Example 1 with Evaluator
use of kodkod.engine.Evaluator in project org.alloytools.alloy by AlloyTools.
the class A4Solution method solve.
// ===================================================================================================//
/**
* Solve for the solution if not solved already; if cmd==null, we will simply
* use the lowerbound of each relation as its value.
*/
A4Solution solve(final A4Reporter rep, Command cmd, Simplifier simp, boolean tryBookExamples) throws Err, IOException {
// If already solved, then return this object as is
if (solved)
return this;
// the lower bound of each relation
if (cmd == null) {
Instance inst = new Instance(bounds.universe());
for (int max = max(), i = min(); i <= max; i++) {
Tuple it = factory.tuple("" + i);
inst.add(i, factory.range(it, it));
}
for (Relation r : bounds.relations()) inst.add(r, bounds.lowerBound(r));
eval = new Evaluator(inst, solver.options());
rename(this, null, null, new UniqueNameGenerator());
solved();
return this;
}
// Otherwise, prepare to do the solve...
final A4Options opt = originalOptions;
long time = System.currentTimeMillis();
rep.debug("Simplifying the bounds...\n");
if (opt.inferPartialInstance && simp != null && formulas.size() > 0 && !simp.simplify(rep, this, formulas))
addFormula(Formula.FALSE, Pos.UNKNOWN);
rep.translate(opt.solver.id(), bitwidth, maxseq, solver.options().skolemDepth(), solver.options().symmetryBreaking());
Formula fgoal = Formula.and(formulas);
rep.debug("Generating the solution...\n");
kEnumerator = null;
Solution sol = null;
final Reporter oldReporter = solver.options().reporter();
final boolean[] solved = new boolean[] { true };
solver.options().setReporter(new // Set up a
AbstractReporter() {
// reporter to
// catch the
// type+pos of
// skolems
@Override
public void skolemizing(Decl decl, Relation skolem, List<Decl> predecl) {
try {
Type t = kv2typepos(decl.variable()).a;
if (t == Type.EMPTY)
return;
for (int i = (predecl == null ? -1 : predecl.size() - 1); i >= 0; i--) {
Type pp = kv2typepos(predecl.get(i).variable()).a;
if (pp == Type.EMPTY)
return;
t = pp.product(t);
}
kr2type(skolem, t);
}// Exception here is not fatal
catch (Throwable ex) {
}
}
@Override
public void solvingCNF(int primaryVars, int vars, int clauses) {
if (solved[0])
return;
else
// initially solved[0] is true, so we
solved[0] = true;
// won't report the # of vars/clauses
if (rep != null)
rep.solve(primaryVars, vars, clauses);
}
});
if (!opt.solver.equals(SatSolver.CNF) && !opt.solver.equals(SatSolver.KK) && tryBookExamples) {
// try
// book
// examples
A4Reporter r = AlloyCore.isDebug() ? rep : null;
try {
sol = BookExamples.trial(r, this, fgoal, solver, cmd.check);
} catch (Throwable ex) {
sol = null;
}
}
// this allows the reporter to report the # of
solved[0] = false;
// vars/clauses
for (Relation r : bounds.relations()) {
formulas.add(r.eq(r));
}
// Without this, kodkod refuses to grow unmentioned relations
fgoal = Formula.and(formulas);
// Now pick the solver and solve it!
if (opt.solver.equals(SatSolver.KK)) {
File tmpCNF = File.createTempFile("tmp", ".java", new File(opt.tempDirectory));
String out = tmpCNF.getAbsolutePath();
Util.writeAll(out, debugExtractKInput());
rep.resultCNF(out);
return null;
}
if (opt.solver.equals(SatSolver.CNF)) {
File tmpCNF = File.createTempFile("tmp", ".cnf", new File(opt.tempDirectory));
String out = tmpCNF.getAbsolutePath();
solver.options().setSolver(WriteCNF.factory(out));
try {
sol = solver.solve(fgoal, bounds);
} catch (WriteCNF.WriteCNFCompleted ex) {
rep.resultCNF(out);
return null;
}
// The formula is trivial (otherwise, it would have thrown an
// exception)
// Since the user wants it in CNF format, we manually generate a
// trivially satisfiable (or unsatisfiable) CNF file.
Util.writeAll(out, sol.instance() != null ? "p cnf 1 1\n1 0\n" : "p cnf 1 2\n1 0\n-1 0\n");
rep.resultCNF(out);
return null;
}
if (!solver.options().solver().incremental()) /*
* || solver.options().solver()==SATFactory. ZChaffMincost
*/
{
if (sol == null)
sol = solver.solve(fgoal, bounds);
} else {
kEnumerator = new Peeker<Solution>(solver.solveAll(fgoal, bounds));
if (sol == null)
sol = kEnumerator.next();
}
if (!solved[0])
rep.solve(0, 0, 0);
final Instance inst = sol.instance();
// To ensure no more output during SolutionEnumeration
solver.options().setReporter(oldReporter);
// If unsatisfiable, then retreive the unsat core if desired
if (inst == null && solver.options().solver() == SATFactory.MiniSatProver) {
try {
lCore = new LinkedHashSet<Node>();
Proof p = sol.proof();
if (sol.outcome() == UNSATISFIABLE) {
// only perform the minimization if it was UNSATISFIABLE,
// rather than TRIVIALLY_UNSATISFIABLE
int i = p.highLevelCore().size();
rep.minimizing(cmd, i);
if (opt.coreMinimization == 0)
try {
p.minimize(new RCEStrategy(p.log()));
} catch (Throwable ex) {
}
if (opt.coreMinimization == 1)
try {
p.minimize(new HybridStrategy(p.log()));
} catch (Throwable ex) {
}
rep.minimized(cmd, i, p.highLevelCore().size());
}
for (Iterator<TranslationRecord> it = p.core(); it.hasNext(); ) {
Object n = it.next().node();
if (n instanceof Formula)
lCore.add((Formula) n);
}
Map<Formula, Node> map = p.highLevelCore();
hCore = new LinkedHashSet<Node>(map.keySet());
hCore.addAll(map.values());
} catch (Throwable ex) {
lCore = hCore = null;
}
}
// If satisfiable, then add/rename the atoms and skolems
if (inst != null) {
eval = new Evaluator(inst, solver.options());
rename(this, null, null, new UniqueNameGenerator());
}
// report the result
solved();
time = System.currentTimeMillis() - time;
if (inst != null)
rep.resultSAT(cmd, time, this);
else
rep.resultUNSAT(cmd, time, this);
return this;
}
Also used :
HybridStrategy(kodkod.engine.ucore.HybridStrategy)
Instance(kodkod.instance.Instance)
Node(kodkod.ast.Node)
BinaryFormula(kodkod.ast.BinaryFormula)
Formula(kodkod.ast.Formula)
Relation(kodkod.ast.Relation)
RCEStrategy(kodkod.engine.ucore.RCEStrategy)
Solution(kodkod.engine.Solution)
A4Reporter(edu.mit.csail.sdg.alloy4.A4Reporter)
A4Reporter(edu.mit.csail.sdg.alloy4.A4Reporter)
AbstractReporter(kodkod.engine.config.AbstractReporter)
Reporter(kodkod.engine.config.Reporter)
TranslationRecord(kodkod.engine.fol2sat.TranslationRecord)
Decl(kodkod.ast.Decl)
Evaluator(kodkod.engine.Evaluator)
UniqueNameGenerator(edu.mit.csail.sdg.alloy4.UniqueNameGenerator)
Type(edu.mit.csail.sdg.ast.Type)
Proof(kodkod.engine.Proof)
File(java.io.File)
Tuple(kodkod.instance.Tuple)
Example 2 with Evaluator
use of kodkod.engine.Evaluator in project org.alloytools.alloy by AlloyTools.
the class BGPTest method main.
