// resolve two clauses, if possible.
int
resolveClauses(Array<OrderedSet<Clause> > &clausesArray,
Clause &cl1, Clause &cl2, int &clausesAdded, unsigned int currentDepth)
{
// clear this flag
clausesAdded = 0;
// check if any of the clauses are empty
if (cl1.isEmpty() || cl2.isEmpty())
{
return(VALID);
}
// check if clauses can be resolved
if (!cl1.getSOS() && cl2.getSOS())
{
// one clause must be in the set-of-support
return(NOMATCH);
}
if ((cl1.getType() == Clause::Negative &&
cl2.getType() == Clause::Negative) ||
(cl1.getType() == Clause::Positive &&
cl2.getType() == Clause::Positive))
{
// two positive clauses or two negative clauses
// can not be resolved.
return(NOMATCH);
}
// attempt to resolve two clauses. use A-ordering resolution,
// try to resolve maximal literals.
//
Literal maxlit1;
if (cl1.getMaximalLiteral(maxlit1) != OK)
{
return(NOTOK);
}
Literal maxlit2;
if (cl2.getMaximalLiteral(maxlit2) != OK)
{
return(NOTOK);
}
if (maxlit1 != ~maxlit2)
{
return(NOMATCH);
}
// factor clauses
if (factor(maxlit1, cl1) == NOTOK)
{
return(NOTOK);
}
if (factor(maxlit2, cl2) == NOTOK)
{
return(NOTOK);
}
// attempt to unify the clauses
Substitutions subs;
if (unify(maxlit1, ~maxlit2, subs) != OK)
{
return(NOMATCH);
}
// can resolve, remove literals from clauses
Clause newcl1(cl1);
if (newcl1.remove(maxlit1, 1) != OK)
{
return(NOTOK);
}
if (subs.applyTo(newcl1) != OK)
{
return(NOTOK);
}
Clause newcl2(cl2);
if (newcl2.remove(maxlit2, 1) != OK)
{
return(NOTOK);
}
if (subs.applyTo(newcl2) != OK)
{
return(NOTOK);
}
// store new clause and update flag
Clause newcl = newcl1+newcl2;
if (newcl.renameVariables() != OK)
{
return(NOTOK);
}
newcl.setDepth(currentDepth+1);
newcl.setNumber(nextClause++);
if (clausesArray[currentDepth+1].insert(newcl) != OK)
{
return(NOTOK);
}
clausesAdded = 1;
// indicate the clauses that were resolved
dumpnewclause(cl1, cl2, newcl);
// check if we found an empty clause
if (newcl.isEmpty())
{
return(VALID);
}
else
{
return(OK);
}
}
// check if a clause is a subset of another. only compares
// equivalent sets.
//
int
subset(const Clause &cl1, const Clause &cl2)
{
// verify smaller clause subsumes larger clause
if (cl1.getTotalMembers() > cl2.getTotalMembers())
{
return(NOMATCH);
}
// certain types of clauses cannot subsume others,
// p = positive, n = negative, m = mixed.
//
// clause 1 clause 2 can
// type type subsume?
// -------------------------------------------
// P P yes
// P N no
// P M yes
// N P no
// N N yes
// N M yes
// M P yes
// M N yes
// M M yes
//
if (((cl1.getType() == Clause::Positive) &&
(cl2.getType() == Clause::Negative)) ||
((cl1.getType() == Clause::Negative) &&
(cl2.getType() == Clause::Positive)))
{
return(NOMATCH);
}
// start checking every literal equivalent class. every equivalent
// class in clause 1 should be in clause2. absolute equality
// is checked with unification.
