            continue;
        assert( p->pTrail[i] == pReason->pLits[0] );

        // add the variables to seen
        for ( v = 1; v < (int)pReason->nLits; v++ )
            p->pSeens[lit_var(pReason->pLits[v])] = 1;


        // record the reason clause
        assert( Intp_ManProofGet(p, pReason) > 0 );
        p->Counter++;
        if ( p->fProofWrite )
            fprintf( p->pFile, "%d * %d %d 0\n", p->Counter, PrevId, Intp_ManProofGet(p, pReason) );
        PrevId = p->Counter;

//        if ( p->pCnf->nClausesA )
//       {
//            if ( p->pVarTypes[Var] == 1 ) // var of A
//                Intp_ManAigOr( p, Intp_ManAigRead(p, pFinal), Intp_ManAigRead(p, pReason) );
//            else
//                Intp_ManAigAnd( p, Intp_ManAigRead(p, pFinal), Intp_ManAigRead(p, pReason) );
//        }
 
        // resolve the temporary resolvent with the reason clause
        if ( p->fProofVerif )
        {
            int v1, v2; 
            if ( fPrint )
                Intp_ManPrintResolvent( p->pResLits, p->nResLits );
            // check that the var is present in the resolvent
            for ( v1 = 0; v1 < p->nResLits; v1++ )
                if ( lit_var(p->pResLits[v1]) == Var )
                    break;
            if ( v1 == p->nResLits )
                printf( "Recording clause %d: Cannot find variable %d in the temporary resolvent.\n", pFinal->Id, Var );
            if ( p->pResLits[v1] != lit_neg(pReason->pLits[0]) )
                printf( "Recording clause %d: The resolved variable %d is in the wrong polarity.\n", pFinal->Id, Var );
            // remove this variable from the resolvent
            assert( lit_var(p->pResLits[v1]) == Var );
            p->nResLits--;
            for ( ; v1 < p->nResLits; v1++ )
                p->pResLits[v1] = p->pResLits[v1+1];
            // add variables of the reason clause
            for ( v2 = 1; v2 < (int)pReason->nLits; v2++ )
            {
                for ( v1 = 0; v1 < p->nResLits; v1++ )
                    if ( lit_var(p->pResLits[v1]) == lit_var(pReason->pLits[v2]) )
                        break;
                // if it is a new variable, add it to the resolvent
                if ( v1 == p->nResLits ) 
                {
                    if ( p->nResLits == p->nResLitsAlloc )
                        printf( "Recording clause %d: Ran out of space for intermediate resolvent.\n", pFinal->Id );
                    p->pResLits[ p->nResLits++ ] = pReason->pLits[v2];
                    continue;
                }
                // if the variable is the same, the literal should be the same too
                if ( p->pResLits[v1] == pReason->pLits[v2] )
                    continue;
                // the literal is different
                printf( "Recording clause %d: Trying to resolve the clause with more than one opposite literal.\n", pFinal->Id );
            }
        }

//        Vec_PtrPush( pFinal->pAntis, pReason );
//        Vec_IntPush( p->vAnties, pReason->Id );
        Vec_IntPush( (Vec_Int_t *)Vec_PtrEntryLast(p->vAntClas), pReason->Id );
    }

    // unmark all seen variables
//    for ( i = p->nTrailSize - 1; i >= 0; i-- )
//        p->pSeens[lit_var(p->pTrail[i])] = 0;
    // check that the literals are unmarked
//    for ( i = p->nTrailSize - 1; i >= 0; i-- )
//        assert( p->pSeens[lit_var(p->pTrail[i])] == 0 );

    // use the resulting clause to check the correctness of resolution
    if ( p->fProofVerif )
    {
        int v1, v2; 
        if ( fPrint )
            Intp_ManPrintResolvent( p->pResLits, p->nResLits );
        for ( v1 = 0; v1 < p->nResLits; v1++ )
        {
            for ( v2 = 0; v2 < (int)pFinal->nLits; v2++ )
                if ( pFinal->pLits[v2] == p->pResLits[v1] )
                    break;
            if ( v2 < (int)pFinal->nLits )
                continue;
            break;
        }
        if ( v1 < p->nResLits )
        {
            printf( "Recording clause %d: The final resolvent is wrong.\n", pFinal->Id );
            Intp_ManPrintClause( p, pConflict );
            Intp_ManPrintResolvent( p->pResLits, p->nResLits );
            Intp_ManPrintClause( p, pFinal );
        }