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/Natural");
Relation x7 = Relation.unary("ord/Ord");
Relation x8 = Relation.unary("this/Zero");
Relation x9 = Relation.unary("this/One");
Relation x10 = Relation.nary("this/Natural.data", 4);
Relation x11 = Relation.unary("ord/Ord.First");
Relation x12 = Relation.nary("ord/Ord.Next", 2);
Relation x13 = Relation.unary("");
List<String> atomlist = Arrays.asList("-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "0", "1", "2", "3", "4", "5", "6", "7", "Natural$0", "Natural$1", "Natural$2", "Natural$3", "ord/Ord$0");
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("Natural$0"));
x6_upper.add(factory.tuple("Natural$1"));
x6_upper.add(factory.tuple("Natural$2"));
x6_upper.add(factory.tuple("Natural$3"));
bounds.boundExactly(x6, x6_upper);
TupleSet x7_upper = factory.noneOf(1);
x7_upper.add(factory.tuple("ord/Ord$0"));
bounds.boundExactly(x7, x7_upper);
TupleSet x8_upper = factory.noneOf(1);
x8_upper.add(factory.tuple("Natural$0"));
x8_upper.add(factory.tuple("Natural$1"));
x8_upper.add(factory.tuple("Natural$2"));
x8_upper.add(factory.tuple("Natural$3"));
bounds.bound(x8, x8_upper);
TupleSet x9_upper = factory.noneOf(1);
x9_upper.add(factory.tuple("Natural$0"));
x9_upper.add(factory.tuple("Natural$1"));
x9_upper.add(factory.tuple("Natural$2"));
x9_upper.add(factory.tuple("Natural$3"));
bounds.bound(x9, x9_upper);
TupleSet x10_upper = factory.noneOf(4);
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")).product(factory.tuple("Natural$3")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$0")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$1")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$2")));
x10_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")).product(factory.tuple("Natural$3")));
bounds.bound(x10, x10_upper);
TupleSet x11_upper = factory.noneOf(1);
x11_upper.add(factory.tuple("Natural$0"));
x11_upper.add(factory.tuple("Natural$1"));
x11_upper.add(factory.tuple("Natural$2"));
x11_upper.add(factory.tuple("Natural$3"));
bounds.bound(x11, x11_upper);
TupleSet x12_upper = factory.noneOf(2);
x12_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$0")));
x12_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$1")));
x12_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$2")));
x12_upper.add(factory.tuple("Natural$0").product(factory.tuple("Natural$3")));
x12_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$0")));
x12_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$1")));
x12_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$2")));
x12_upper.add(factory.tuple("Natural$1").product(factory.tuple("Natural$3")));
x12_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$0")));
x12_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$1")));
x12_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$2")));
x12_upper.add(factory.tuple("Natural$2").product(factory.tuple("Natural$3")));
x12_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$0")));
x12_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$1")));
x12_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$2")));
x12_upper.add(factory.tuple("Natural$3").product(factory.tuple("Natural$3")));
bounds.bound(x12, x12_upper);
TupleSet x13_upper = factory.noneOf(1);
x13_upper.add(factory.tuple("Natural$0"));
x13_upper.add(factory.tuple("Natural$1"));
x13_upper.add(factory.tuple("Natural$2"));
x13_upper.add(factory.tuple("Natural$3"));
bounds.bound(x13, x13_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")));
Formula x15 = x8.in(x6);
Formula x16 = x9.in(x6);
Formula x17 = x8.one();
Formula x18 = x9.lone();
Variable x21 = Variable.unary("checkOneSolvable3ToNinjaWheel_this");
Decls x20 = x21.oneOf(x6);
Expression x23 = x21.join(x10);
Expression x25 = x6.product(x6);
Expression x24 = x6.product(x25);
Formula x22 = x23.in(x24);
Formula x19 = x22.forAll(x20);
Expression x29 = x10.join(Expression.UNIV);
Expression x28 = x29.join(Expression.UNIV);
Expression x27 = x28.join(Expression.UNIV);
Formula x26 = x27.in(x6);
Expression x33 = x7.product(x11);
Expression x32 = x7.join(x33);
Formula x31 = x32.in(x6);
Expression x36 = x7.product(x12);
Expression x35 = x7.join(x36);
Expression x37 = x6.product(x6);
Formula x34 = x35.in(x37);
Formula x38 = x12.totalOrder(x6, x11, x13);
Formula x39 = x11.in(x8);
Expression x41 = x11.join(x12);
Formula x40 = x41.in(x9);
Expression x46 = x10.join(x6);
Expression x45 = x46.join(x6);
Expression x44 = x45.join(x6);
Expression x47 = x44.join(x12);
Expression x43 = x44.difference(x47);
Formula x42 = x43.in(x11);
Variable x50 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x49 = x50.oneOf(x6);
Expression x55 = x50.join(x10);
Expression x54 = x55.join(x6);
Expression x53 = x54.join(x6);
Expression x56 = x53.join(x12);
Expression x52 = x53.difference(x56);
Formula x51 = x52.in(x11);
Formula x48 = x51.forAll(x49);
Variable x59 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x58 = x59.oneOf(x6);
Variable x62 = Variable.unary("checkOneSolvable3ToNinjaWheel_pathPref");
Decls x61 = x62.oneOf(x6);
Expression x67 = x59.join(x10);
Expression x66 = x62.join(x67);
Expression x65 = x66.join(x6);
Expression x68 = x65.join(x12);
Expression x64 = x65.difference(x68);
Formula x63 = x64.in(x11);
Formula x60 = x63.forAll(x61);
Formula x57 = x60.forAll(x58);
Variable x71 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x70 = x71.oneOf(x6);
Variable x74 = Variable.unary("checkOneSolvable3ToNinjaWheel_pathPref");
Decls x73 = x74.oneOf(x6);
Variable x77 = Variable.unary("checkOneSolvable3ToNinjaWheel_pathIndex");
Decls x76 = x77.oneOf(x6);
Expression x81 = x71.join(x10);
Expression x80 = x74.join(x81);
Expression x79 = x77.join(x80);
Formula x78 = x79.lone();
Formula x75 = x78.forAll(x76);
Formula x72 = x75.forAll(x73);
Formula x69 = x72.forAll(x70);
Variable x84 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x83 = x84.oneOf(x44);
Expression x86 = x84.join(x10);
Formula x85 = x86.some();
Formula x82 = x85.forAll(x83);
Variable x89 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x88 = x89.oneOf(x44);
Variable x92 = Variable.unary("checkOneSolvable3ToNinjaWheel_pathPref");
Expression x95 = x89.join(x10);
Expression x94 = x95.join(x6);
Expression x93 = x94.join(x6);
Decls x91 = x92.oneOf(x93);
Expression x101 = x89.join(x10);
Expression x100 = x92.join(x101);
Expression x99 = x6.join(x100);
Formula x98 = x99.in(x44);
Expression x104 = x100.join(x6);
IntExpression x103 = x104.count();
Expression x106 = x6.join(x100);
IntExpression x105 = x106.count();
Formula x102 = x103.eq(x105);
Formula x97 = x98.and(x102);
Expression x108 = x8.join(x100);
Formula x107 = x108.eq(x89);
Formula x96 = x97.and(x107);
Formula x90 = x96.forAll(x91);
Formula x87 = x90.forAll(x88);
Variable x111 = Variable.unary("checkOneSolvable3ToNinjaWheel_node");
Decls x110 = x111.oneOf(x44);
Variable x115 = Variable.unary("checkOneSolvable3ToNinjaWheel_i");
Expression x118 = x111.join(x10);
Expression x117 = x118.join(x6);
Expression x116 = x117.join(x6);
Decls x114 = x115.oneOf(x116);
Variable x120 = Variable.unary("checkOneSolvable3ToNinjaWheel_j");
Decls x119 = x120.oneOf(x116);
Decls x113 = x114.and(x119);
Expression x124 = x115.intersection(x120);
Formula x123 = x124.no();
Expression x127 = x111.join(x10);
Expression x126 = x115.join(x127);
Expression x129 = x111.join(x10);
Expression x128 = x120.join(x129);
Formula x125 = x126.eq(x128);
Formula x122 = x123.and(x125);
Formula x121 = x122.not();
Formula x112 = x121.forAll(x113);
Formula x109 = x112.forAll(x110);
Expression x134 = x6.join(x10);
Expression x133 = x134.join(x6);
Expression x132 = x133.join(x6);
IntExpression x131 = x132.count();
IntExpression x135 = x6.count();
Formula x130 = x131.lt(x135);
IntExpression x141 = x44.count();
Expression x140 = x141.toExpression();
