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qe-lite: case-split BV vars constrained by constant equalities
Agent-Logs-Url: https://github.com/Z3Prover/z3/sessions/53219443-a721-4e6d-a7c3-21a6387b3396 Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
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copilot-swe-agent[bot]
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2 changed files with 193 additions and 1 deletions
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@ -2242,7 +2242,8 @@ class qe_lite::impl {
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// so we return it directly without re-wrapping.
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if (is_exists(q) || is_forall(q)) {
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expr_ref expanded(m);
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if (m_imp.try_expand_bounded_quantifier(q, result, expanded)) {
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if (m_imp.try_expand_bounded_quantifier(q, result, expanded) ||
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m_imp.try_expand_bv_eq_quantifier(q, result, expanded)) {
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if (is_forall(q))
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expanded = push_not(expanded);
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m_imp.m_rewriter(expanded, result, result_pr);
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@ -2287,6 +2288,8 @@ private:
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bool m_use_array_der;
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static const unsigned EXPAND_BOUND_LIMIT = 10000;
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static const unsigned BV_EQ_CASE_SPLIT_LIMIT = 256;
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static const unsigned BV_EQ_CASES_PER_VAR_LIMIT = 8;
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bool has_unique_non_ground(expr_ref_vector const& fmls, unsigned& index) {
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index = fmls.size();
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@ -2503,6 +2506,141 @@ private:
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return true;
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}
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bool collect_bv_eq_constants(expr* e, unsigned idx, obj_hashtable<expr>& values) {
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ptr_buffer<expr> todo;
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ast_mark visited;
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todo.push_back(e);
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while (!todo.empty()) {
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expr* n = todo.back();
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todo.pop_back();
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if (visited.is_marked(n))
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continue;
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visited.mark(n, true);
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if (is_var(n)) {
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if (to_var(n)->get_idx() == idx)
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return false;
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continue;
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}
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if (is_quantifier(n))
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return false;
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if (!is_app(n))
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continue;
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expr *lhs = nullptr, *rhs = nullptr;
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if (m.is_eq(n, lhs, rhs)) {
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bool lhs_is_var = is_var(lhs) && to_var(lhs)->get_idx() == idx;
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bool rhs_is_var = is_var(rhs) && to_var(rhs)->get_idx() == idx;
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if (lhs_is_var || rhs_is_var) {
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if (lhs_is_var == rhs_is_var)
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return false;
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expr* c = lhs_is_var ? rhs : lhs;
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if (!m.is_value(c))
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return false;
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values.insert(c);
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continue;
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}
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}
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todo.append(to_app(n)->get_num_args(), to_app(n)->get_args());
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}
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return true;
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}
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bool mk_bv_default_case(unsigned bv_size, obj_hashtable<expr> const& values, expr_ref& value) {
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bv_util bv(m);
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uint64_t max_num = values.size() + 1;
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if (bv_size < 63)
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max_num = std::min<uint64_t>(max_num, uint64_t(1) << bv_size);
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for (uint64_t i = 0; i < max_num; ++i) {
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value = bv.mk_numeral(rational(static_cast<unsigned>(i)), bv_size);
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if (!values.contains(value))
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return true;
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}
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return false;
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}
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bool try_expand_bv_eq_quantifier(quantifier* q, expr* body, expr_ref& result) {
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unsigned num_decls = q->get_num_decls();
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if (num_decls == 0)
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return false;
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used_vars uv;
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uv(body);
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struct bv_var_cases {
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unsigned idx;
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expr_ref_vector values;
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bv_var_cases(ast_manager& m, unsigned i): idx(i), values(m) {}
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};
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vector<bv_var_cases> case_vars;
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rational num_cases(1);
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for (unsigned i = 0; i < num_decls; ++i) {
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if (!uv.contains(i))
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continue;
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sort* s = uv.contains(i);
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if (!s)
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return false;
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bv_util bv(m);
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if (!bv.is_bv_sort(s))
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return false;
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obj_hashtable<expr> values;
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if (!collect_bv_eq_constants(body, i, values) || values.empty())
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return false;
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if (values.size() > BV_EQ_CASES_PER_VAR_LIMIT)
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return false;
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case_vars.push_back(bv_var_cases(m, i));
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auto& var_cases = case_vars.back();
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for (expr* v : values)
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var_cases.values.push_back(v);
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expr_ref other(m);
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if (mk_bv_default_case(bv.get_bv_size(s), values, other))
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var_cases.values.push_back(other);
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if (var_cases.values.empty())
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return false;
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num_cases *= rational(var_cases.values.size());
