Example #1
0
    /**
     * 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);
      }
    }
Example #2
0
 /**
  * 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;
 }
Example #3
0
 /**
  * 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);
 }
Example #4
0
 /**
  * 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)));
 }
Example #5
0
  /**
   * 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);
  }
Example #6
0
 /**
  * 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);
  }
Example #8
0
    /**
     * 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);
  }