IntExpression x143 = IntConstant.constant(3);
Expression x142 = x143.toExpression();
Formula x139 = x140.eq(x142);
Formula x138 = x139.not();
Variable x149 = Variable.unary("oneSolvableFun3_i1");
Decls x148 = x149.oneOf(x6);
Variable x151 = Variable.unary("oneSolvableFun3_i2");
Decls x150 = x151.oneOf(x6);
Variable x153 = Variable.unary("oneSolvableFun3_i3");
Decls x152 = x153.oneOf(x6);
Decls x147 = x148.and(x150).and(x152);
Expression x160 = x8.join(x10);
Expression x159 = x160.join(x6);
Expression x158 = x159.join(x6);
Expression x165 = x8.join(x10);
Expression x164 = x165.join(x6);
Expression x163 = x164.join(x6);
Expression x168 = x12.transpose();
Expression x167 = x168.closure();
Expression x166 = x163.join(x167);
Expression x162 = x163.difference(x166);
Expression x161 = x162.join(x12);
Expression x157 = x158.union(x161);
Formula x156 = x149.in(x157);
Expression x174 = x9.join(x10);
Expression x173 = x174.join(x6);
Expression x172 = x173.join(x6);
Expression x179 = x9.join(x10);
Expression x178 = x179.join(x6);
Expression x177 = x178.join(x6);
Expression x182 = x12.transpose();
Expression x181 = x182.closure();
Expression x180 = x177.join(x181);
Expression x176 = x177.difference(x180);
Expression x175 = x176.join(x12);
Expression x171 = x172.union(x175);
Formula x170 = x151.in(x171);
Expression x186 = x8.product(x149);
Expression x187 = x9.product(x151);
Expression x185 = x186.union(x187);
Expression x189 = x9.join(x12);
Expression x188 = x189.product(x153);
Expression x184 = x185.union(x188);
Variable x193 = Variable.unary("ValidBest_node");
Decls x192 = x193.oneOf(x6);
Variable x195 = Variable.unary("ValidBest_pref");
Decls x194 = x195.oneOf(x6);
Decls x191 = x192.and(x194);
Variable x202 = Variable.unary("ValidChoices_n");
Decls x201 = x202.oneOf(x6);
Variable x204 = Variable.unary("ValidChoices_p");
Decls x203 = x204.oneOf(x6);
Decls x200 = x201.and(x203);
Expression x210 = x202.join(x10);
Expression x209 = x210.join(x6);
Expression x208 = x209.join(x6);
Expression x215 = x202.join(x10);
Expression x214 = x215.join(x6);
Expression x213 = x214.join(x6);
Expression x218 = x12.transpose();
Expression x217 = x218.closure();
Expression x216 = x213.join(x217);
Expression x212 = x213.difference(x216);
Expression x211 = x212.join(x12);
Expression x207 = x208.union(x211);
Formula x206 = x204.in(x207);
Expression x224 = x202.join(x10);
Expression x223 = x224.join(x6);
Expression x222 = x223.join(x6);
Formula x221 = x204.in(x222);
Formula x220 = x221.not();
Expression x230 = x202.join(x10);
Expression x229 = x204.join(x230);
Expression x228 = x9.join(x229);
Formula x227 = x228.some();
Formula x226 = x227.not();
Expression x237 = x202.join(x10);
Expression x236 = x237.join(x6);
Expression x235 = x236.join(x6);
Formula x234 = x204.in(x235);
Formula x233 = x234.not();
Formula x232 = x233.not();
Expression x241 = x202.join(x10);
Expression x240 = x204.join(x241);
Expression x239 = x12.join(x240);
Expression x243 = x228.join(x184);
Expression x244 = x228.join(x10);
Expression x242 = x243.join(x244);
Formula x238 = x239.eq(x242);
Formula x231 = x232.and(x238);
Formula x225 = x226.or(x231);
Formula x219 = x220.or(x225);
Formula x205 = x206.and(x219);
Expression x199 = x205.comprehension(x200);
Expression x198 = x193.join(x199);
Formula x197 = x195.in(x198);
Variable x247 = Variable.unary("ValidBest_j");
Expression x248 = x193.join(x199);
Decls x246 = x247.oneOf(x248);
Expression x253 = x12.transpose();
Expression x252 = x253.closure();
Expression x251 = x195.join(x252);
Formula x250 = x247.in(x251);
Formula x249 = x250.not();
Formula x245 = x249.forAll(x246);
Formula x196 = x197.and(x245);
Expression x190 = x196.comprehension(x191);
Formula x183 = x184.eq(x190);
Formula x169 = x170.and(x183);
Formula x155 = x156.and(x169);
Expression x258 = x189.join(x10);
Expression x257 = x258.join(x6);
Expression x256 = x257.join(x6);
Expression x263 = x189.join(x10);
Expression x262 = x263.join(x6);
Expression x261 = x262.join(x6);
Expression x266 = x12.transpose();
Expression x265 = x266.closure();
Expression x264 = x261.join(x265);
Expression x260 = x261.difference(x264);
Expression x259 = x260.join(x12);
Expression x255 = x256.union(x259);
Formula x254 = x153.in(x255);
Formula x154 = x155.and(x254);
Expression x146 = x154.comprehension(x147);
Formula x145 = x146.one();
Variable x272 = Variable.unary("DW3NE_p1");
Expression x276 = x8.join(x10);
Expression x275 = x276.join(x6);
Expression x274 = x275.join(x6);
Expression x281 = x8.join(x10);
Expression x280 = x281.join(x6);
Expression x279 = x280.join(x6);
Expression x284 = x12.transpose();
Expression x283 = x284.closure();
Expression x282 = x279.join(x283);
Expression x278 = x279.difference(x282);
Expression x277 = x278.join(x12);
Expression x273 = x274.union(x277);
Decls x271 = x272.oneOf(x273);
Variable x286 = Variable.unary("DW3NE_p2");
Expression x290 = x9.join(x10);
Expression x289 = x290.join(x6);
Expression x288 = x289.join(x6);
Expression x295 = x9.join(x10);
Expression x294 = x295.join(x6);
Expression x293 = x294.join(x6);
Expression x298 = x12.transpose();
Expression x297 = x298.closure();
Expression x296 = x293.join(x297);
Expression x292 = x293.difference(x296);
Expression x291 = x292.join(x12);
Expression x287 = x288.union(x291);
Decls x285 = x286.oneOf(x287);
Variable x300 = Variable.unary("DW3NE_p3");
Expression x305 = x9.join(x12);
Expression x304 = x305.join(x10);
Expression x303 = x304.join(x6);
Expression x302 = x303.join(x6);
Expression x310 = x305.join(x10);
Expression x309 = x310.join(x6);
Expression x308 = x309.join(x6);
Expression x313 = x12.transpose();
Expression x312 = x313.closure();
Expression x311 = x308.join(x312);
Expression x307 = x308.difference(x311);
Expression x306 = x307.join(x12);
Expression x301 = x302.union(x306);
Decls x299 = x300.oneOf(x301);
Decls x270 = x271.and(x285).and(x299);
Variable x316 = Variable.unary("DW3NE_p1h");
Variable x319 = Variable.unary("DW3NE_i");
Decls x318 = x319.oneOf(x6);
Expression x323 = x12.transpose();
Expression x322 = x323.closure();
Expression x321 = x272.join(x322);
Formula x320 = x319.in(x321);
Expression x317 = x320.comprehension(x318);
Decls x315 = x316.oneOf(x317);
Variable x326 = Variable.unary("DW3NE_p2h");
Variable x329 = Variable.unary("DW3NE_i");
Decls x328 = x329.oneOf(x6);
Expression x333 = x12.transpose();
Expression x332 = x333.closure();
Expression x331 = x286.join(x332);
Formula x330 = x329.in(x331);
Expression x327 = x330.comprehension(x328);
Decls x325 = x326.oneOf(x327);
Variable x336 = Variable.unary("DW3NE_p3h");
Variable x339 = Variable.unary("DW3NE_i");
Decls x338 = x339.oneOf(x6);
Expression x343 = x12.transpose();
Expression x342 = x343.closure();
Expression x341 = x300.join(x342);
Formula x340 = x339.in(x341);
Expression x337 = x340.comprehension(x338);
Decls x335 = x336.oneOf(x337);
Variable x347 = Variable.unary("DW3NE_pa2h");
Expression x349 = x9.union(x8);
Expression x350 = x9.join(x12);
Expression x348 = x349.union(x350);
Decls x346 = x347.oneOf(x348);
Variable x352 = Variable.unary("DW3NE_pa3h");
Decls x351 = x352.oneOf(x348);
Decls x345 = x346.and(x351);
Variable x355 = Variable.unary("DW3NE_pa2l");
Expression x358 = x9.union(x8);
Expression x359 = x9.join(x12);
Expression x357 = x358.union(x359);
Expression x356 = x357.difference(x347);
Decls x354 = x355.oneOf(x356);
Variable x362 = Variable.unary("DW3NE_pa3l");
Expression x365 = x9.union(x8);
Expression x366 = x9.join(x12);
Expression x364 = x365.union(x366);
Expression x363 = x364.difference(x352);
Decls x361 = x362.oneOf(x363);
Variable x373 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x379 = x8.join(x10);
Expression x378 = x316.join(x379);
Expression x377 = x9.join(x378);
Expression x376 = x377.join(x10);
Expression x375 = x376.join(x6);
Expression x374 = x375.join(x6);
Decls x372 = x373.oneOf(x374);