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if (num_cases > rational(BV_EQ_CASE_SPLIT_LIMIT))
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return false;
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}
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if (case_vars.empty())
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return false;
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expr_ref_vector subst_map(m);
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subst_map.resize(num_decls);
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for (unsigned i = 0; i < num_decls; ++i)
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if (!uv.contains(i))
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subst_map.set(i, m.mk_var(i, q->get_decl_sort(num_decls - i - 1)));
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unsigned_vector case_ix;
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case_ix.resize(case_vars.size(), 0);
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var_subst vs(m, false);
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expr_ref_vector disjuncts(m);
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while (true) {
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for (unsigned i = 0; i < case_vars.size(); ++i) {
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auto& c = case_vars[i];
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subst_map.set(c.idx, c.values.get(case_ix[i]));
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}
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expr_ref inst(vs(body, subst_map.size(), subst_map.data()), m);
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m_rewriter(inst);
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disjuncts.push_back(inst);
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unsigned j = case_ix.size();
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while (j > 0) {
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--j;
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++case_ix[j];
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if (case_ix[j] < case_vars[j].values.size())
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break;
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case_ix[j] = 0;
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}
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if (j == 0 && case_ix[0] == 0)
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break;
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}
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bool_rewriter(m).mk_or(disjuncts.size(), disjuncts.data(), result);
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return true;
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}
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public:
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impl(ast_manager & m, params_ref const & p, bool use_array_der):
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m(m),
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@ -6,12 +6,14 @@ Copyright (c) 2015 Microsoft Corporation
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#include "qe/mbp/mbp_arith.h"
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#include "qe/qe.h"
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#include "qe/lite/qe_lite_tactic.h"
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#include "ast/rewriter/th_rewriter.h"
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#include "parsers/smt2/smt2parser.h"
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#include "ast/arith_decl_plugin.h"
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#include "ast/reg_decl_plugins.h"
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#include "ast/rewriter/arith_rewriter.h"
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#include "ast/ast_pp.h"
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#include "ast/for_each_expr.h"
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#include "smt/smt_context.h"
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#include "ast/expr_abstract.h"
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#include "ast/rewriter/expr_safe_replace.h"
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@ -42,6 +44,57 @@ static expr_ref parse_fml(ast_manager& m, char const* str) {
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return result;
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}
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static expr_ref parse_smt2_assertion(ast_manager& m, char const* script) {
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expr_ref result(m);
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cmd_context ctx(false, &m);
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ctx.set_ignore_check(true);
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std::istringstream is(script);
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VERIFY(parse_smt2_commands(ctx, is));
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result = ctx.assertions().get(0);
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return result;
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}
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namespace qe_arith_test {
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struct find_q_proc {
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quantifier* m_q = nullptr;
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void operator()(var*) {}
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void operator()(app*) {}
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void operator()(quantifier* q) { m_q = q; }
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};
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}
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static quantifier* find_quantifier(expr* n) {
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qe_arith_test::find_q_proc p;
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for_each_expr(p, n);
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return p.m_q;
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}
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static void test_qe_lite_bv_eq_cases() {
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ast_manager m;
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reg_decl_plugins(m);
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expr_ref fml = parse_smt2_assertion(m, R"(
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(set-logic BV)
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(declare-const cv1 (_ BitVec 1))
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(assert
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(exists ((x (_ BitVec 48)) (y (_ BitVec 9)))
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(and
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(not (= y (_ bv511 9)))
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(not (= x (_ bv1 48)))
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(not (and (= x (_ bv1 48)) (= cv1 (_ bv1 1))))
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(not (and (= x (_ bv1 48)) (not (= cv1 (_ bv1 1))))))))
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)");
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expr_ref original(fml, m);
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qe_lite qel(m, params_ref());
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proof_ref pr(m);
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qel(fml, pr);
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VERIFY(find_quantifier(fml) == nullptr);
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smt_params params;
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smt::context ctx(m, params);
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ctx.assert_expr(m.mk_not(m.mk_iff(original, fml)));
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VERIFY(ctx.check() == l_false);
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}
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static char const* example1 = "(and (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
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static char const* example2 = "(and (<= z x) (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
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static char const* example3 = "(and (<= z x) (<= x 3.0) (< (* 3.0 x) y) (<= z y))";
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@ -594,6 +647,7 @@ static void test_project() {
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void tst_qe_arith() {
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test_project();
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test_qe_lite_bv_eq_cases();
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return;
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check_random_ineqs();
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return;
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