/**
*
*/
package kodkod.examples.tptp;
import static kodkod.ast.Expression.UNIV;
import java.util.ArrayList;
import java.util.List;
import kodkod.ast.Expression;
import kodkod.ast.Formula;
import kodkod.ast.Relation;
import kodkod.ast.Variable;
import kodkod.engine.Solution;
import kodkod.engine.Solver;
import kodkod.engine.satlab.SATFactory;
import kodkod.instance.Bounds;
import kodkod.instance.TupleFactory;
import kodkod.instance.Universe;
/**
* A KK encoding of SET943+1.p from http://www.cs.miami.edu/~tptp/
* @author Emina Torlak
*/
public final class SET943 {
private final Relation empty;
private final Relation subset, in, union;
private final Relation union2;
/**
* Constructs a new instance of SET943.
*/
public SET943() {
empty = Relation.unary("empty");
subset = Relation.binary("subset");
in = Relation.binary("in");
union = Relation.binary("union");
union2 = Relation.ternary("set_union2");
}
/**
* Returns set_union2[A][B]
* @return set_union2[A][B]
*/
final Expression set_union2(Expression a, Expression b) {
return b.join(a.join(union2));
}
/**
* Returns union[a]
* @return union[a]
*/
final Expression union(Expression a) {
return a.join(union);
}
/**
* Returns a in empty
* @return a in empty
*/
final Formula empty(Expression a) {
return a.in(empty);
}
/**
* Returns a->b in subset.
* @return a->b in subset.
*/
final Formula subset(Expression a, Expression b) {
return a.product(b).in(subset);
}
/**
* Returns a->b in in.
* @return a->b in in
*/
final Formula in(Expression a, Expression b) {
return a.product(b).in(in);
}
/**
* Returns the declarations.
* @return declarations
*/
public final Formula decls() {
final Formula f0 = union.function(UNIV, UNIV);
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
final Formula f1 = set_union2(a, b).one();
return f0.and(f1.forAll(a.oneOf(UNIV).and(b.oneOf(UNIV))));
}
/**
* Returns antisymmetry_r2_hidden axiom.
* @return antisymmetry_r2_hidden
*/
public final Formula antisymmetry_r2_hidden() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return in(a,b).implies(in(b,a).not()).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns commutativity_k2_xboole_0 axiom.
* @return commutativity_k2_xboole_0
*/
public final Formula commutativity_k2_xboole_0() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return set_union2(a, b).eq(set_union2(b, a)).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns d10_xboole_0 axiom.
* @return d10_xboole_0
*/
public final Formula d10_xboole_0() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return a.eq(b).iff(subset(a,b).and(subset(b,a))).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns d2_xboole_0 axiom.
* @return d2_xboole_0
*/
public final Formula d2_xboole_0() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
final Variable c = Variable.unary("C");
return c.eq(set_union2(a, b)).iff(in.join(c).eq(in.join(a).union(in.join(b)))).
forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)).and(c.oneOf(UNIV)));
}
/**
* Returns d3_tarski axiom.
* @return d3_tarski
*/
public final Formula d3_tarski() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return subset(a,b).iff(in.join(a).in(in.join(b))).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns d4_tarski axiom.
* @return d4_tarski
*/
public final Formula d4_tarski() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return b.eq(union(a)).iff(in.join(b).eq(in.join(in.join(a)))).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns fc2_xboole_0 axiom.
* @return fc2_xboole_0
*/
public final Formula fc2_xboole_0() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return empty(a).not().implies(empty(set_union2(a, b)).not()).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns fc3_xboole_0 axiom.
* @return fc3_xboole_0
*/
public final Formula fc3_xboole_0() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return empty(a).not().implies(empty(set_union2(b, a)).not()).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns idempotence_k2_xboole_0 axiom.
* @return idempotence_k2_xboole_0
*/
public final Formula idempotence_k2_xboole_0() {
final Variable a = Variable.unary("A");
return set_union2(a, a).eq(a).forAll(a.oneOf(UNIV));
}
/**
* Returns rc1_xboole_0 axiom.
