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https://github.com/Z3Prover/z3
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bug fixes and cleanup
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
54661a7d22
commit
8a708a85e6
3 changed files with 369 additions and 192 deletions
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@ -1443,7 +1443,238 @@ static void tst_unsound_lws_x3() {
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std::cout << "=== END tst_unsound_lws_x3 ===\n\n";
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}
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// Test case for unsound lemma from From_AProVE_2014__Et4-rec.jar-obl-8__p28996_terminationG_0.smt2
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// Sample: x0=4, x1=5, x2=3.5, x3=-8, x4=5
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// Counterexample: x0=5, x3=3, x4=0, x5=0
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// Polynomials:
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// p[0]: x0
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// p[1]: 2 x0 x4^2 + 2 x3 x4 - x0 x4 - 2 x3
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// p[2]: 2 x0 x4^2 x5 + 2 x3 x4 x5 - x0 x4 x5 - 2 x3 x5 + 4 x3 x4^2 + 9 x0 x3 x4 - 26 x3 x4 - 3 x0 x4
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// p[3]: x5 - 9
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static void tst_unsound_lws_et4() {
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std::cout << "=== tst_unsound_lws_et4 ===\n";
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params_ref ps;
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ps.set_bool("lws", true);
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reslimit rlim;
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nlsat::solver s(rlim, ps, false);
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anum_manager & am = s.am();
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nlsat::pmanager & pm = s.pm();
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nlsat::assignment sample_as(am);
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nlsat::assignment counter_as(am);
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polynomial::cache cache(pm);
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// Create 6 variables x0, x1, x2, x3, x4, x5
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nlsat::var x0 = s.mk_var(false);
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nlsat::var x1 = s.mk_var(false);
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nlsat::var x2 = s.mk_var(false);
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nlsat::var x3 = s.mk_var(false);
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nlsat::var x4 = s.mk_var(false);
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nlsat::var x5 = s.mk_var(false);
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polynomial_ref _x0(pm), _x1(pm), _x2(pm), _x3(pm), _x4(pm), _x5(pm);
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_x0 = pm.mk_polynomial(x0);
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_x1 = pm.mk_polynomial(x1);
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_x2 = pm.mk_polynomial(x2);
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_x3 = pm.mk_polynomial(x3);
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_x4 = pm.mk_polynomial(x4);
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_x5 = pm.mk_polynomial(x5);
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// p[0]: x0
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polynomial_ref p0(pm);
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p0 = _x0;
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// p[1]: 2 x0 x4^2 + 2 x3 x4 - x0 x4 - 2 x3
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polynomial_ref p1(pm);
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p1 = 2 * _x0 * (_x4^2) + 2 * _x3 * _x4 - _x0 * _x4 - 2 * _x3;
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// p[2]: 2 x0 x4^2 x5 + 2 x3 x4 x5 - x0 x4 x5 - 2 x3 x5 + 4 x3 x4^2 + 9 x0 x3 x4 - 26 x3 x4 - 3 x0 x4
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polynomial_ref p2(pm);
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p2 = 2 * _x0 * (_x4^2) * _x5
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+ 2 * _x3 * _x4 * _x5
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- _x0 * _x4 * _x5
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- 2 * _x3 * _x5
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+ 4 * _x3 * (_x4^2)
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+ 9 * _x0 * _x3 * _x4
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- 26 * _x3 * _x4
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- 3 * _x0 * _x4;
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// p[3]: x5 - 9
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polynomial_ref p3(pm);
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p3 = _x5 - 9;
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std::cout << "p0: " << p0 << "\n";
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std::cout << "p1: " << p1 << "\n";
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std::cout << "p2: " << p2 << "\n";
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std::cout << "p3: " << p3 << "\n\n";
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// Sample: x0=4, x1=5, x2=3.5, x3=-8, x4=5
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scoped_anum val(am);
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am.set(val, 4); sample_as.set(x0, val);
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am.set(val, 5); sample_as.set(x1, val);
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rational q(7, 2); // 3.5
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am.set(val, q.to_mpq()); sample_as.set(x2, val);
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am.set(val, -8); sample_as.set(x3, val);
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am.set(val, 5); sample_as.set(x4, val);
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// x5 not assigned (top level)
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// Counterexample: x0=5, x3=3, x4=0, x5=0
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am.set(val, 5); counter_as.set(x0, val);
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am.set(val, 5); counter_as.set(x1, val); // use same as sample
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am.set(val, q.to_mpq()); counter_as.set(x2, val); // use same as sample