//
ClauseIterator cl1Iter(cl1);
ClauseIterator cl2Iter(cl2);
for ( ; !cl1Iter.done(); cl1Iter++)
{
// search for literal in clause 2
int found = 0;
while (!cl2Iter.done() && !found)
{
if (cl2Iter().lt(cl1Iter()))
{
cl2Iter++;
}
else if (cl2Iter().gt(cl1Iter()))
{
return(NOMATCH);
}
else
{
found = 1;
}
}
if (!found)
{
return(NOMATCH);
}
}
// all done
return(OK);
}
// resolve two clauses, if possible.
int
resolveClauses(Array<BinaryTree_AVL<Clause> > &clausesArray,
Clause &cl1, Clause &cl2, int &clausesAdded, unsigned int currentDepth)
{
// check if any of the clauses are empty
statistics[ResolutionsAttempted] += 1;
totalstatistics[TotalResolutionsAttempted] += 1;
if (cl1.isEmpty() || cl2.isEmpty())
{
return(VALID);
}
// check if clauses can be resolved
if (!cl1.getSOS() && !cl2.getSOS())
{
// one clause must be in the set-of-support
return(NOMATCH);
}
if ((cl1.getType() == Clause::Negative &&
cl2.getType() == Clause::Negative) ||
(cl1.getType() == Clause::Positive &&
cl2.getType() == Clause::Positive))
{
// two positive clauses or two negative clauses
// can not be resolved.
return(NOMATCH);
}
// attempt to resolve two clauses. use A-ordering resolution,
// try to resolve maximal literals.
//
Literal maxlit1;
if (cl1.getMaximalLiteral(maxlit1) != OK)
{
ERROR("getMaximalLiteral failed.", errno);
return(NOTOK);
}
Literal maxlit2;
if (cl2.getMaximalLiteral(maxlit2) != OK)
{
ERROR("getMaximalLiteral failed.", errno);
return(NOTOK);
}
if ((cl1.getTotalMembers() > maxliterals) ||
(cl2.getTotalMembers() > maxliterals))
{
statistics[MaximumLiteralsClausesRejected] += 1;
totalstatistics[TotalMaximumLiteralsClausesRejected] += 1;
return(NOMATCH);
}
if (maxlit1.unify_ne(~maxlit2))
{
return(NOMATCH);
}
// factor clauses
Substitutions subs;
if (factor(maxlit1, cl1, subs) == NOTOK)
{
ERROR("factor failed.", errno);
return(NOTOK);
}
if (factor(maxlit2, cl2, subs) == NOTOK)
{
ERROR("factor failed.", errno);
return(NOTOK);
}
// attempt to unify the clauses
subs.clear();
int status = unify(maxlit1, ~maxlit2, subs);
switch (status)
{
case OK:
if (verbose)
{
cout << endl;
Literal ml1(maxlit1);
cout << "max literal 1 (before subs): " << ml1 << endl;
subs.applyTo(ml1);
cout << "max literal 1 (after subs): " << ml1 << endl;
Literal ml2(maxlit2);
cout << "max literal 2 (before subs): " << ml2 << endl;
subs.applyTo(ml2);
cout << "max literal 2 (after subs): " << ml2 << endl;
MustBeTrue(equal(ml1, ~ml2));
}
break;
case NOMATCH:
return(NOMATCH);
default:
ERROR("unify failed.", errno);
return(status);
}
// can resolve, remove literals from clauses
Clause newcl1(cl1);
if (newcl1.remove(maxlit1) != OK)
{
ERROR("remove failed.", errno);
return(NOTOK);
}
if (subs.applyTo(newcl1) != OK)
{
ERROR("applyTo failed.", errno);
return(NOTOK);
}
Clause newcl2(cl2);
if (newcl2.remove(maxlit2) != OK)
{
ERROR("remove failed.", errno);
return(NOTOK);
}
if (subs.applyTo(newcl2) != OK)
{
ERROR("applyTo failed.", errno);
return(NOTOK);
}
// store new clause and update flag
Clause newcl = newcl1+newcl2;
if (newcl.renameVariables() != OK)
{
ERROR("renameVariables failed.", errno);
return(NOTOK);
}
newcl.setDepth(currentDepth+1);
newcl.setNumber(nextClause++);
if (clausesArray[currentDepth+1].insert(newcl) != OK)
{
ERROR("insert failed.", errno);
return(NOTOK);
}
clausesAdded = 1;
// indicate the clauses that were resolved
statistics[ClausesGenerated] += 1;
totalstatistics[TotalClausesGenerated] += 1;
dumpnewclause(cl1, cl2, newcl);
// check if we found an empty clause
if (newcl.isEmpty())
{
return(VALID);
}
else
{
return(OK);
}
}
