@Test
public void testExistsRestrictedRange() throws SolverException, InterruptedException {
BooleanFormula f;
BooleanFormula _exists_10_20_bx_0 =
qfm.exists(_x, ifm.makeNumber(10), ifm.makeNumber(20), _b_at_x_eq_0);
BooleanFormula _exists_10_20_bx_1 =
qfm.exists(_x, ifm.makeNumber(10), ifm.makeNumber(20), _b_at_x_eq_1);
// (exists x in [10..20] . b[x] = 0) AND (forall x . b[x] = 0) is SAT
f = bfm.and(_exists_10_20_bx_0, _forall_x_bx_0);
assertThat(solver.isUnsat(f)).isFalse();
// (exists x in [10..20] . b[x] = 1) AND (forall x . b[x] = 0) is UNSAT
f = bfm.and(_exists_10_20_bx_1, _forall_x_bx_0);
assertThat(solver.isUnsat(f)).isTrue();
// (exists x in [10..20] . b[x] = 1) AND (forall x . b[x] = 1) is SAT
f = bfm.and(_exists_10_20_bx_1, _forall_x_bx_1);
assertThat(solver.isUnsat(f)).isFalse();
// (exists x in [10..20] . b[x] = 1) AND (b[10] = 0) is SAT
f =
bfm.and(
_exists_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(10)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isFalse();
// (exists x in [10..20] . b[x] = 1) AND (b[1000] = 0) is SAT
f =
bfm.and(
_exists_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(1000)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isFalse();
}
@Test
public void testNotExistsArrayConjunct() throws SolverException, InterruptedException {
BooleanFormula f;
// (not exists x . not b[x] = 0) AND (b[123] = 1) is UNSAT
f =
bfm.and(
Lists.newArrayList(
bfm.not(qfm.exists(_x, bfm.not(_b_at_x_eq_0))),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(1))));
assertThat(solver.isUnsat(f)).isTrue();
// (not exists x . not b[x] = 0) AND (b[123] = 0) is SAT
f =
bfm.and(
bfm.not(qfm.exists(_x, bfm.not(_b_at_x_eq_0))),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isFalse();
// (not exists x . b[x] = 0) AND (b[123] = 0) is UNSAT
f =
bfm.and(
bfm.not(qfm.exists(_x, _b_at_x_eq_0)),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isTrue();
}
@Test
public void testContradiction() throws SolverException, InterruptedException {
// forall x . x = x+1 is UNSAT
BooleanFormula f = qfm.forall(_x, ifm.equal(_x, ifm.add(_x, ifm.makeNumber(1))));
assertThat(solver.isUnsat(f)).isTrue();
BooleanFormula g = qfm.exists(_x, ifm.equal(_x, ifm.add(_x, ifm.makeNumber(1))));
assertThat(solver.isUnsat(g)).isTrue();
}
@Test
public void testExistsArrayDisjunct() throws SolverException, InterruptedException {
BooleanFormula f;
// (exists x . b[x] = 0) OR (forall x . b[x] = 1) is SAT
f = bfm.or(qfm.exists(_x, _b_at_x_eq_0), qfm.forall(_x, _b_at_x_eq_1));
assertThat(solver.isUnsat(f)).isFalse();
// (exists x . b[x] = 1) OR (exists x . b[x] = 1) is SAT
f = bfm.or(qfm.exists(_x, _b_at_x_eq_1), qfm.exists(_x, _b_at_x_eq_1));
assertThat(solver.isUnsat(f)).isFalse();
}
@Test
public void testForallRestrictedRange() throws SolverException, InterruptedException {
BooleanFormula f;
BooleanFormula _forall_10_20_bx_0 =
qfm.forall(_x, ifm.makeNumber(10), ifm.makeNumber(20), _b_at_x_eq_0);
BooleanFormula _forall_10_20_bx_1 =
qfm.forall(_x, ifm.makeNumber(10), ifm.makeNumber(20), _b_at_x_eq_1);
// (forall x in [10..20] . b[x] = 0) AND (forall x . b[x] = 0) is SAT
