/** * If this formula should be visited, then we visit its children only if they could have * contributed to the unsatisfiability of the top-level formula. For example, let binFormula = * "p && q", binFormula simplified to FALSE, p simplified to FALSE and q was not simplified, * then only p should be visited since p caused binFormula's reduction to FALSE. */ public void visit(BinaryFormula binFormula) { if (visited(binFormula)) return; relevant.add(binFormula); final Formula l = binFormula.left(), r = binFormula.right(); final Boolean lval = constNodes.get(l), rval = constNodes.get(r); final boolean lvisit, rvisit; switch (binFormula.op()) { case AND: lvisit = (lval == Boolean.FALSE || (lval == null && rval != Boolean.FALSE)); rvisit = (rval != Boolean.TRUE && lval != Boolean.FALSE); break; case OR: lvisit = (lval == Boolean.TRUE || (lval == null && rval != Boolean.TRUE)); rvisit = (rval != Boolean.FALSE && lval != Boolean.TRUE); break; case IMPLIES: // !l || r lvisit = (lval == Boolean.FALSE || (lval == null && rval != Boolean.TRUE)); rvisit = (rval != Boolean.FALSE && lval != Boolean.FALSE); break; case IFF: // (!l || r) && (l || !r) lvisit = rvisit = true; break; default: throw new IllegalArgumentException("Unknown operator: " + binFormula.op()); } if (lvisit) { l.accept(this); } if (rvisit) { r.accept(this); } }
/** * Returns the nodes necessary for proving the trivial unsatisfiability of log.formula. * * @requires some r: log.records | r.node = log.formula && r.literal = * BooleanConstant.FALSE.label * @requires highLevelCore in log.roots() and unsatisfiable(highLevelCore, log.bounds, * log.options) * @return nodes necessary for proving the trivial unsatisfiability of log.formula. */ static Set<Node> relevantNodes(TranslationLog log, Set<Formula> highLevelCore) { final NodePruner finder = new NodePruner(log); for (Formula root : highLevelCore) { if (!finder.isTrue(root)) { root.accept(finder); } } return finder.relevant; }
/** * Returns the declaration constraints. * * @return declaration constraints */ public final Formula decls() { // File and Dir partition object final Formula f0 = Obj.eq(File.union(Dir)).and(File.intersection(Dir).no()); // Root and Cur are in Dir and do not intersect final Formula f1 = Root.in(Dir).and(Cur.in(Dir)).and(Root.intersection(Cur).no()); // don't need to specify that Dir, Name, and DirEntry are disjoint; implied by bounds final Formula f2 = entries.in(Dir.product(DirEntry)); final Formula f3 = parent.partialFunction(Dir, Dir); final Formula f4 = name.function(DirEntry, Name); final Formula f5 = contents.function(DirEntry, Obj); return f0.and(f1).and(f2).and(f3).and(f4).and(f5); }
/** * Returns the conjecture proposition_2_14_1. * * @return proposition_2_14_1 */ public final Formula proposition2141() { // all c1, c2: curve, p: point | // p->c1->c2 in meet && c1->c2 in sum.open => // all q: point - p | c1 + c2 !in q.incident final Variable c1 = Variable.unary("C1"); final Variable c2 = Variable.unary("C2"); final Variable p = Variable.unary("P"); final Variable q = Variable.unary("Q"); final Expression e0 = c1.product(c2); final Formula f0 = p.product(e0).in(meet).and(e0.in(sum.join(open))); final Formula f1 = c1.union(c2).in(q.join(incident)).not().forAll(q.oneOf(point.difference(p))); return f0.implies(f1).forAll(c1.oneOf(curve).and(c2.oneOf(curve)).and(p.oneOf(point))); }
/** * Returns all facts in the model. * * @return the facts. */ public final Formula facts() { // sig File extends Object {} { some d: Dir | this in d.entries.contents } final Variable file = Variable.unary("this"); final Variable d = Variable.unary("d"); final Formula f0 = file.in(d.join(entries).join(contents)).forSome(d.oneOf(Dir)).forAll(file.oneOf(File)); // sig Dir extends Object { // entries: set DirEntry, // parent: lone Dir // } { // parent = this.~@contents.~@entries // all e1, e2 : entries | e1.name = e2.name => e1 = e2 // this !in this.^@parent // this != Root => Root in this.^@parent // } final Variable dir = Variable.unary("this"); final Variable e1 = Variable.unary("e1"), e2 = Variable.unary("e2"); final Formula f1 = (dir.join(parent)).eq(dir.join(contents.transpose()).join(entries.transpose())); final Expression e0 = dir.join(entries); final Formula f2 = e1.join(name).eq(e2.join(name)).implies(e1.eq(e2)).forAll(e1.oneOf(e0).and(e2.oneOf(e0))); final Formula f3 = dir.in(dir.join(parent.closure())).not(); final Formula f4 = dir.eq(Root).not().implies(Root.in(dir.join(parent.closure()))); final Formula f5 = f1.and(f2).and(f3).and(f4).forAll(dir.oneOf(Dir)); // one sig Root extends Dir {} { no parent } final Formula f6 = Root.join(parent).no(); // sig DirEntry { // name: Name, // contents: Object // } { one this.~entries } final Variable entry = Variable.unary("this"); final Formula f7 = entry.join(entries.transpose()).one().forAll(entry.oneOf(DirEntry)); // fact OneParent { // // all directories besides root xhave one parent // all d: Dir - Root | one d.parent // } final Formula f8 = d.join(parent).one().forAll(d.oneOf(Dir.difference(Root))); return f0.and(f5).and(f6).and(f7).and(f8); }
