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https://github.com/Z3Prover/z3
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testing qe_arith
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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@ -67,7 +67,7 @@ namespace qe {
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ts.push_back(a.mk_numeral(mul*mul1, m.get_sort(t)));
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}
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else if ((*m_var)(t)) {
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IF_VERBOSE(1, verbose_stream() << mk_pp(t, m) << "\n";);
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IF_VERBOSE(1, verbose_stream() << "can't project:" << mk_pp(t, m) << "\n";);
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throw cant_project();
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}
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else if (mul.is_one()) {
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@ -111,6 +111,7 @@ namespace qe {
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is_strict = false;
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}
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else {
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IF_VERBOSE(1, verbose_stream() << "can't project:" << mk_pp(lit, m) << "\n";);
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throw cant_project();
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}
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if (ts.empty()) {
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@ -125,6 +126,9 @@ namespace qe {
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void project(model& model, expr_ref_vector& lits) {
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unsigned num_pos = 0;
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unsigned num_neg = 0;
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m_ineq_terms.reset();
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m_ineq_coeffs.reset();
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m_ineq_strict.reset();
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expr_ref_vector new_lits(m);
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for (unsigned i = 0; i < lits.size(); ++i) {
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rational c(0);
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@ -134,12 +138,16 @@ namespace qe {
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m_ineq_coeffs.push_back(c);
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m_ineq_terms.push_back(t);
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m_ineq_strict.push_back(is_strict);
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if (c.is_pos()) {
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if (c.is_zero()) {
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m_rw(lits[i].get(), t);
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new_lits.push_back(t);
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}
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else if (c.is_pos()) {
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++num_pos;
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}
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else {
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++num_neg;
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}
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}
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}
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else {
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new_lits.push_back(lits[i].get());
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@ -208,14 +216,15 @@ namespace qe {
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expr_ref as = mk_mul(abs(ac), s);
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expr_ref ts = mk_add(bt, as);
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expr* z = a.mk_numeral(rational(0), m.get_sort(t));
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expr_ref result(m);
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expr_ref result1(m), result2(m);
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if (m_ineq_strict[i] || m_ineq_strict[j]) {
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result = a.mk_lt(ts, z);
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result1 = a.mk_lt(ts, z);
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}
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else {
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result = a.mk_le(ts, z);
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result1 = a.mk_le(ts, z);
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}
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return result;
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m_rw(result1, result2);
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return result2;
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}
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// ax + t <= 0
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@ -232,12 +241,15 @@ namespace qe {
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expr* s = m_ineq_terms[j].get();
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expr_ref bt = mk_mul(abs(bc), t);
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expr_ref as = mk_mul(abs(ac), s);
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expr_ref result1(m), result2(m);
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if (m_ineq_strict[j] && !m_ineq_strict[i]) {
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return expr_ref(a.mk_lt(bt, as), m);
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result1 = a.mk_lt(bt, as);
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}
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else {
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return expr_ref(a.mk_le(bt, as), m);
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result1 = a.mk_le(bt, as);
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}
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m_rw(result1, result2);
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return result2;
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}
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@ -257,20 +269,23 @@ namespace qe {
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app_ref_vector new_vars(m);
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expr_ref_vector result(lits);
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for (unsigned i = 0; i < vars.size(); ++i) {
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m_var = alloc(contains_app, m, vars[i].get());
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app* v = vars[i].get();
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m_var = alloc(contains_app, m, v);
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try {
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project(model, result);
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TRACE("qe", tout << "projected: " << mk_pp(v, m) << " ";
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for (unsigned i = 0; i < result.size(); ++i) {
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tout << mk_pp(result[i].get(), m) << "\n";
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});
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}
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catch (cant_project) {
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new_vars.push_back(vars[i].get());
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IF_VERBOSE(1, verbose_stream() << "can't project:" << mk_pp(v, m) << "\n";);
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new_vars.push_back(v);
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}
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}
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vars.reset();
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vars.append(new_vars);
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expr_ref res1(m);
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expr_ref tmp = qe::mk_and(result);
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m_rw(tmp, res1);
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return res1;
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return qe::mk_and(result);
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}
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};
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@ -280,4 +295,12 @@ namespace qe {
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return ap(model, vars, lits);
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}
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expr_ref arith_project(model& model, app_ref_vector& vars, expr* fml) {
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ast_manager& m = vars.get_manager();
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arith_project_util ap(m);
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expr_ref_vector lits(m);
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qe::flatten_and(fml, lits);
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return ap(model, vars, lits);
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}
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}
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@ -11,6 +11,8 @@ namespace qe {
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return vector of variables that could not be projected.