* @return rc1_xboole_0
*/
public final Formula rc1_xboole_0() {
return empty.some();
}
/**
* Returns rc2_xboole_0 axiom.
* @return rc2_xboole_0
*/
public final Formula rc2_xboole_0() {
return UNIV.difference(empty).some();
}
/**
* Returns reflexivity_r1_tarski axiom.
* @return reflexivity_r1_tarski
*/
public final Formula reflexivity_r1_tarski() {
final Variable a = Variable.unary("A");
return subset(a,a).forAll(a.oneOf(UNIV));
}
// all A, B: Atom | subset(A,set_union2(A,B))
/**
* Returns t7_xboole_1 axiom.
* @return t7_xboole_1
*/
public final Formula t7_xboole_1() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return subset(a, set_union2(a, b)).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns t8_xboole_1 axiom.
* @return t8_xboole_1
*/
public final Formula t8_xboole_1() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
final Variable c = Variable.unary("C");
return subset(a,b).and(subset(c,b)).implies(subset(set_union2(a, c),b)).
forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)).and(c.oneOf(UNIV)));
}
/**
* Returns t95_zfmisc_1 axiom.
* @return t95_zfmisc_1
*/
public final Formula t95_zfmisc_1() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return subset(a, b).implies(subset(union(a),union(b))).forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns the conjunction of all axioms.
* @return conjunction of all axioms.
*/
public final Formula axioms() {
return decls().and(antisymmetry_r2_hidden()).and(commutativity_k2_xboole_0()).
and(d10_xboole_0()).and(d2_xboole_0()).and(d3_tarski()).
and(d4_tarski()).and(fc2_xboole_0()).and(fc3_xboole_0()).and(idempotence_k2_xboole_0()).
and(rc1_xboole_0()).and(rc2_xboole_0()).
and(reflexivity_r1_tarski()).and(t7_xboole_1()).and(t8_xboole_1()).
and(t95_zfmisc_1());
}
/**
* Returns t96_zfmisc_1 conjecture.
* @return t96_zfmisc_1
*/
public final Formula t96_zfmisc_1() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
return union(set_union2(a, b)).eq(set_union2(union(a), union(b))).
forAll(a.oneOf(UNIV).and(b.oneOf(UNIV)));
}
/**
* Returns the conjunction of the axioms and the negation of the hypothesis.
* @return axioms() && !t96_zfmisc_1()
*/
public final Formula checkT96_zfmisc_1() {
return axioms().and(t96_zfmisc_1().not());
}
/**
* Returns bounds for the given scope.
* @return bounds for the given scope.
*/
public final Bounds bounds(int n) {
assert n > 0;
final List<String> atoms = new ArrayList<String>(n);
for(int i = 0; i < n; i++)
atoms.add("a"+i);
final Universe u = new Universe(atoms);
final Bounds b = new Bounds(u);
final TupleFactory f = u.factory();
b.bound(empty, f.allOf(1));
b.bound(subset, f.allOf(2));
b.bound(in, f.allOf(2));
b.bound(union, f.allOf(2));
b.bound(union2, f.allOf(3));
return b;
}
private static void usage() {
System.out.println("java examples.tptp.SET943 [univ size]");
System.exit(1);
}
/**
* Usage: java examples.tptp.SET943 [univ size]
*/
public static void main(String[] args) {
if (args.length < 1)
usage();
try {
final int n = Integer.parseInt(args[0]);
if (n < 1)
usage();
final SET943 model = new SET943();
final Solver solver = new Solver();
solver.options().setSolver(SATFactory.MiniSat);
// solver.options().setSymmetryBreaking(1000);
// solver.options().setFlatten(false);
final Formula f = model.checkT96_zfmisc_1();
final Bounds b = model.bounds(n);
System.out.println(f);
final Solution sol = solver.solve(f, b);
System.out.println(sol);
} catch (NumberFormatException nfe) {
usage();
}
}
}