/** * Returns the conjecture theorem_3_8_5. * * @return theorem_3_8_5 */ public final Formula theorem385() { // all c: curve, p, q, r: point | // c->p->q->r in between => // incident.c - q in q.(p.(c.between)) + ((c.between).r).q final Variable c = Variable.unary("C"); final Variable p = Variable.unary("P"); final Variable q = Variable.unary("Q"); final Variable r = Variable.unary("R"); final Formula f0 = c.product(p).product(q).product(r).in(between); final Expression e0 = q.join(p.join(c.join(between))); final Expression e1 = c.join(between).join(r).join(q); final Formula f1 = incident.join(c).difference(q).in(e0.union(e1)); return f0.implies(f1) .forAll(p.oneOf(point).and(q.oneOf(point)).and(r.oneOf(point)).and(c.oneOf(curve))); }
/** * Returns a relational encoding of the problem. * * @return a relational encoding of the problem. */ public Formula rules() { final List<Formula> rules = new ArrayList<Formula>(); rules.add(x.function(queen, num)); rules.add(y.function(queen, num)); final Variable i = Variable.unary("n"); final Variable q1 = Variable.unary("q1"), q2 = Variable.unary("q2"); // at most one queen in each row: all i: num | lone x.i rules.add(x.join(i).lone().forAll(i.oneOf(num))); // at most one queen in each column: all i: num | lone y.i rules.add(y.join(i).lone().forAll(i.oneOf(num))); // no queen in a blocked position: all q: Queen | q.x->q.y !in blocked rules.add(q1.join(x).product(q1.join(y)).intersection(blocked).no().forAll(q1.oneOf(queen))); // at most one queen on each diagonal // all q1: Queen, q2: Queen - q1 | // let xu = prevs[q2.x] + prevs[q1.x], // xi = prevs[q2.x] & prevs[q1.x], // yu = prevs[q2.y] + prevs[q1.y], // yi = prevs[q2.y] & prevs[q1.y] | // #(xu - xi) != #(yu - yi) final Expression ordClosure = ord.closure(); final Expression q2xPrevs = ordClosure.join(q2.join(x)), q1xPrevs = ordClosure.join(q1.join(x)); final Expression q2yPrevs = ordClosure.join(q2.join(y)), q1yPrevs = ordClosure.join(q1.join(y)); final IntExpression xDiff = (q2xPrevs.union(q1xPrevs)).difference(q2xPrevs.intersection(q1xPrevs)).count(); final IntExpression yDiff = (q2yPrevs.union(q1yPrevs)).difference(q2yPrevs.intersection(q1yPrevs)).count(); rules.add(xDiff.eq(yDiff).not().forAll(q1.oneOf(queen).and(q2.oneOf(queen.difference(q1))))); return Formula.and(rules); }
/** * If this formula should be visited, then we visit its children only if they could have * contributed to the unsatisfiability of the top-level formula. For example, let binFormula = * "p && q", binFormula simplified to FALSE, p simplified to FALSE and q was not simplified, * then only p should be visited since p caused binFormula's reduction to FALSE. */ public void visit(NaryFormula formula) { if (visited(formula)) return; relevant.add(formula); final Boolean val = constNodes.get(formula); final Boolean cancel; switch (formula.op()) { case AND: cancel = Boolean.FALSE; break; case OR: cancel = Boolean.TRUE; break; default: throw new IllegalArgumentException("Unknown nary operator: " + formula.op()); } final Boolean iden = Boolean.valueOf(!cancel); if (val != iden) { for (Formula child : formula) { if (constNodes.get(child) == cancel) { child.accept(this); return; } } for (Formula child : formula) { if (constNodes.get(child) != iden) { child.accept(this); } } return; } for (Formula child : formula) { child.accept(this); } }
public static void main(String[] args) throws Exception { Relation x0 = Relation.unary("Int/min"); Relation x1 = Relation.unary("Int/zero"); Relation x2 = Relation.unary("Int/max"); Relation x3 = Relation.nary("Int/next", 2); Relation x4 = Relation.unary("seq/Int"); Relation x5 = Relation.unary("String"); Relation x6 = Relation.unary("this/A"); Relation x7 = Relation.unary("this/Relation"); Relation x8 = Relation.nary("this/Relation.r", 4); List<String> atomlist = Arrays.asList( "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "0", "1", "2", "3", "4", "5", "6", "7", "A$0", "A$1", "A$2", "Relation$0", "unused0", "unused1"); Universe universe = new Universe(atomlist); TupleFactory factory = universe.factory(); Bounds bounds = new Bounds(universe); TupleSet x0_upper = factory.noneOf(1); x0_upper.add(factory.tuple("-8")); bounds.boundExactly(x0, x0_upper); TupleSet x1_upper = factory.noneOf(1); x1_upper.add(factory.tuple("0")); bounds.boundExactly(x1, x1_upper); TupleSet x2_upper = factory.noneOf(1); x2_upper.add(factory.tuple("7")); bounds.boundExactly(x2, x2_upper); TupleSet x3_upper = factory.noneOf(2); x3_upper.add(factory.tuple("-8").product(factory.tuple("-7"))); x3_upper.add(factory.tuple("-7").product(factory.tuple("-6"))); x3_upper.add(factory.tuple("-6").product(factory.tuple("-5"))); x3_upper.add(factory.tuple("-5").product(factory.tuple("-4"))); x3_upper.add(factory.tuple("-4").product(factory.tuple("-3"))); x3_upper.add(factory.tuple("-3").product(factory.tuple("-2"))); x3_upper.add(factory.tuple("-2").product(factory.tuple("-1"))); x3_upper.add(factory.tuple("-1").product(factory.tuple("0"))); x3_upper.add(factory.tuple("0").product(factory.tuple("1"))); x3_upper.add(factory.tuple("1").product(factory.tuple("2"))); x3_upper.add(factory.tuple("2").product(factory.tuple("3"))); x3_upper.add(factory.tuple("3").product(factory.tuple("4"))); x3_upper.add(factory.tuple("4").product(factory.tuple("5"))); x3_upper.add(factory.tuple("5").product(factory.tuple("6"))); x3_upper.add(factory.tuple("6").product(factory.tuple("7"))); bounds.boundExactly(x3, x3_upper); TupleSet x4_upper = factory.noneOf(1); x4_upper.add(factory.tuple("0")); x4_upper.add(factory.tuple("1")); x4_upper.add(factory.tuple("2")); bounds.boundExactly(x4, x4_upper); TupleSet x5_upper = factory.noneOf(1); bounds.boundExactly(x5, x5_upper); TupleSet x6_upper = factory.noneOf(1); x6_upper.add(factory.tuple("A$0")); x6_upper.add(factory.tuple("A$1")); x6_upper.add(factory.tuple("A$2")); bounds.boundExactly(x6, x6_upper); TupleSet x7_upper = factory.noneOf(1); x7_upper.add(factory.tuple("unused0")); x7_upper.add(factory.tuple("unused1")); x7_upper.add(factory.tuple("Relation$0")); bounds.bound(x7, x7_upper); TupleSet x8_upper = factory.noneOf(4); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("unused1") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$0")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$1")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$0")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$1")) .product(factory.tuple("A$2"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$0"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$1"))); x8_upper.add( factory .tuple("Relation$0") .product(factory.tuple("A$2")) .product(factory.tuple("A$2")) .product(factory.tuple("A$2"))); bounds.bound(x8, x8_upper); bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8"))); bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7"))); bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6"))); bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5"))); bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4"))); bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3"))); bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2"))); bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1"))); bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0"))); bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1"))); bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2"))); bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3"))); bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4"))); bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5"))); bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6"))); bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7"))); Variable x12 = Variable.unary("this"); Decls x11 = x12.oneOf(x7); Expression x16 = x12.join(x8); Expression x18 = x6.product(x6); Expression x17 = x6.product(x18); Formula x15 = x16.in(x17); Variable x21 = Variable.unary("x21"); Decls x20 = x21.oneOf(x6); Expression x25 = x21.join(x16); Expression x26 = x6.product(x6); Formula x24 = x25.in(x26); Variable x29 = Variable.unary("x29"); Decls x28 = x29.oneOf(x6); Expression x32 = x29.join(x25); Formula x31 = x32.one(); Formula x33 = x32.in(x6); Formula x30 = x31.and(x33); Formula x27 = x30.forAll(x28); Formula x23 = x24.and(x27); Variable x36 = Variable.unary("x36"); Decls x35 = x36.oneOf(x6); Expression x38 = x25.join(x36); Formula x37 = x38.in(x6); Formula x34 = x37.forAll(x35); Formula x22 = x23.and(x34); Formula x19 = x22.forAll(x20); Formula x14 = x15.and(x19); Variable x42 = Variable.unary("x42"); Decls x41 = x42.oneOf(Expression.UNIV); Variable x45 = Variable.unary("x45"); Decls x44 = x45.oneOf(Expression.UNIV); Decls x40 = x41.and(x44); Expression x50 = x42.product(x45); Expression x51 = x6.product(x6); Formula x49 = x50.in(x51); Variable x54 = Variable.unary("x54"); Decls x53 = x54.oneOf(x6); Expression x57 = x54.join(x50); Formula x56 = x57.one(); Formula x58 = x57.in(x6); Formula x55 = x56.and(x58); Formula x52 = x55.forAll(x53); Formula x48 = x49.and(x52); Variable x61 = Variable.unary("x61"); Decls x60 = x61.oneOf(x6); Expression x63 = x50.join(x61); Formula x62 = x63.in(x6); Formula x59 = x62.forAll(x60); Formula x47 = x48.and(x59); Expression x66 = x16.join(x45); Expression x65 = x66.join(x42); Formula x64 = x65.in(x6); Formula x46 = x47.implies(x64); Formula x39 = x46.forAll(x40); Formula x13 = x14.and(x39); Formula x10 = x13.forAll(x11); Expression x70 = x8.join(Expression.UNIV); Expression x69 = x70.join(Expression.UNIV); Expression x68 = x69.join(Expression.UNIV); Formula x67 = x68.in(x7); Formula x71 = x0.eq(x0); Formula x72 = x1.eq(x1); Formula x73 = x2.eq(x2); Formula x74 = x3.eq(x3); Formula x75 = x4.eq(x4); Formula x76 = x5.eq(x5); Formula x77 = x6.eq(x6); Formula x78 = x7.eq(x7); Formula x79 = x8.eq(x8); Formula x9 = Formula.compose(FormulaOperator.AND, x10, x67, x71, x72, x73, x74, x75, x76, x77, x78, x79); Solver