        // if there are literals in the clause that are not in the resolvent
        // it means that the derived resolvent is stronger than the clause
        // we can replace the clause with the resolvent by removing these literals
        if ( p->nResLits != (int)pFinal->nLits )
        {
            for ( v1 = 0; v1 < (int)pFinal->nLits; v1++ )
            {
                for ( v2 = 0; v2 < p->nResLits; v2++ )
                    if ( pFinal->pLits[v1] == p->pResLits[v2] )
                        break;
                if ( v2 < p->nResLits )
                    continue;
                // remove literal v1 from the final clause
                pFinal->nLits--;
                for ( v2 = v1; v2 < (int)pFinal->nLits; v2++ )
                    pFinal->pLits[v2] = pFinal->pLits[v2+1];
                v1--;
            }
            assert( p->nResLits == (int)pFinal->nLits );
        }
    }
p->timeTrace += Abc_Clock() - clk;

    // return the proof pointer 
//    if ( p->pCnf->nClausesA )
//    {
//        Intp_ManPrintInterOne( p, pFinal );
//    }
    Intp_ManProofSet( p, pFinal, p->Counter );
    // make sure the same proof ID is not asssigned to two consecutive clauses
    assert( p->pProofNums[pFinal->Id-1] != p->Counter );
//    if ( p->pProofNums[pFinal->Id] == p->pProofNums[pFinal->Id-1] )
//        p->pProofNums[pFinal->Id] = p->pProofNums[pConflict->Id];
    return p->Counter;
}

/**Function*************************************************************

  Synopsis    [Records the proof for one clause.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int Intp_ManProofRecordOne( Intp_Man_t * p, Sto_Cls_t * pClause )
{
    Sto_Cls_t * pConflict;
    int i;

    // empty clause never ends up there
    assert( pClause->nLits > 0 );
    if ( pClause->nLits == 0 )
        printf( "Error: Empty clause is attempted.\n" );

    assert( !pClause->fRoot );
    assert( p->nTrailSize == p->nRootSize );

    // if any of the clause literals are already assumed
    // it means that the clause is redundant and can be skipped
    for ( i = 0; i < (int)pClause->nLits; i++ )
        if ( p->pAssigns[lit_var(pClause->pLits[i])] == pClause->pLits[i] )
        {
//            Vec_IntPush( p->vBreaks, Vec_IntSize(p->vAnties) );
            Vec_PtrPush( p->vAntClas, Vec_IntAlloc(0) );
            return 1;
        }

    // add assumptions to the trail
    for ( i = 0; i < (int)pClause->nLits; i++ )
        if ( !Intp_ManEnqueue( p, lit_neg(pClause->pLits[i]), NULL ) )
        {
            assert( 0 ); // impossible
            return 0;
        }

    // propagate the assumptions
    pConflict = Intp_ManPropagate( p, p->nRootSize );
    if ( pConflict == NULL )
    {
        assert( 0 ); // cannot prove
        return 0;
    }

    // skip the clause if it is weaker or the same as the conflict clause
    if ( pClause->nLits >= pConflict->nLits )
    {
        // check if every literal of conflict clause can be found in the given clause
        int j;
        for ( i = 0; i < (int)pConflict->nLits; i++ )
        {
            for ( j = 0; j < (int)pClause->nLits; j++ )
                if ( pConflict->pLits[i] == pClause->pLits[j] )
                    break;
            if ( j == (int)pClause->nLits ) // literal pConflict->pLits[i] is not found
                break;
        }
        if ( i == (int)pConflict->nLits ) // all lits are found
        {
            // undo to the root level
            Intp_ManCancelUntil( p, p->nRootSize );
//            Vec_IntPush( p->vBreaks, Vec_IntSize(p->vAnties) );
            Vec_PtrPush( p->vAntClas, Vec_IntAlloc(0) );
            return 1;
        }
    }

    // construct the proof
    Intp_ManProofTraceOne( p, pConflict, pClause );

    // undo to the root level
    Intp_ManCancelUntil( p, p->nRootSize );

    // add large clauses to the watched lists
    if ( pClause->nLits > 1 )
    {
        Intp_ManWatchClause( p, pClause, pClause->pLits[0] );
        Intp_ManWatchClause( p, pClause, pClause->pLits[1] );
        return 1;
    }
    assert( pClause->nLits == 1 );