Expression x384 = x8.join(x10);
Expression x383 = x316.join(x384);
Expression x382 = x12.join(x383);
Expression x386 = x377.join(x10);
Expression x385 = x373.join(x386);
Formula x381 = x382.eq(x385);
Expression x396 = x272.product(x9);
Expression x395 = x8.product(x396);
Expression x398 = x316.product(x8);
Expression x397 = x8.product(x398);
Expression x394 = x395.union(x397);
Expression x400 = x286.product(x355);
Expression x399 = x9.product(x400);
Expression x393 = x394.union(x399);
Expression x402 = x326.product(x347);
Expression x401 = x9.product(x402);
Expression x392 = x393.union(x401);
Expression x404 = x300.product(x362);
Expression x403 = x305.product(x404);
Expression x391 = x392.union(x403);
Expression x406 = x336.product(x352);
Expression x405 = x305.product(x406);
Expression x390 = x391.union(x405);
Expression x389 = x8.join(x390);
Expression x388 = x316.join(x389);
Expression x408 = x377.join(x390);
Expression x407 = x373.join(x408);
Formula x387 = x388.eq(x407);
Formula x380 = x381.and(x387);
Formula x371 = x380.forSome(x372);
Expression x415 = x8.join(x10);
Expression x414 = x415.join(x6);
Expression x413 = x414.join(x6);
Formula x412 = x272.in(x413);
Formula x411 = x412.not();
Expression x419 = x8.join(x10);
Expression x418 = x272.join(x419);
Expression x417 = x9.join(x418);
Formula x416 = x417.no();
Formula x410 = x411.or(x416);
Variable x422 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x428 = x8.join(x10);
Expression x427 = x272.join(x428);
Expression x426 = x9.join(x427);
Expression x425 = x426.join(x10);
Expression x424 = x425.join(x6);
Expression x423 = x424.join(x6);
Decls x421 = x422.oneOf(x423);
Expression x433 = x8.join(x10);
Expression x432 = x272.join(x433);
Expression x431 = x12.join(x432);
Expression x435 = x426.join(x10);
Expression x434 = x422.join(x435);
Formula x430 = x431.eq(x434);
Expression x438 = x8.join(x390);
Expression x437 = x272.join(x438);
Expression x440 = x426.join(x390);
Expression x439 = x422.join(x440);
Formula x436 = x437.eq(x439);
Formula x429 = x430.and(x436);
Formula x420 = x429.forSome(x421);
Formula x409 = x410.or(x420);
Formula x370 = x371.and(x409);
Variable x443 = Variable.unary("DWNodeCheckNE_k");
Variable x446 = Variable.unary("DWNodeCheckNE_i");
Decls x445 = x446.oneOf(x6);
Expression x451 = x12.transpose();
Expression x450 = x451.closure();
Expression x449 = x272.join(x450);
Formula x448 = x446.in(x449);
Formula x453 = x446.eq(x316);
Formula x452 = x453.not();
Formula x447 = x448.and(x452);
Expression x444 = x447.comprehension(x445);
Decls x442 = x443.oneOf(x444);
Expression x459 = x8.join(x10);
Expression x458 = x443.join(x459);
Expression x457 = x9.join(x458);
Formula x456 = x457.no();
Formula x455 = x456.not();
Variable x462 = Variable.unary("DWNodeCheckNE_first_hop_k_pref");
Expression x466 = x8.join(x10);
Expression x465 = x443.join(x466);
Expression x464 = x9.join(x465);
Expression x472 = x8.product(x272);
Expression x473 = x8.product(x316);
Expression x471 = x472.union(x473);
Expression x474 = x9.product(x286);
Expression x470 = x471.union(x474);
Expression x475 = x9.product(x326);
Expression x469 = x470.union(x475);
Expression x476 = x305.product(x300);
Expression x468 = x469.union(x476);
Expression x477 = x305.product(x336);
Expression x467 = x468.union(x477);
Expression x463 = x464.join(x467);
Decls x461 = x462.oneOf(x463);
Expression x486 = x8.join(x10);
Expression x485 = x486.join(x6);
Expression x484 = x485.join(x6);
Formula x483 = x443.in(x484);
Formula x482 = x483.not();
Formula x481 = x482.not();
Expression x490 = x8.join(x10);
Expression x489 = x443.join(x490);
Expression x488 = x12.join(x489);
Expression x492 = x464.join(x10);
Expression x491 = x462.join(x492);
Formula x487 = x488.eq(x491);
Formula x480 = x481.and(x487);
Formula x479 = x480.not();
Expression x496 = x464.join(x390);
Expression x495 = x462.join(x496);
Expression x498 = x8.join(x390);
Expression x497 = x316.join(x498);
Formula x494 = x495.eq(x497);
Expression x501 = x12.closure();
Expression x500 = x316.join(x501);
Formula x499 = x443.in(x500);
Formula x493 = x494.and(x499);
Formula x478 = x479.or(x493);
Formula x460 = x478.forAll(x461);
Formula x454 = x455.and(x460);
Formula x441 = x454.forAll(x442);
Formula x369 = x370.and(x441);
Variable x506 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x512 = x9.join(x10);
Expression x511 = x326.join(x512);
Expression x510 = x9.join(x511);
Expression x509 = x510.join(x10);
Expression x508 = x509.join(x6);
Expression x507 = x508.join(x6);
Decls x505 = x506.oneOf(x507);
Expression x517 = x9.join(x10);
Expression x516 = x326.join(x517);
Expression x515 = x12.join(x516);
Expression x519 = x510.join(x10);
Expression x518 = x506.join(x519);
Formula x514 = x515.eq(x518);
Expression x522 = x9.join(x390);
Expression x521 = x326.join(x522);
Expression x524 = x510.join(x390);
Expression x523 = x506.join(x524);
Formula x520 = x521.eq(x523);
Formula x513 = x514.and(x520);
Formula x504 = x513.forSome(x505);
Expression x531 = x9.join(x10);
Expression x530 = x531.join(x6);
Expression x529 = x530.join(x6);
Formula x528 = x286.in(x529);
Formula x527 = x528.not();
Expression x535 = x9.join(x10);
Expression x534 = x286.join(x535);
Expression x533 = x9.join(x534);
Formula x532 = x533.no();
Formula x526 = x527.or(x532);
Variable x538 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x544 = x9.join(x10);
Expression x543 = x286.join(x544);
Expression x542 = x9.join(x543);
Expression x541 = x542.join(x10);
Expression x540 = x541.join(x6);
Expression x539 = x540.join(x6);
Decls x537 = x538.oneOf(x539);
Expression x549 = x9.join(x10);
Expression x548 = x286.join(x549);
Expression x547 = x12.join(x548);
Expression x551 = x542.join(x10);
Expression x550 = x538.join(x551);
Formula x546 = x547.eq(x550);
Expression x554 = x9.join(x390);
Expression x553 = x286.join(x554);
Expression x556 = x542.join(x390);
Expression x555 = x538.join(x556);
Formula x552 = x553.eq(x555);
Formula x545 = x546.and(x552);
Formula x536 = x545.forSome(x537);
Formula x525 = x526.or(x536);
Formula x503 = x504.and(x525);
Variable x559 = Variable.unary("DWNodeCheckNE_k");
Variable x562 = Variable.unary("DWNodeCheckNE_i");
Decls x561 = x562.oneOf(x6);
Expression x567 = x12.transpose();
Expression x566 = x567.closure();
Expression x565 = x286.join(x566);
Formula x564 = x562.in(x565);
Formula x569 = x562.eq(x326);
Formula x568 = x569.not();
Formula x563 = x564.and(x568);
Expression x560 = x563.comprehension(x561);
Decls x558 = x559.oneOf(x560);
Expression x575 = x9.join(x10);
Expression x574 = x559.join(x575);
Expression x573 = x9.join(x574);
Formula x572 = x573.no();
Formula x571 = x572.not();
Variable x578 = Variable.unary("DWNodeCheckNE_first_hop_k_pref");
Expression x582 = x9.join(x10);
Expression x581 = x559.join(x582);
Expression x580 = x9.join(x581);
Expression x579 = x580.join(x467);
Decls x577 = x578.oneOf(x579);
Expression x591 = x9.join(x10);
Expression x590 = x591.join(x6);
Expression x589 = x590.join(x6);
Formula x588 = x559.in(x589);
Formula x587 = x588.not();
Formula x586 = x587.not();
Expression x595 = x9.join(x10);
Expression x594 = x559.join(x595);
Expression x593 = x12.join(x594);
Expression x597 = x580.join(x10);
Expression x596 = x578.join(x597);
Formula x592 = x593.eq(x596);
Formula x585 = x586.and(x592);
Formula x584 = x585.not();
Expression x601 = x580.join(x390);
Expression x600 = x578.join(x601);
Expression x603 = x9.join(x390);
Expression x602 = x326.join(x603);
Formula x599 = x600.eq(x602);
Expression x606 = x12.closure();
Expression x605 = x326.join(x606);
Formula x604 = x559.in(x605);
Formula x598 = x599.and(x604);
Formula x583 = x584.or(x598);
Formula x576 = x583.forAll(x577);
Formula x570 = x571.and(x576);
Formula x557 = x570.forAll(x558);
Formula x502 = x503.and(x557);
Formula x368 = x369.and(x502);