solver = new Solver(); solver.options().setSolver(SATFactory.DefaultSAT4J); solver.options().setBitwidth(4); solver.options().setFlatten(false); solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT); solver.options().setSymmetryBreaking(20); solver.options().setSkolemDepth(0); System.out.println(PrettyPrinter.print(x9, 0)); System.out.println(bounds); System.out.println("Solving..."); System.out.flush(); Solution sol = solver.solve(x9, bounds); System.out.println(sol.toString()); Instance inst = sol.instance(); Evaluator ev = new Evaluator(inst); System.out.println("Universe: " + ev.evaluate(Expression.UNIV)); Formula xx = x46.forAll(x40).forAll(x11); System.out.println(PrettyPrinter.print(xx, 2)); System.out.println(ev.evaluate(xx)); System.out.println(PrettyPrinter.print(x46, 4)); // Variable r = Variable.unary("this"); // Variable u1 = Variable.unary("u1"); // Variable u2 = Variable.unary("u2"); // // Formula ff = // u1.product(u2).in(x6.product(x6)).forAll(u1.oneOf(Expression.UNIV).and(u2.oneOf(Expression.UNIV))).forAll(r.oneOf(x7)); // System.out.println(PrettyPrinter.print(ff, 0)); // System.out.println(ev.evaluate(ff)); }
public static void main(String[] args) throws Exception { Relation x0 = Relation.unary("Int/min"); Relation x1 = Relation.unary("Int/zero"); Relation x2 = Relation.unary("Int/max"); Relation x3 = Relation.nary("Int/next", 2); Relation x4 = Relation.unary("seq/Int"); Relation x5 = Relation.unary("String"); Relation x6 = Relation.unary("this/Test"); Relation x7 = Relation.nary("this/Test.weight", 2); Relation x8 = Relation.nary("this/Test.x", 2); Relation x9 = Relation.nary("this/Test.y", 2); List<String> atomlist = Arrays.asList( "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "0", "1", "2", "3", "4", "5", "6", "7", "Test$0", "Test$1", "Test$2"); Universe universe = new Universe(atomlist); TupleFactory factory = universe.factory(); Bounds bounds = new Bounds(universe); TupleSet x0_upper = factory.noneOf(1); x0_upper.add(factory.tuple("-8")); bounds.boundExactly(x0, x0_upper); TupleSet x1_upper = factory.noneOf(1); x1_upper.add(factory.tuple("0")); bounds.boundExactly(x1, x1_upper); TupleSet x2_upper = factory.noneOf(1); x2_upper.add(factory.tuple("7")); bounds.boundExactly(x2, x2_upper); TupleSet x3_upper = factory.noneOf(2); x3_upper.add(factory.tuple("-8").product(factory.tuple("-7"))); x3_upper.add(factory.tuple("-7").product(factory.tuple("-6"))); x3_upper.add(factory.tuple("-6").product(factory.tuple("-5"))); x3_upper.add(factory.tuple("-5").product(factory.tuple("-4"))); x3_upper.add(factory.tuple("-4").product(factory.tuple("-3"))); x3_upper.add(factory.tuple("-3").product(factory.tuple("-2"))); x3_upper.add(factory.tuple("-2").product(factory.tuple("-1"))); x3_upper.add(factory.tuple("-1").product(factory.tuple("0"))); x3_upper.add(factory.tuple("0").product(factory.tuple("1"))); x3_upper.add(factory.tuple("1").product(factory.tuple("2"))); x3_upper.add(factory.tuple("2").product(factory.tuple("3"))); x3_upper.add(factory.tuple("3").product(factory.tuple("4"))); x3_upper.add(factory.tuple("4").product(factory.tuple("5"))); x3_upper.add(factory.tuple("5").product(factory.tuple("6"))); x3_upper.add(factory.tuple("6").product(factory.tuple("7"))); bounds.boundExactly(x3, x3_upper); TupleSet x4_upper = factory.noneOf(1); x4_upper.add(factory.tuple("0")); x4_upper.add(factory.tuple("1")); x4_upper.add(factory.tuple("2")); x4_upper.add(factory.tuple("3")); bounds.boundExactly(x4, x4_upper); TupleSet x5_upper = factory.noneOf(1); bounds.boundExactly(x5, x5_upper); TupleSet x6_upper = factory.noneOf(1); x6_upper.add(factory.tuple("Test$0")); x6_upper.add(factory.tuple("Test$1")); x6_upper.add(factory.tuple("Test$2")); bounds.boundExactly(x6, x6_upper); TupleSet x7_upper = factory.noneOf(2); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-8"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-7"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-6"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-5"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-4"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-3"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-2"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-1"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("0"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("1"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("2"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("3"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("4"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("5"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("6"))); x7_upper.add(factory.tuple("Test$0").product(factory.tuple("7"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-8"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-7"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-6"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-5"