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*/
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expr_ref arith_project(model& model, app_ref_vector& vars, expr_ref_vector const& lits);
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expr_ref arith_project(model& model, app_ref_vector& vars, expr* fml);
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};
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#endif
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@ -1,4 +1,5 @@
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#include "qe_arith.h"
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#include "qe.h"
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#include "th_rewriter.h"
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#include "smt2parser.h"
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#include "arith_decl_plugin.h"
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@ -7,7 +8,7 @@
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#include "ast_pp.h"
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#include "qe_util.h"
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#include "smt_context.h"
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#include "expr_abstract.h"
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static expr_ref parse_fml(ast_manager& m, char const* str) {
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expr_ref result(m);
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@ -36,6 +37,15 @@ static char const* example3 = "(and (<= z x) (<= x 3.0) (< (* 3.0 x) y) (<= z y)
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static char const* example4 = "(and (<= z x) (<= x 3.0) (not (>= (* 3.0 x) y)) (<= z y))";
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static char const* example5 = "(and (<= y x) (<= z x) (<= x u) (<= x v) (<= x t))";
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static char const* example6 = "(and (<= 0 (+ x z))\
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(>= y x) \
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(<= y x)\
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(<= (- u y) 0.0)\
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(>= x (+ v z))\
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(>= x 0.0)\
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(<= x 1.0))";
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static void test(char const *ex) {
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smt_params params;
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params.m_model = true;
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@ -58,9 +68,65 @@ static void test(char const *ex) {
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std::cout << mk_pp(fml, m) << "\n";
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std::cout << mk_pp(pr, m) << "\n";
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}
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static void test2(char const *ex) {
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smt_params params;
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params.m_model = true;
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ast_manager m;
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reg_decl_plugins(m);
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arith_util a(m);
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expr_ref fml = parse_fml(m, ex);
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app_ref_vector vars(m);
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expr_ref_vector lits(m);
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vars.push_back(m.mk_const(symbol("x"), a.mk_real()));
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vars.push_back(m.mk_const(symbol("y"), a.mk_real()));
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vars.push_back(m.mk_const(symbol("z"), a.mk_real()));
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qe::flatten_and(fml, lits);
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smt::context ctx(m, params);
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ctx.push();
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ctx.assert_expr(fml);
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lbool result = ctx.check();
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SASSERT(result == l_true);
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ref<model> md;
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ctx.get_model(md);
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ctx.pop(1);
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std::cout << mk_pp(fml, m) << "\n";
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expr_ref pr2(m), fml2(m);
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expr_ref_vector bound(m);
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ptr_vector<sort> sorts;
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svector<symbol> names;
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for (unsigned i = 0; i < vars.size(); ++i) {
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bound.push_back(vars[i].get());
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names.push_back(vars[i]->get_decl()->get_name());
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sorts.push_back(m.get_sort(vars[i].get()));
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}
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expr_abstract(m, 0, 3, bound.c_ptr(), fml, fml2);
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fml2 = m.mk_exists(3, sorts.c_ptr(), names.c_ptr(), fml2);
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qe::expr_quant_elim qe(m, params);
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expr_ref pr1 = qe::arith_project(*md, vars, lits);
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qe(m.mk_true(), fml2, pr2);
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std::cout << mk_pp(pr1, m) << "\n";
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std::cout << mk_pp(pr2, m) << "\n";
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expr_ref npr2(m);
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npr2 = m.mk_not(pr2);
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ctx.push();
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ctx.assert_expr(pr1);
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ctx.assert_expr(npr2);
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VERIFY(l_false == ctx.check());
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ctx.pop(1);
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}
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void tst_qe_arith() {
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test2(example6);
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return;
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test(example1);
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test(example2);
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test(example3);
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