Variable x611 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x617 = x305.join(x10);
Expression x616 = x336.join(x617);
Expression x615 = x9.join(x616);
Expression x614 = x615.join(x10);
Expression x613 = x614.join(x6);
Expression x612 = x613.join(x6);
Decls x610 = x611.oneOf(x612);
Expression x622 = x305.join(x10);
Expression x621 = x336.join(x622);
Expression x620 = x12.join(x621);
Expression x624 = x615.join(x10);
Expression x623 = x611.join(x624);
Formula x619 = x620.eq(x623);
Expression x627 = x305.join(x390);
Expression x626 = x336.join(x627);
Expression x629 = x615.join(x390);
Expression x628 = x611.join(x629);
Formula x625 = x626.eq(x628);
Formula x618 = x619.and(x625);
Formula x609 = x618.forSome(x610);
Expression x636 = x305.join(x10);
Expression x635 = x636.join(x6);
Expression x634 = x635.join(x6);
Formula x633 = x300.in(x634);
Formula x632 = x633.not();
Expression x640 = x305.join(x10);
Expression x639 = x300.join(x640);
Expression x638 = x9.join(x639);
Formula x637 = x638.no();
Formula x631 = x632.or(x637);
Variable x643 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x649 = x305.join(x10);
Expression x648 = x300.join(x649);
Expression x647 = x9.join(x648);
Expression x646 = x647.join(x10);
Expression x645 = x646.join(x6);
Expression x644 = x645.join(x6);
Decls x642 = x643.oneOf(x644);
Expression x654 = x305.join(x10);
Expression x653 = x300.join(x654);
Expression x652 = x12.join(x653);
Expression x656 = x647.join(x10);
Expression x655 = x643.join(x656);
Formula x651 = x652.eq(x655);
Expression x659 = x305.join(x390);
Expression x658 = x300.join(x659);
Expression x661 = x647.join(x390);
Expression x660 = x643.join(x661);
Formula x657 = x658.eq(x660);
Formula x650 = x651.and(x657);
Formula x641 = x650.forSome(x642);
Formula x630 = x631.or(x641);
Formula x608 = x609.and(x630);
Variable x664 = Variable.unary("DWNodeCheckNE_k");
Variable x667 = Variable.unary("DWNodeCheckNE_i");
Decls x666 = x667.oneOf(x6);
Expression x672 = x12.transpose();
Expression x671 = x672.closure();
Expression x670 = x300.join(x671);
Formula x669 = x667.in(x670);
Formula x674 = x667.eq(x336);
Formula x673 = x674.not();
Formula x668 = x669.and(x673);
Expression x665 = x668.comprehension(x666);
Decls x663 = x664.oneOf(x665);
Expression x680 = x305.join(x10);
Expression x679 = x664.join(x680);
Expression x678 = x9.join(x679);
Formula x677 = x678.no();
Formula x676 = x677.not();
Variable x683 = Variable.unary("DWNodeCheckNE_first_hop_k_pref");
Expression x687 = x305.join(x10);
Expression x686 = x664.join(x687);
Expression x685 = x9.join(x686);
Expression x684 = x685.join(x467);
Decls x682 = x683.oneOf(x684);
Expression x696 = x305.join(x10);
Expression x695 = x696.join(x6);
Expression x694 = x695.join(x6);
Formula x693 = x664.in(x694);
Formula x692 = x693.not();
Formula x691 = x692.not();
Expression x700 = x305.join(x10);
Expression x699 = x664.join(x700);
Expression x698 = x12.join(x699);
Expression x702 = x685.join(x10);
Expression x701 = x683.join(x702);
Formula x697 = x698.eq(x701);
Formula x690 = x691.and(x697);
Formula x689 = x690.not();
Expression x706 = x685.join(x390);
Expression x705 = x683.join(x706);
Expression x708 = x305.join(x390);
Expression x707 = x336.join(x708);
Formula x704 = x705.eq(x707);
Expression x711 = x12.closure();
Expression x710 = x336.join(x711);
Formula x709 = x664.in(x710);
Formula x703 = x704.and(x709);
Formula x688 = x689.or(x703);
Formula x681 = x688.forAll(x682);
Formula x675 = x676.and(x681);
Formula x662 = x675.forAll(x663);
Formula x607 = x608.and(x662);
Formula x367 = x368.and(x607);
Formula x360 = x367.forSome(x361);
Formula x353 = x360.forSome(x354);
Formula x344 = x353.forSome(x345);
Formula x334 = x344.forSome(x335);
Formula x324 = x334.forSome(x325);
Formula x314 = x324.forSome(x315);
Formula x269 = x314.forSome(x270);
Variable x714 = Variable.unary("checkOneSolvable3ToNinjaWheel_n1");
Expression x716 = x8.union(x9);
Expression x717 = x9.join(x12);
Expression x715 = x716.union(x717);
Decls x713 = x714.oneOf(x715);
Variable x720 = Variable.unary("checkOneSolvable3ToNinjaWheel_n2");
Expression x723 = x8.union(x9);
Expression x724 = x9.join(x12);
Expression x722 = x723.union(x724);
Expression x721 = x722.difference(x714);
Decls x719 = x720.oneOf(x721);
Variable x727 = Variable.unary("checkOneSolvable3ToNinjaWheel_n3");
Expression x730 = x8.union(x9);
Expression x731 = x9.join(x12);
Expression x729 = x730.union(x731);
Expression x732 = x714.union(x720);
Expression x728 = x729.difference(x732);
Decls x726 = x727.oneOf(x728);
Variable x735 = Variable.unary("DW2E1_p1");
Expression x739 = x714.join(x10);
Expression x738 = x739.join(x6);
Expression x737 = x738.join(x6);
Expression x744 = x714.join(x10);
Expression x743 = x744.join(x6);
Expression x742 = x743.join(x6);
Expression x747 = x12.transpose();
Expression x746 = x747.closure();
Expression x745 = x742.join(x746);
Expression x741 = x742.difference(x745);
Expression x740 = x741.join(x12);
Expression x736 = x737.union(x740);
Decls x734 = x735.oneOf(x736);
Variable x750 = Variable.unary("DW2E1_p1h");
Variable x753 = Variable.unary("DW2E1_i");
Decls x752 = x753.oneOf(x6);
Expression x757 = x12.transpose();
Expression x756 = x757.closure();
Expression x755 = x735.join(x756);
Formula x754 = x753.in(x755);
Expression x751 = x754.comprehension(x752);
Decls x749 = x750.oneOf(x751);
Variable x760 = Variable.unary("DW2E1_p2");
Expression x764 = x720.join(x10);
Expression x763 = x764.join(x6);
Expression x762 = x763.join(x6);
Expression x769 = x720.join(x10);
Expression x768 = x769.join(x6);
Expression x767 = x768.join(x6);
Expression x772 = x12.transpose();
Expression x771 = x772.closure();
Expression x770 = x767.join(x771);
Expression x766 = x767.difference(x770);
Expression x765 = x766.join(x12);
Expression x761 = x762.union(x765);
Decls x759 = x760.oneOf(x761);
Variable x775 = Variable.unary("DW2E1_p2h");
Variable x778 = Variable.unary("DW2E1_i");
Decls x777 = x778.oneOf(x6);
Expression x782 = x12.transpose();
Expression x781 = x782.closure();
Expression x780 = x760.join(x781);
Formula x779 = x778.in(x780);
Expression x776 = x779.comprehension(x777);
Decls x774 = x775.oneOf(x776);
Variable x785 = Variable.unary("DW2E1_p3");
Expression x789 = x727.join(x10);
Expression x788 = x789.join(x6);
Expression x787 = x788.join(x6);
Expression x794 = x727.join(x10);
Expression x793 = x794.join(x6);
Expression x792 = x793.join(x6);
Expression x797 = x12.transpose();
Expression x796 = x797.closure();
Expression x795 = x792.join(x796);
Expression x791 = x792.difference(x795);
Expression x790 = x791.join(x12);
Expression x786 = x787.union(x790);
Decls x784 = x785.oneOf(x786);
Variable x800 = Variable.unary("DW2E1_pa2h");
Expression x802 = x9.union(x8);
Expression x803 = x9.join(x12);
Expression x801 = x802.union(x803);
Decls x799 = x800.oneOf(x801);
Variable x806 = Variable.unary("DW2E1_pa2l");
Expression x809 = x9.union(x8);
Expression x810 = x9.join(x12);
Expression x808 = x809.union(x810);
Expression x807 = x808.difference(x800);
Decls x805 = x806.oneOf(x807);
Expression x814 = x727.product(x785);
Variable x818 = Variable.unary("ValidBest_node");
Decls x817 = x818.oneOf(x6);
Variable x820 = Variable.unary("ValidBest_pref");
Decls x819 = x820.oneOf(x6);
Decls x816 = x817.and(x819);
Variable x827 = Variable.unary("ValidChoices2_n");
Decls x826 = x827.oneOf(x6);
Variable x829 = Variable.unary("ValidChoices2_p");
Decls x828 = x829.oneOf(x6);
Decls x825 = x826.and(x828);
Expression x835 = x827.join(x10);
Expression x834 = x835.join(x6);
Expression x833 = x834.join(x6);
Expression x840 = x827.join(x10);
Expression x839 = x840.join(x6);
Expression x838 = x839.join(x6);
Expression x843 = x12.transpose();
Expression x842 = x843.closure();
Expression x841 = x838.join(x842);
Expression x837 = x838.difference(x841);
Expression x836 = x837.join(x12);
Expression x832 = x833.union(x836);