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am.set(val, 3); counter_as.set(x3, val);
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am.set(val, 0); counter_as.set(x4, val);
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am.set(val, 0); counter_as.set(x5, val);
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std::cout << "Sample point: x0=4, x1=5, x2=3.5, x3=-8, x4=5\n";
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std::cout << "Counterexample: x0=5, x3=3, x4=0, x5=0\n\n";
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// Evaluate polynomials at sample (need to set x5 for evaluation)
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scoped_anum sample_x5(am);
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am.set(sample_x5, 0); // pick some value in the cell
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nlsat::assignment sample_full(am);
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am.set(val, 4); sample_full.set(x0, val);
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am.set(val, 5); sample_full.set(x1, val);
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am.set(val, q.to_mpq()); sample_full.set(x2, val);
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am.set(val, -8); sample_full.set(x3, val);
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am.set(val, 5); sample_full.set(x4, val);
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am.set(val, 0); sample_full.set(x5, val);
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std::cout << "Polynomial signs at SAMPLE (with x5=0):\n";
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std::cout << " p0 sign: " << am.eval_sign_at(p0, sample_full) << "\n";
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std::cout << " p1 sign: " << am.eval_sign_at(p1, sample_full) << "\n";
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std::cout << " p2 sign: " << am.eval_sign_at(p2, sample_full) << "\n";
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std::cout << " p3 sign: " << am.eval_sign_at(p3, sample_full) << "\n\n";
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// Evaluate polynomials at counterexample
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std::cout << "Polynomial signs at COUNTEREXAMPLE:\n";
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std::cout << " p0 sign: " << am.eval_sign_at(p0, counter_as) << "\n";
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std::cout << " p1 sign: " << am.eval_sign_at(p1, counter_as) << "\n";
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std::cout << " p2 sign: " << am.eval_sign_at(p2, counter_as) << "\n";
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std::cout << " p3 sign: " << am.eval_sign_at(p3, counter_as) << "\n\n";
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// Set solver assignment for levelwise (without x5)
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s.set_rvalues(sample_as);
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// Build polynomial vector
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polynomial_ref_vector polys(pm);
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polys.push_back(p0);
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polys.push_back(p1);
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polys.push_back(p2);
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polys.push_back(p3);
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unsigned max_x = x5;
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// Print roots of each polynomial at sample
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std::cout << "Roots of polynomials at sample (in x5):\n";
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for (unsigned i = 0; i < polys.size(); ++i) {
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polynomial_ref p(polys.get(i), pm);
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if (pm.max_var(p) != x5) {
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std::cout << " p" << i << ": max_var is not x5, skipping\n";
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continue;
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}
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scoped_anum_vector roots(am);
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am.isolate_roots(p, nlsat::undef_var_assignment(sample_as, x5), roots);
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std::cout << " p" << i << " roots: ";
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if (roots.empty()) {
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std::cout << "(none)";
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} else {
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for (unsigned j = 0; j < roots.size(); ++j) {
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if (j > 0) std::cout << ", ";
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am.display_decimal(std::cout, roots[j], 5);
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}
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}
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std::cout << "\n";
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}
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std::cout << "\n";
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std::cout << "Running levelwise with max_x = x5\n";
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// Run levelwise
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nlsat::levelwise lws(s, polys, max_x, s.sample(), pm, am, cache);
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auto cell = lws.single_cell();
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std::cout << "Levelwise " << (lws.failed() ? "FAILED" : "succeeded") << "\n";
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std::cout << "Cell intervals (count=" << cell.size() << "):\n";
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for (auto const& interval : cell) {
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nlsat::display(std::cout << " ", s, interval) << "\n";
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}
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// Evaluate cell bounds at counterexample to check if counterexample is in cell
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std::cout << "\n--- Checking if counterexample is in cell ---\n";
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bool counterexample_outside_cell = false;