    // if the clause proved is unit, add it and propagate
    if ( !Intp_ManEnqueue( p, pClause->pLits[0], pClause ) )
    {
        assert( 0 ); // impossible
        return 0;
    }

    // propagate the assumption
    pConflict = Intp_ManPropagate( p, p->nRootSize );
    if ( pConflict )
    {
        // insert place-holders till the empty clause
        while ( Vec_PtrSize(p->vAntClas) < p->pCnf->pEmpty->Id - p->nAntStart )
            Vec_PtrPush( p->vAntClas, Vec_IntAlloc(0) );
        // construct the proof for the empty clause
        Intp_ManProofTraceOne( p, pConflict, p->pCnf->pEmpty );
//        if ( p->fVerbose )
//            printf( "Found last conflict after adding unit clause number %d!\n", pClause->Id );
        return 0;
    }

    // update the root level
    p->nRootSize = p->nTrailSize;
    return 1;
}

/**Function*************************************************************

  Synopsis    [Propagate the root clauses.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int Intp_ManProcessRoots( Intp_Man_t * p )
{
    Sto_Cls_t * pClause;
    int Counter;

    // make sure the root clauses are preceeding the learnt clauses
    Counter = 0;
    Sto_ManForEachClause( p->pCnf, pClause )
    {
        assert( (int)pClause->fA    == (Counter < (int)p->pCnf->nClausesA) );
        assert( (int)pClause->fRoot == (Counter < (int)p->pCnf->nRoots)    );
        Counter++;
    }
    assert( p->pCnf->nClauses == Counter );

    // make sure the last clause if empty
    assert( p->pCnf->pTail->nLits == 0 );

    // go through the root unit clauses
    p->nTrailSize = 0;
    Sto_ManForEachClauseRoot( p->pCnf, pClause )
    {
        // create watcher lists for the root clauses
        if ( pClause->nLits > 1 )
        {
            Intp_ManWatchClause( p, pClause, pClause->pLits[0] );
            Intp_ManWatchClause( p, pClause, pClause->pLits[1] );
        }
        // empty clause and large clauses
        if ( pClause->nLits != 1 )
            continue;
        // unit clause
        assert( lit_check(pClause->pLits[0], p->pCnf->nVars) );
        if ( !Intp_ManEnqueue( p, pClause->pLits[0], pClause ) )
        {
            // detected root level conflict
//            printf( "Error in Intp_ManProcessRoots(): Detected a root-level conflict too early!\n" );
//            assert( 0 );
            // detected root level conflict
            Intp_ManProofTraceOne( p, pClause, p->pCnf->pEmpty );
            if ( p->fVerbose )
                printf( "Found root level conflict!\n" );
            return 0;
        }
    }

    // propagate the root unit clauses
    pClause = Intp_ManPropagate( p, 0 );
    if ( pClause )
    {
        // detected root level conflict
        Intp_ManProofTraceOne( p, pClause, p->pCnf->pEmpty );
        if ( p->fVerbose )
            printf( "Found root level conflict!\n" );
        return 0;
    }

    // set the root level
    p->nRootSize = p->nTrailSize;
    return 1;
}


/**Function*************************************************************

  Synopsis    [Verifies the UNSAT core.]