Formula x831 = x829.in(x832);
Expression x849 = x827.join(x10);
Expression x848 = x849.join(x6);
Expression x847 = x848.join(x6);
Formula x846 = x829.in(x847);
Formula x845 = x846.not();
Expression x855 = x827.join(x10);
Expression x854 = x829.join(x855);
Expression x853 = x9.join(x854);
Formula x852 = x853.some();
Formula x851 = x852.not();
Variable x858 = Variable.unary("ValidPathChoice2_p");
Expression x863 = x714.product(x735);
Expression x864 = x720.product(x760);
Expression x862 = x863.union(x864);
Expression x866 = x714.product(x750);
Expression x867 = x720.product(x775);
Expression x865 = x866.union(x867);
Expression x861 = x862.union(x865);
Expression x860 = x814.union(x861);
Expression x859 = x853.join(x860);
Decls x857 = x858.oneOf(x859);
Expression x874 = x827.join(x10);
Expression x873 = x874.join(x6);
Expression x872 = x873.join(x6);
Formula x871 = x829.in(x872);
Formula x870 = x871.not();
Formula x869 = x870.not();
Expression x878 = x827.join(x10);
Expression x877 = x829.join(x878);
Expression x876 = x12.join(x877);
Expression x880 = x853.join(x10);
Expression x879 = x858.join(x880);
Formula x875 = x876.eq(x879);
Formula x868 = x869.and(x875);
Formula x856 = x868.forSome(x857);
Formula x850 = x851.or(x856);
Formula x844 = x845.or(x850);
Formula x830 = x831.and(x844);
Expression x824 = x830.comprehension(x825);
Expression x823 = x818.join(x824);
Formula x822 = x820.in(x823);
Variable x883 = Variable.unary("ValidBest_j");
Expression x884 = x818.join(x824);
Decls x882 = x883.oneOf(x884);
Expression x889 = x12.transpose();
Expression x888 = x889.closure();
Expression x887 = x820.join(x888);
Formula x886 = x883.in(x887);
Formula x885 = x886.not();
Formula x881 = x885.forAll(x882);
Formula x821 = x822.and(x881);
Expression x815 = x821.comprehension(x816);
Formula x813 = x814.in(x815);
Variable x893 = Variable.unary("DW2E_n");
Decls x892 = x893.oneOf(x727);
Expression x898 = x893.join(x814);
Expression x899 = x893.join(x10);
Expression x897 = x898.join(x899);
Expression x896 = x6.join(x897);
Expression x900 = x44.difference(x727);
Expression x895 = x896.intersection(x900);
Formula x894 = x895.no();
Formula x891 = x894.forAll(x892);
Variable x905 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x911 = x720.join(x10);
Expression x910 = x775.join(x911);
Expression x909 = x9.join(x910);
Expression x908 = x909.join(x10);
Expression x907 = x908.join(x6);
Expression x906 = x907.join(x6);
Decls x904 = x905.oneOf(x906);
Expression x916 = x720.join(x10);
Expression x915 = x775.join(x916);
Expression x914 = x12.join(x915);
Expression x918 = x909.join(x10);
Expression x917 = x905.join(x918);
Formula x913 = x914.eq(x917);
Expression x925 = x735.product(x9);
Expression x924 = x714.product(x925);
Expression x927 = x760.product(x806);
Expression x926 = x720.product(x927);
Expression x923 = x924.union(x926);
Expression x930 = x750.product(x8);
Expression x929 = x714.product(x930);
Expression x932 = x775.product(x800);
Expression x931 = x720.product(x932);
Expression x928 = x929.union(x931);
Expression x922 = x923.union(x928);
Expression x921 = x720.join(x922);
Expression x920 = x775.join(x921);
Expression x934 = x909.join(x922);
Expression x933 = x905.join(x934);
Formula x919 = x920.eq(x933);
Formula x912 = x913.and(x919);
Formula x903 = x912.forSome(x904);
Expression x941 = x720.join(x10);
Expression x940 = x941.join(x6);
Expression x939 = x940.join(x6);
Formula x938 = x760.in(x939);
Formula x937 = x938.not();
Expression x946 = x720.join(x10);
Expression x945 = x760.join(x946);
Expression x944 = x9.join(x945);
Formula x943 = x944.no();
Variable x949 = Variable.unary("isLeg_pref2");
Expression x950 = x944.join(x814);
Decls x948 = x949.oneOf(x950);
Expression x957 = x720.join(x10);
Expression x956 = x957.join(x6);
Expression x955 = x956.join(x6);
Formula x954 = x760.in(x955);
Formula x953 = x954.not();
Formula x952 = x953.not();
Expression x961 = x720.join(x10);
Expression x960 = x760.join(x961);
Expression x959 = x12.join(x960);
Expression x963 = x944.join(x10);
Expression x962 = x949.join(x963);
Formula x958 = x959.eq(x962);
Formula x951 = x952.and(x958);
Formula x947 = x951.forSome(x948);
Formula x942 = x943.or(x947);
Formula x936 = x937.or(x942);
Variable x966 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x972 = x720.join(x10);
Expression x971 = x760.join(x972);
Expression x970 = x9.join(x971);
Expression x969 = x970.join(x10);
Expression x968 = x969.join(x6);
Expression x967 = x968.join(x6);
Decls x965 = x966.oneOf(x967);
Expression x977 = x720.join(x10);
Expression x976 = x760.join(x977);
Expression x975 = x12.join(x976);
Expression x979 = x970.join(x10);
Expression x978 = x966.join(x979);
Formula x974 = x975.eq(x978);
Expression x982 = x720.join(x922);
Expression x981 = x760.join(x982);
Expression x984 = x970.join(x922);
Expression x983 = x966.join(x984);
Formula x980 = x981.eq(x983);
Formula x973 = x974.and(x980);
Formula x964 = x973.forSome(x965);
Formula x935 = x936.or(x964);
Formula x902 = x903.and(x935);
Variable x987 = Variable.unary("DWNodeCheck_k");
Variable x990 = Variable.unary("DWNodeCheck_i");
Decls x989 = x990.oneOf(x6);
Expression x995 = x12.transpose();
Expression x994 = x995.closure();
Expression x993 = x760.join(x994);
Formula x992 = x990.in(x993);
Formula x997 = x990.eq(x775);
Formula x996 = x997.not();
Formula x991 = x992.and(x996);
Expression x988 = x991.comprehension(x989);
Decls x986 = x987.oneOf(x988);
Expression x1004 = x720.join(x10);
Expression x1003 = x987.join(x1004);
Expression x1002 = x9.join(x1003);
Formula x1001 = x1002.no();
Variable x1007 = Variable.unary("isLeg_pref2");
Expression x1008 = x1002.join(x814);
Decls x1006 = x1007.oneOf(x1008);
Expression x1015 = x720.join(x10);
Expression x1014 = x1015.join(x6);
Expression x1013 = x1014.join(x6);
Formula x1012 = x987.in(x1013);
Formula x1011 = x1012.not();
Formula x1010 = x1011.not();
Expression x1019 = x720.join(x10);
Expression x1018 = x987.join(x1019);
Expression x1017 = x12.join(x1018);
Expression x1021 = x1002.join(x10);
Expression x1020 = x1007.join(x1021);
Formula x1016 = x1017.eq(x1020);
Formula x1009 = x1010.and(x1016);
Formula x1005 = x1009.forSome(x1006);
Formula x1000 = x1001.or(x1005);
Formula x999 = x1000.not();
Variable x1024 = Variable.unary("DWNodeCheck_first_hop_k_pref");
Expression x1028 = x720.join(x10);
Expression x1027 = x987.join(x1028);
Expression x1026 = x9.join(x1027);
Expression x1025 = x1026.join(x861);
Decls x1023 = x1024.oneOf(x1025);
Expression x1037 = x720.join(x10);
Expression x1036 = x1037.join(x6);
Expression x1035 = x1036.join(x6);
Formula x1034 = x987.in(x1035);
Formula x1033 = x1034.not();
Formula x1032 = x1033.not();
Expression x1041 = x720.join(x10);
Expression x1040 = x987.join(x1041);
Expression x1039 = x12.join(x1040);
Expression x1043 = x1026.join(x10);
Expression x1042 = x1024.join(x1043);
Formula x1038 = x1039.eq(x1042);
Formula x1031 = x1032.and(x1038);
Formula x1030 = x1031.not();
Expression x1047 = x1026.join(x922);
Expression x1046 = x1024.join(x1047);
Expression x1049 = x720.join(x922);
Expression x1048 = x775.join(x1049);
Formula x1045 = x1046.eq(x1048);
Expression x1052 = x12.closure();
Expression x1051 = x775.join(x1052);
Formula x1050 = x987.in(x1051);
Formula x1044 = x1045.and(x1050);
Formula x1029 = x1030.or(x1044);
Formula x1022 = x1029.forAll(x1023);
Formula x998 = x999.and(x1022);
Formula x985 = x998.forAll(x986);
Formula x901 = x902.and(x985);
Formula x890 = x891.and(x901);
Formula x812 = x813.and(x890);
Variable x1057 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x1063 = x714.join(x10);
Expression x1062 = x750.join(x1063);
Expression x1061 = x9.join(x1062);
Expression x1060 = x1061.join(x10);
Expression x1059 = x1060.join(x6);
Expression x1058 = x1059.join(x6);
Decls x1056 = x1057.oneOf(x1058);
Expression x1068 = x714.join(x10);