f = bfm.and(_forall_10_20_bx_0, qfm.forall(_x, _b_at_x_eq_0));
assert_().about(BooleanFormula()).that(f).isSatisfiable();
// (forall x in [10..20] . b[x] = 1) AND (exits x in [15..17] . b[x] = 0) is UNSAT
f =
bfm.and(
_forall_10_20_bx_1,
qfm.exists(_x, ifm.makeNumber(15), ifm.makeNumber(17), _b_at_x_eq_0));
assertThat(solver.isUnsat(f)).isTrue();
// (forall x in [10..20] . b[x] = 1) AND b[10] = 0 is UNSAT
f =
bfm.and(
_forall_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(10)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isTrue();
// (forall x in [10..20] . b[x] = 1) AND b[20] = 0 is UNSAT
f =
bfm.and(
_forall_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(20)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isTrue();
// (forall x in [10..20] . b[x] = 1) AND b[9] = 0 is SAT
f =
bfm.and(
_forall_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(9)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isFalse();
// (forall x in [10..20] . b[x] = 1) AND b[21] = 0 is SAT
f =
bfm.and(
_forall_10_20_bx_1, ifm.equal(afm.select(_b, ifm.makeNumber(21)), ifm.makeNumber(0)));
assertThat(solver.isUnsat(f)).isFalse();
// (forall x in [10..20] . b[x] = 1) AND (forall x in [0..20] . b[x] = 0) is UNSAT
f =
bfm.and(
_forall_10_20_bx_1,
qfm.forall(_x, ifm.makeNumber(0), ifm.makeNumber(20), _b_at_x_eq_0));
assertThat(solver.isUnsat(f)).isTrue();
// (forall x in [10..20] . b[x] = 1) AND (forall x in [0..9] . b[x] = 0) is SAT
f =
bfm.and(
_forall_10_20_bx_1, qfm.forall(_x, ifm.makeNumber(0), ifm.makeNumber(9), _b_at_x_eq_0));
assertThat(solver.isUnsat(f)).isFalse();
}
@Test
public void testExistsArrayConjunct() throws SolverException, InterruptedException {
BooleanFormula f;
// (exists x . b[x] = 0) AND (b[123] = 1) is SAT
f =
bfm.and(
qfm.exists(_x, _b_at_x_eq_0),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(1)));
assertThat(solver.isUnsat(f)).isFalse();
// (exists x . b[x] = 1) AND (forall x . b[x] = 0) is UNSAT
f = bfm.and(qfm.exists(_x, _b_at_x_eq_1), _forall_x_bx_0);
assertThat(solver.isUnsat(f)).isTrue();
// (exists x . b[x] = 0) AND (forall x . b[x] = 0) is SAT
f = bfm.and(qfm.exists(_x, _b_at_x_eq_0), _forall_x_bx_0);
assertThat(solver.isUnsat(f)).isFalse();
}
@Test
public void testSimple() throws SolverException, InterruptedException {
// forall x . x+2 = x+1+1 is SAT
BooleanFormula f =
qfm.forall(
_x,
ifm.equal(
ifm.add(_x, ifm.makeNumber(2)),
ifm.add(ifm.add(_x, ifm.makeNumber(1)), ifm.makeNumber(1))));
assertThat(solver.isUnsat(f)).isFalse();
}
@Test
public void testForallArrayDisjunct() throws SolverException, InterruptedException {
BooleanFormula f;
// (forall x . b[x] = 0) AND (b[123] = 1 OR b[123] = 0) is SAT
f =
bfm.and(
qfm.forall(_x, _b_at_x_eq_0),
bfm.or(
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(1)),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(0))));
assertThat(solver.isUnsat(f)).isFalse();
// (forall x . b[x] = 0) OR (b[123] = 1) is SAT
f =
bfm.or(
qfm.forall(_x, _b_at_x_eq_0),
ifm.equal(afm.select(_b, ifm.makeNumber(123)), ifm.makeNumber(1)));
assertThat(solver.isUnsat(f)).isFalse();
}