  Description [Takes the interpolation manager, the CNF derived by the SAT
  solver, which includes the root clauses and the learned clauses. Returns
  the array of integers representing the number of root clauses that are in
  the UNSAT core.]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManUnsatCoreVerify( Sto_Man_t * pCnf, Vec_Int_t * vCore )
{
    int fVerbose = 0;
    int nConfMax = 1000000;
    sat_solver * pSat;
    Sto_Cls_t * pClause;
    Vec_Ptr_t * vClauses;
    int i, iClause, RetValue;
    abctime clk = Abc_Clock();
    // collect the clauses
    vClauses = Vec_PtrAlloc( 1000 );
    Sto_ManForEachClauseRoot( pCnf, pClause )
    {
        assert( Vec_PtrSize(vClauses) == pClause->Id );
        Vec_PtrPush( vClauses, pClause );
    }
    // create new SAT solver
    pSat = sat_solver_new();
//    sat_solver_setnvars( pSat, nSatVars );
    Vec_IntForEachEntry( vCore, iClause, i )
    {
        pClause = (Sto_Cls_t *)Vec_PtrEntry( vClauses, iClause );
        if ( !sat_solver_addclause( pSat, pClause->pLits, pClause->pLits+pClause->nLits ) )
        {
            printf( "The core verification problem is trivially UNSAT.\n" );
            break;
        }
    }
    Vec_PtrFree( vClauses );
    // solve the problem
    RetValue = sat_solver_solve( pSat, NULL, NULL, (ABC_INT64_T)nConfMax, (ABC_INT64_T)0, (ABC_INT64_T)0, (ABC_INT64_T)0 );
    sat_solver_delete( pSat );
    if ( fVerbose )
    {
        if ( RetValue == l_Undef )
            printf( "Conflict limit is reached.  " );
        else if ( RetValue == l_True )
            printf( "UNSAT core verification FAILED.  " );
        else
            printf( "UNSAT core verification succeeded.  " );
        ABC_PRT( "Time", Abc_Clock() - clk );
    }
    else
    {
        if ( RetValue == l_True )
            printf( "UNSAT core verification FAILED.  \n" );
    }
}

/**Function*************************************************************

  Synopsis    [Recursively computes the UNSAT core.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManUnsatCore_rec( Vec_Ptr_t * vAntClas, int iThis, Vec_Int_t * vCore, int nRoots, Vec_Str_t * vVisited, int fLearned )
{
//    int i, iStop, iStart;
    Vec_Int_t * vAnt;
    int i, Entry;
    // skip visited clauses
    if ( Vec_StrEntry( vVisited, iThis ) )
        return;
    Vec_StrWriteEntry( vVisited, iThis, 1 );
    // add a root clause to the core
    if ( iThis < nRoots )
    {
        if ( !fLearned )
            Vec_IntPush( vCore, iThis );
        return; 
    }
    // iterate through the clauses
//    iStart = Vec_IntEntry( vBreaks, iThis );
//    iStop = Vec_IntEntry( vBreaks, iThis+1 );
//    assert( iStop != -1 );
//    for ( i = iStart; i < iStop; i++ )
    vAnt = (Vec_Int_t *)Vec_PtrEntry( vAntClas, iThis - nRoots );
    Vec_IntForEachEntry( vAnt, Entry, i )
//        Intp_ManUnsatCore_rec( vAntClas, Vec_IntEntry(vAnties, i), vCore, nRoots, vVisited );
        Intp_ManUnsatCore_rec( vAntClas, Entry, vCore, nRoots, vVisited, fLearned );
    // collect learned clause
    if ( fLearned )
        Vec_IntPush( vCore, iThis );
}

/**Function*************************************************************

  Synopsis    [Computes UNSAT core of the satisfiablity problem.]

  Description [Takes the interpolation manager, the CNF derived by the SAT
  solver, which includes the root clauses and the learned clauses. Returns
  the array of integers representing the number of root clauses that are in
  the UNSAT core.]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void * Intp_ManUnsatCore( Intp_Man_t * p, Sto_Man_t * pCnf, int fLearned, int fVerbose )
{
    Vec_Int_t * vCore;
    Vec_Str_t * vVisited;
    Sto_Cls_t * pClause;
    int RetValue = 1;
    abctime clkTotal = Abc_Clock();

    // check that the CNF makes sense
    assert( pCnf->nVars > 0 && pCnf->nClauses > 0 );
    p->pCnf = pCnf;
    p->fVerbose = fVerbose;

    // adjust the manager
    Intp_ManResize( p ); 

    // construct proof for each clause
    // start the proof
    if ( p->fProofWrite )
    {
        p->pFile = fopen( "proof.cnf_", "w" );
        p->Counter = 0;
    }

    // write the root clauses
//    Vec_IntClear( p->vAnties );
//    Vec_IntFill( p->vBreaks, p->pCnf->nRoots, 0 );
    Vec_PtrClear( p->vAntClas );
    p->nAntStart = p->pCnf->nRoots;

    Sto_ManForEachClauseRoot( p->pCnf, pClause )
        Intp_ManProofWriteOne( p, pClause );