Expression x1067 = x750.join(x1068);
Expression x1066 = x12.join(x1067);
Expression x1070 = x1061.join(x10);
Expression x1069 = x1057.join(x1070);
Formula x1065 = x1066.eq(x1069);
Expression x1073 = x714.join(x922);
Expression x1072 = x750.join(x1073);
Expression x1075 = x1061.join(x922);
Expression x1074 = x1057.join(x1075);
Formula x1071 = x1072.eq(x1074);
Formula x1064 = x1065.and(x1071);
Formula x1055 = x1064.forSome(x1056);
Expression x1082 = x714.join(x10);
Expression x1081 = x1082.join(x6);
Expression x1080 = x1081.join(x6);
Formula x1079 = x735.in(x1080);
Formula x1078 = x1079.not();
Expression x1087 = x714.join(x10);
Expression x1086 = x735.join(x1087);
Expression x1085 = x9.join(x1086);
Formula x1084 = x1085.no();
Variable x1090 = Variable.unary("isLeg_pref2");
Expression x1091 = x1085.join(x814);
Decls x1089 = x1090.oneOf(x1091);
Expression x1098 = x714.join(x10);
Expression x1097 = x1098.join(x6);
Expression x1096 = x1097.join(x6);
Formula x1095 = x735.in(x1096);
Formula x1094 = x1095.not();
Formula x1093 = x1094.not();
Expression x1102 = x714.join(x10);
Expression x1101 = x735.join(x1102);
Expression x1100 = x12.join(x1101);
Expression x1104 = x1085.join(x10);
Expression x1103 = x1090.join(x1104);
Formula x1099 = x1100.eq(x1103);
Formula x1092 = x1093.and(x1099);
Formula x1088 = x1092.forSome(x1089);
Formula x1083 = x1084.or(x1088);
Formula x1077 = x1078.or(x1083);
Variable x1107 = Variable.unary("goesThruItsOwnParity_pref2");
Expression x1113 = x714.join(x10);
Expression x1112 = x735.join(x1113);
Expression x1111 = x9.join(x1112);
Expression x1110 = x1111.join(x10);
Expression x1109 = x1110.join(x6);
Expression x1108 = x1109.join(x6);
Decls x1106 = x1107.oneOf(x1108);
Expression x1118 = x714.join(x10);
Expression x1117 = x735.join(x1118);
Expression x1116 = x12.join(x1117);
Expression x1120 = x1111.join(x10);
Expression x1119 = x1107.join(x1120);
Formula x1115 = x1116.eq(x1119);
Expression x1123 = x714.join(x922);
Expression x1122 = x735.join(x1123);
Expression x1125 = x1111.join(x922);
Expression x1124 = x1107.join(x1125);
Formula x1121 = x1122.eq(x1124);
Formula x1114 = x1115.and(x1121);
Formula x1105 = x1114.forSome(x1106);
Formula x1076 = x1077.or(x1105);
Formula x1054 = x1055.and(x1076);
Variable x1128 = Variable.unary("DWNodeCheck_k");
Variable x1131 = Variable.unary("DWNodeCheck_i");
Decls x1130 = x1131.oneOf(x6);
Expression x1136 = x12.transpose();
Expression x1135 = x1136.closure();
Expression x1134 = x735.join(x1135);
Formula x1133 = x1131.in(x1134);
Formula x1138 = x1131.eq(x750);
Formula x1137 = x1138.not();
Formula x1132 = x1133.and(x1137);
Expression x1129 = x1132.comprehension(x1130);
Decls x1127 = x1128.oneOf(x1129);
Expression x1145 = x714.join(x10);
Expression x1144 = x1128.join(x1145);
Expression x1143 = x9.join(x1144);
Formula x1142 = x1143.no();
Variable x1148 = Variable.unary("isLeg_pref2");
Expression x1149 = x1143.join(x814);
Decls x1147 = x1148.oneOf(x1149);
Expression x1156 = x714.join(x10);
Expression x1155 = x1156.join(x6);
Expression x1154 = x1155.join(x6);
Formula x1153 = x1128.in(x1154);
Formula x1152 = x1153.not();
Formula x1151 = x1152.not();
Expression x1160 = x714.join(x10);
Expression x1159 = x1128.join(x1160);
Expression x1158 = x12.join(x1159);
Expression x1162 = x1143.join(x10);
Expression x1161 = x1148.join(x1162);
Formula x1157 = x1158.eq(x1161);
Formula x1150 = x1151.and(x1157);
Formula x1146 = x1150.forSome(x1147);
Formula x1141 = x1142.or(x1146);
Formula x1140 = x1141.not();
Variable x1165 = Variable.unary("DWNodeCheck_first_hop_k_pref");
Expression x1169 = x714.join(x10);
Expression x1168 = x1128.join(x1169);
Expression x1167 = x9.join(x1168);
Expression x1166 = x1167.join(x861);
Decls x1164 = x1165.oneOf(x1166);
Expression x1178 = x714.join(x10);
Expression x1177 = x1178.join(x6);
Expression x1176 = x1177.join(x6);
Formula x1175 = x1128.in(x1176);
Formula x1174 = x1175.not();
Formula x1173 = x1174.not();
Expression x1182 = x714.join(x10);
Expression x1181 = x1128.join(x1182);
Expression x1180 = x12.join(x1181);
Expression x1184 = x1167.join(x10);
Expression x1183 = x1165.join(x1184);
Formula x1179 = x1180.eq(x1183);
Formula x1172 = x1173.and(x1179);
Formula x1171 = x1172.not();
Expression x1188 = x1167.join(x922);
Expression x1187 = x1165.join(x1188);
Expression x1190 = x714.join(x922);
Expression x1189 = x750.join(x1190);
Formula x1186 = x1187.eq(x1189);
Expression x1193 = x12.closure();
Expression x1192 = x750.join(x1193);
Formula x1191 = x1128.in(x1192);
Formula x1185 = x1186.and(x1191);
Formula x1170 = x1171.or(x1185);
Formula x1163 = x1170.forAll(x1164);
Formula x1139 = x1140.and(x1163);
Formula x1126 = x1139.forAll(x1127);
Formula x1053 = x1054.and(x1126);
Formula x811 = x812.and(x1053);
Formula x804 = x811.forSome(x805);
Formula x798 = x804.forSome(x799);
Formula x783 = x798.forSome(x784);
Formula x773 = x783.forSome(x774);
Formula x758 = x773.forSome(x759);
Formula x748 = x758.forSome(x749);
Formula x733 = x748.forSome(x734);
Formula x725 = x733.forSome(x726);
Formula x718 = x725.forSome(x719);
Formula x712 = x718.forSome(x713);
Formula x268 = x269.or(x712);
Formula x267 = x268.not();
Formula x144 = x145.iff(x267);
Formula x137 = x138.or(x144);
Formula x136 = x137.not();
Formula x1194 = x0.eq(x0);
Formula x1195 = x1.eq(x1);
Formula x1196 = x2.eq(x2);
Formula x1197 = x3.eq(x3);
Formula x1198 = x4.eq(x4);
Formula x1199 = x5.eq(x5);
Formula x1200 = x6.eq(x6);
Formula x1201 = x7.eq(x7);
Formula x1202 = x8.eq(x8);
Formula x1203 = x9.eq(x9);
Formula x1204 = x10.eq(x10);
Formula x1205 = x11.eq(x11);
Formula x1206 = x12.eq(x12);
Formula x1207 = x13.eq(x13);
Formula[] fs = new Formula[] { x15, x16, x17, x18, x19, x26, x31, x34, x38, x39, x40, x42, x48, x57, x69, x82, x87, x109, x130, x136, x1194, x1195, x1196, x1197, x1198, x1199, x1200, x1201, x1202, x1203, x1204, x1205, x1206, x1207 };
String[] fsn = new String[] { "x15", "x16", "x17", "x18", "x19", "x26", "x31", "x34", "x38", "x39", "x40", "x42", "x48", "x57", "x69", "x82", "x87", "x109", "x130", "x136", "x1194", "x1195", "x1196", "x1197", "x1198", "x1199", "x1200", "x1201", "x1202", "x1203", "x1204", "x1205", "x1206", "x1207" };
Formula x14 = Formula.compose(FormulaOperator.AND, fs);
Solver solver = new Solver();
solver.options().setSolver(SATFactory.MiniSat);
solver.options().setBitwidth(4);
// solver.options().setFlatten(false);
solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
solver.options().setSymmetryBreaking(20);
solver.options().setSkolemDepth(0);
solver.options().setReporter(new ConsoleReporter());
System.out.println("Solving...");
System.out.flush();
Solution sol = solver.solve(x14, bounds);
System.out.println(sol.toString());
if (sol.instance() != null) {
System.out.println("Evaluating...");
Evaluator ev = new Evaluator(sol.instance(), solver.options());
for (int i = 0; i < fs.length; i++) {
System.out.println(fsn[i] + " =\n" + PrettyPrinter.print(fs[i], 2));
}
System.out.println("\n===========================\n");
for (int i = 0; i < fs.length; i++) {
System.out.println(fsn[i] + " = " + ev.evaluate(fs[i]));
}
final boolean val = ev.evaluate(x14);
System.out.println("x14 = " + val);
throw new AssertionError("bad instance");
}
}
Also used :
TupleSet(kodkod.instance.TupleSet)
Solver(kodkod.engine.Solver)
Variable(kodkod.ast.Variable)
Decls(kodkod.ast.Decls)
ConsoleReporter(kodkod.engine.config.ConsoleReporter)
Bounds(kodkod.instance.Bounds)
IntExpression(kodkod.ast.IntExpression)
TupleFactory(kodkod.instance.TupleFactory)
Universe(kodkod.instance.Universe)
Evaluator(kodkod.engine.Evaluator)
Formula(kodkod.ast.Formula)
Relation(kodkod.ast.Relation)
IntExpression(kodkod.ast.IntExpression)
Expression(kodkod.ast.Expression)
Solution(kodkod.engine.Solution)
Example 3 with Evaluator
use of kodkod.engine.Evaluator in project org.alloytools.alloy by AlloyTools.