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-4"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-3"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-2"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-1"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("0"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("1"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("2"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("3"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("4"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("5"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("6"))); x7_upper.add(factory.tuple("Test$1").product(factory.tuple("7"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-8"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-7"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-6"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-5"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-4"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-3"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-2"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-1"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("0"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("1"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("2"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("3"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("4"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("5"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("6"))); x7_upper.add(factory.tuple("Test$2").product(factory.tuple("7"))); bounds.bound(x7, x7_upper); TupleSet x8_upper = factory.noneOf(2); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-8"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-7"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-6"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-5"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-4"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-3"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-2"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-1"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("0"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("1"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("2"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("3"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("4"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("5"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("6"))); x8_upper.add(factory.tuple("Test$0").product(factory.tuple("7"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-8"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-7"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-6"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-5"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-4"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-3"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-2"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-1"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("0"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("1"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("2"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("3"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("4"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("5"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("6"))); x8_upper.add(factory.tuple("Test$1").product(factory.tuple("7"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-8"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-7"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-6"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-5"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-4"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-3"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-2"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-1"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("0"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("1"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("2"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("3"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("4"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("5"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("6"))); x8_upper.add(factory.tuple("Test$2").product(factory.tuple("7"))); bounds.bound(x8, x8_upper); TupleSet x9_upper = factory.noneOf(2); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-8"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-7"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-6"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-5"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-4"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-3"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-2"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-1"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("0"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("1"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("2"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("3"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("4"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("5"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("6"))); x9_upper.add(factory.tuple("Test$0").product(factory.tuple("7"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-8"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-7"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-6"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-5"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-4"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-3"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-2"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-1"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("0"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("1"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("2"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("3"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("4"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("5"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("6"))); x9_upper.add(factory.tuple("Test$1").product(factory.tuple("7"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-8"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-7"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-6"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-5"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-4"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-3"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-2"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-1"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("0"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("1"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("2"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("3"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("4"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("5"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("6"))); x9_upper.add(factory.tuple("Test$2").product(factory.tuple("7"))); bounds.bound(x9, x9_upper); bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8"))); bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7"))); bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6"))); bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5"))); bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4"))); bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3"))); bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2"))); bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1"))); bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0"))); bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1"))); bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2"))); bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3"))); bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4"))); bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5"))); bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6"))); bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7"))); Variable x13 = Variable.unary("this"); Decls x12 = x13.oneOf(x6); Expression x16 = x13.join(x7); Formula x15 = x16.one(); Formula x17 = x16.in(Expression.INTS); Formula x14 = x15.and(x17); Formula x11 = x14.forAll(x12); Expression x20 = x7.join(Expression.UNIV); Formula x19 = x20.in(x6); Variable x24 = Variable.unary("this"); Decls x23 = x24.oneOf(x6); Expression x27 = x24.join(x8); Formula x26 = x27.lone(); Formula x28 = x27.in(Expression.INTS); Formula x25 = x26.and(x28); Formula x22 = x25.forAll(x23); Expression x30 = x8.join(Expression.UNIV); Formula x29 = x30.in(x6); Variable x33 = Variable.unary("this"); Decls x32 = x33.oneOf(x6); Expression x36 = x33.join(x9); Formula x35 = x36.one(); Formula x37 = x36.in(Expression.INTS); Formula x34 = x35.and(x37); Formula x31 = x34.forAll(x32); Expression x39 = x9.join(Expression.UNIV); Formula x38 = x39.in(x6); Variable x42 = Variable.unary("this"); Decls x41 = x42.oneOf(x6); Expression x44 = x42.join(x7); Expression x48 = x42.join(x8); IntExpression x47 = x48.sum(); Expression x50 = x42.join(x9); IntExpression x49 = x50.sum(); IntExpression x46 = x47.plus(x49); Expression x45 = x46.toExpression(); Formula x43 = x44.eq(x45); Formula x40 = x43.forAll(x41); Formula x51 = x0.eq(x0); Formula x52 = x1.eq(x1); Formula x53 = x2.eq(x2); Formula x54 = x3.eq(x3); Formula x55 = x4.eq(x4); Formula x56 = x5.eq(x5); Formula x57 = x6.eq(x6); Formula x58 = x7.eq(x7); Formula x59 = x8.eq(x8); Formula x60 = x9.eq(x9); IntExprReduction ier = new IntExprReduction(); Formula[] formulas = ier.reduceIntExpressions( x11, x19, x22, x29, x31, x38, x40, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60); Formula newFormula = Formula.compose(FormulaOperator.AND, formulas); ier.solve(newFormula, bounds, factory, universe, 32); }