    // propagate root level assignments
    if ( Intp_ManProcessRoots( p ) )
    {
        // if there is no conflict, consider learned clauses
        Sto_ManForEachClause( p->pCnf, pClause )
        {
            if ( pClause->fRoot )
                continue;
            if ( !Intp_ManProofRecordOne( p, pClause ) )
            {
                RetValue = 0;
                break;
            }
        }
    }

    // add the last breaker
//    assert( p->pCnf->pEmpty->Id == Vec_IntSize(p->vBreaks) - 1 );
//    Vec_IntPush( p->vBreaks, Vec_IntSize(p->vAnties) );
    assert( p->pCnf->pEmpty->Id - p->nAntStart == Vec_PtrSize(p->vAntClas) - 1 );
    Vec_PtrPush( p->vAntClas, Vec_IntAlloc(0) );

    // stop the proof
    if ( p->fProofWrite )
    {
        fclose( p->pFile );
//        Sat_ProofChecker( "proof.cnf_" );
        p->pFile = NULL;    
    }

    if ( fVerbose )
    {
//        ABC_PRT( "Core", Abc_Clock() - clkTotal );
    printf( "Vars = %d. Roots = %d. Learned = %d. Resol steps = %d.  Ave = %.2f.  Mem = %.2f MB\n", 
        p->pCnf->nVars, p->pCnf->nRoots, p->pCnf->nClauses-p->pCnf->nRoots, p->Counter,  
        1.0*(p->Counter-p->pCnf->nRoots)/(p->pCnf->nClauses-p->pCnf->nRoots), 
        1.0*Sto_ManMemoryReport(p->pCnf)/(1<<20) );
p->timeTotal += Abc_Clock() - clkTotal;
    }

    // derive the UNSAT core
    vCore = Vec_IntAlloc( 1000 );
    vVisited = Vec_StrStart( p->pCnf->pEmpty->Id+1 );
    Intp_ManUnsatCore_rec( p->vAntClas, p->pCnf->pEmpty->Id, vCore, p->pCnf->nRoots, vVisited, fLearned );
    Vec_StrFree( vVisited );
    if ( fVerbose )
        printf( "Root clauses = %d. Learned clauses = %d. UNSAT core size = %d.\n", 
            p->pCnf->nRoots, p->pCnf->nClauses-p->pCnf->nRoots, Vec_IntSize(vCore) );
//    Intp_ManUnsatCoreVerify( p->pCnf, vCore );
    return vCore;   
}

/**Function*************************************************************

  Synopsis    [Prints learned clauses in terms of original problem varibles.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Intp_ManUnsatCorePrintForBmc( FILE * pFile, Sto_Man_t * pCnf, void * vCore0, void * vVarMap0 )
{
    Vec_Int_t * vCore   = (Vec_Int_t *)vCore0;
    Vec_Int_t * vVarMap = (Vec_Int_t *)vVarMap0;
    Vec_Ptr_t * vClaMap;
    Sto_Cls_t * pClause;
    int v, i, iClause, fCompl, iObj, iFrame;
    // create map of clause
    vClaMap = Vec_PtrAlloc( pCnf->nClauses );
    Sto_ManForEachClause( pCnf, pClause )
        Vec_PtrPush( vClaMap, pClause );
    // print clauses
    fprintf( pFile, "UNSAT contains %d learned clauses:\n", Vec_IntSize(vCore) );
    Vec_IntForEachEntry( vCore, iClause, i )
    {
        pClause = (Sto_Cls_t *)Vec_PtrEntry(vClaMap, iClause);
        fprintf( pFile, "%6d : %6d : ", i, iClause - pCnf->nRoots );
        for ( v = 0; v < (int)pClause->nLits; v++ )
        {
            fCompl = Abc_LitIsCompl(pClause->pLits[v]);
            iObj   = Vec_IntEntry(vVarMap, 2*Abc_Lit2Var(pClause->pLits[v]));
            iFrame = Vec_IntEntry(vVarMap, 2*Abc_Lit2Var(pClause->pLits[v])+1);
            fprintf( pFile, "%s%d(%d) ", fCompl ? "!":"", iObj, iFrame );
        }
        if ( pClause->nLits == 0 )
            fprintf( pFile, "Empty" );
        fprintf( pFile, "\n" );
    }
    Vec_PtrFree( vClaMap );
}

////////////////////////////////////////////////////////////////////////
///                       END OF FILE                                ///
////////////////////////////////////////////////////////////////////////


ABC_NAMESPACE_IMPL_END