the class ConfigAssure method display.
/**
* Displays an instance obtained with the given options.
*
* @requires inst != null and opt != null
*/
private final void display(Instance inst, Options opt) {
final Universe univ = inst.universe();
final Evaluator eval = new Evaluator(inst, opt);
final TupleFactory factory = univ.factory();
final List<TupleSet> subnets = new ArrayList<TupleSet>();
System.out.println("address\t\tnetwork id\tmask\tdevice-interface");
for (int i = 0, ports = univ.size() - 32; i < ports; i++) {
final Object atom = univ.atom(i);
final Relation p = Relation.unary(atom.toString());
inst.add(p, factory.setOf(atom));
System.out.print(toQuad(eval.evaluate(addr(p))) + "\t");
System.out.print(toQuad(eval.evaluate(netid(p))) + "\t");
System.out.print(eval.evaluate(implicitMask(p)) + "\t");
System.out.println(p);
final TupleSet members = eval.evaluate(subnet(p));
if (!members.isEmpty())
subnets.add(members);
}
System.out.println("\nsubnets:");
for (TupleSet sub : subnets) {
System.out.println(sub);
}
}Example 4 with Evaluator
use of kodkod.engine.Evaluator in project org.alloytools.alloy by AlloyTools.
the class BugTests method testGreg_01192006.
public final void testGreg_01192006() {
// circular linked list
Relation Entry = Relation.unary("Entry");
Relation head = Relation.unary("head");
Relation next = Relation.binary("next");
Formula nextFun = next.function(Entry, Entry);
// bijection between indices and entries in linked list
Relation Index = Relation.unary("Index");
Relation index2Entry = Relation.binary("index2Entry");
Expression entries = head.join(next.closure());
Variable e = Variable.unary("e");
Expression preImage = index2Entry.join(e);
Formula index2EntryBij = e.in(entries).implies(preImage.one()).and(e.in(entries).not().implies(preImage.no())).forAll(e.oneOf(Entry));
// try to force list to have three distinct entries
Variable e1 = Variable.unary("e1");
Variable e2 = Variable.unary("e2");
Variable e3 = Variable.unary("e3");
Formula threeEntries = e1.eq(e2).not().and(e1.eq(e3).not()).and(e2.eq(e3).not()).forSome(e1.oneOf(entries).and(e2.oneOf(entries).and(e3.oneOf(entries))));
Formula simulate = head.one().and(nextFun).and(index2EntryBij).and(threeEntries);
Object Entry0 = "Entry0";
Object Entry1 = "Entry1";
Object Entry2 = "Entry2";
Object Entry3 = "Entry3";
Object Index0 = "Index0";
Object Index1 = "Index1";
Object Index2 = "Index2";
Object Index3 = "Index3";
Universe univ = new Universe(Arrays.asList(Entry0, Entry1, Entry2, Entry3, Index0, Index1, Index2, Index3));
TupleFactory factory = univ.factory();
TupleSet entryTuples = factory.setOf(Entry0, Entry1, Entry2, Entry3);
TupleSet indexTuples = factory.setOf(Index0, Index1, Index2, Index3);
Instance instance = new Instance(univ);
instance.add(Entry, entryTuples);
instance.add(head, factory.setOf(Entry0));
instance.add(Index, indexTuples);
Tuple next0 = factory.tuple(Entry0, Entry1);
Tuple next1 = factory.tuple(Entry1, Entry2);
Tuple next2 = factory.tuple(Entry2, Entry3);
Tuple next3 = factory.tuple(Entry3, Entry0);
instance.add(next, factory.setOf(next0, next1, next2, next3));
Tuple i2e0 = factory.tuple(Index0, Entry0);
Tuple i2e1 = factory.tuple(Index1, Entry1);
Tuple i2e2 = factory.tuple(Index2, Entry2);
Tuple i2e3 = factory.tuple(Index3, Entry3);
instance.add(index2Entry, factory.setOf(i2e0, i2e1, i2e2, i2e3));
Evaluator eval = new Evaluator(instance);
assertTrue(eval.evaluate(simulate));
Bounds bounds = new Bounds(univ);
bounds.boundExactly(Entry, entryTuples);
bounds.bound(head, entryTuples);
bounds.bound(next, entryTuples.product(entryTuples));
bounds.bound(Index, indexTuples);
bounds.bound(index2Entry, indexTuples.product(entryTuples));
// Solver solver = new Solver(SATSolverName.Default);
// System.out.println(simulate);
// System.out.println(bounds);
// System.out.println(instance);
instance = solver.solve(simulate, bounds).instance();
// System.out.println(instance);
assertNotNull(instance);
}
Also used :
Formula(kodkod.ast.Formula)
TupleSet(kodkod.instance.TupleSet)
Relation(kodkod.ast.Relation)
Variable(kodkod.ast.Variable)
IntExpression(kodkod.ast.IntExpression)
Expression(kodkod.ast.Expression)
Instance(kodkod.instance.Instance)
Bounds(kodkod.instance.Bounds)
TupleFactory(kodkod.instance.TupleFactory)
Universe(kodkod.instance.Universe)
Evaluator(kodkod.engine.Evaluator)
Tuple(kodkod.instance.Tuple)
Example 5 with Evaluator
use of kodkod.engine.Evaluator in project org.alloytools.alloy by AlloyTools.
the class IncrementalOverflowEnumTest method solveAll.
@Override
protected Iterator<Solution> solveAll(final Formula formula) {
final IncrementalSolver solver = IncrementalSolver.solver(options);
return new Iterator<Solution>() {
Solution sol;
@Override
public boolean hasNext() {
return sol == null || sol.sat();
}
@Override
public Solution next() {
if (sol == null) {
sol = solver.solve(formula, bounds);
} else {
Evaluator ev = new Evaluator(sol.instance());
int a = evalInt(ev, op1);
int b = evalInt(ev, op2);
int r = evalInt(ev, ret);
Formula f = op1.eq(IntConstant.constant(a).toExpression()).and(op2.eq(IntConstant.constant(b).toExpression())).and(ret.eq(IntConstant.constant(r).toExpression())).not();
sol = solver.solve(f, new Bounds(factory.universe()));
}
return sol;
}
@Override
public void remove() {
throw new RuntimeException("Not supported");
}
};
}Aggregations
Evaluator (kodkod.engine.Evaluator)18
Formula (kodkod.ast.Formula)12
Solution (kodkod.engine.Solution)10
Relation (kodkod.ast.Relation)9
TupleFactory (kodkod.instance.TupleFactory)9
Universe (kodkod.instance.Universe)9
Bounds (kodkod.instance.Bounds)8
Instance (kodkod.instance.Instance)8
TupleSet (kodkod.instance.TupleSet)7
IntExpression (kodkod.ast.IntExpression)6
ArrayList (java.util.ArrayList)4
Expression (kodkod.ast.Expression)3
Solver (kodkod.engine.Solver)3
Tuple (kodkod.instance.Tuple)3
HashSet (java.util.HashSet)2
Variable (kodkod.ast.Variable)2
A4Reporter (edu.mit.csail.sdg.alloy4.A4Reporter)1
UniqueNameGenerator (edu.mit.csail.sdg.alloy4.UniqueNameGenerator)1
Type (edu.mit.csail.sdg.ast.Type)1
File (java.io.File)1