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for (unsigned i = 0; i < cell.size(); ++i) {
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auto const& interval = cell[i];
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nlsat::var level = i;
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std::cout << "Level " << level << " (x" << level << "):\n";
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// Build assignment up to this level (exclusive) for root isolation
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nlsat::assignment partial_as(am);
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scoped_anum val(am);
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if (level > 0) { am.set(val, 5); partial_as.set(x0, val); } // counter x0
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if (level > 1) { am.set(val, 5); partial_as.set(x1, val); }
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if (level > 2) { am.set(val, q.to_mpq()); partial_as.set(x2, val); }
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if (level > 3) { am.set(val, 3); partial_as.set(x3, val); } // counter x3
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if (level > 4) { am.set(val, 0); partial_as.set(x4, val); } // counter x4
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scoped_anum counter_val(am);
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if (level == 0) am.set(counter_val, 5); // x0
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else if (level == 1) am.set(counter_val, 5);
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else if (level == 2) am.set(counter_val, q.to_mpq());
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else if (level == 3) am.set(counter_val, 3); // x3
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else if (level == 4) am.set(counter_val, 0); // x4
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else if (level == 5) am.set(counter_val, 0); // x5
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if (interval.is_section()) {
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std::cout << " Section case\n";
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} else {
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// Isolate roots and check bounds
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if (!interval.l_inf()) {
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polynomial_ref lower_p(interval.l, pm);
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scoped_anum_vector lower_roots(am);
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am.isolate_roots(lower_p, nlsat::undef_var_assignment(partial_as, level), lower_roots);
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if (lower_roots.size() >= interval.l_index) {
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std::cout << " Lower root (root[" << interval.l_index << "]): ";
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am.display_decimal(std::cout, lower_roots[interval.l_index - 1], 10);
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std::cout << "\n";
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std::cout << " Counter x" << level << " = ";
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am.display_decimal(std::cout, counter_val, 10);
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int cmp = am.compare(counter_val, lower_roots[interval.l_index - 1]);
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std::cout << " -> " << (cmp > 0 ? "ABOVE" : (cmp < 0 ? "BELOW" : "EQUAL")) << " lower bound\n";
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if (cmp <= 0) counterexample_outside_cell = true;
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}
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}
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if (!interval.u_inf()) {
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polynomial_ref upper_p(interval.u, pm);
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scoped_anum_vector upper_roots(am);
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am.isolate_roots(upper_p, nlsat::undef_var_assignment(partial_as, level), upper_roots);
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if (upper_roots.size() >= interval.u_index) {
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std::cout << " Upper root (root[" << interval.u_index << "]): ";
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am.display_decimal(std::cout, upper_roots[interval.u_index - 1], 10);
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std::cout << "\n";
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std::cout << " Counter x" << level << " = ";
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am.display_decimal(std::cout, counter_val, 10);
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int cmp = am.compare(counter_val, upper_roots[interval.u_index - 1]);
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std::cout << " -> " << (cmp > 0 ? "ABOVE" : (cmp < 0 ? "BELOW" : "EQUAL")) << " upper bound\n";
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if (cmp >= 0) counterexample_outside_cell = true;
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}
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}
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}
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std::cout << "\n";
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}
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// The counterexample has different polynomial signs than the sample.
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// For a sound cell, the counterexample must be OUTSIDE the cell.
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ENSURE(counterexample_outside_cell);
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std::cout << "SUCCESS: Counterexample is OUTSIDE the cell (cell is sound)\n";
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std::cout << "=== END tst_unsound_lws_et4 ===\n\n";
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}
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void tst_nlsat() {
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tst_unsound_lws_et4();
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std::cout << "------------------\n";
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tst_unsound_lws_x3();
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std::cout << "------------------\n";
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tst_unsound_lws2380();
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