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https://github.com/Z3Prover/z3
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add sorting-based pb encoding in the style of minisat+
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
c347018cb8
commit
dc588b54f7
3 changed files with 263 additions and 88 deletions
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@ -96,10 +96,10 @@ struct pb2bv_rewriter::imp {
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case l_undef: tout << "= "; break;
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case l_false: tout << ">= "; break;
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}
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tout << m_k << "\n";);
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tout << k << "\n";);
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if (k.is_zero()) {
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if (is_le != l_false) {
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return expr_ref(m.mk_not(mk_or(m, sz, args)), m);
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return expr_ref(m.mk_not(::mk_or(m, sz, args)), m);
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}
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else {
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return expr_ref(m.mk_true(), m);
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@ -108,6 +108,15 @@ struct pb2bv_rewriter::imp {
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if (k.is_neg()) {
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return expr_ref((is_le == l_false)?m.mk_true():m.mk_false(), m);
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}
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expr_ref result(m);
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switch (is_le) {
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case l_true: if (mk_le(sz, args, k, result)) return result; else break;
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case l_false: if (mk_ge(sz, args, k, result)) return result; else break;
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case l_undef: if (mk_eq(sz, args, k, result)) return result; else break;
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}
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// fall back to divide and conquer encoding.
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SASSERT(k.is_pos());
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expr_ref zero(m), bound(m);
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expr_ref_vector es(m), fmls(m);
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@ -139,12 +148,12 @@ struct pb2bv_rewriter::imp {
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}
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switch (is_le) {
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case l_true:
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return mk_and(fmls);
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return ::mk_and(fmls);
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case l_false:
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if (!es.empty()) {
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fmls.push_back(bv.mk_ule(bound, es.back()));
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}
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return mk_or(fmls);
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return ::mk_or(fmls);
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case l_undef:
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if (es.empty()) {
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fmls.push_back(m.mk_bool_val(k.is_zero()));
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@ -152,13 +161,180 @@ struct pb2bv_rewriter::imp {
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else {
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fmls.push_back(m.mk_eq(bound, es.back()));
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}
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return mk_and(fmls);
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return ::mk_and(fmls);
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default:
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UNREACHABLE();
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return expr_ref(m.mk_true(), m);
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}
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}
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/**
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\brief MiniSat+ based encoding of PB constraints.
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The procedure is described in "Translating Pseudo-Boolean Constraints into SAT "
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Niklas Een, Niklas Sörensson, JSAT 2006.
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*/
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const unsigned primes[7] = { 2, 3, 5, 7, 11, 13, 17};
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vector<rational> m_min_base;
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rational m_min_cost;
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vector<rational> m_base;
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void create_basis(vector<rational> const& seq, rational carry_in, rational cost) {
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if (cost >= m_min_cost) {
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return;
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}
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rational delta_cost(0);
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for (unsigned i = 0; i < seq.size(); ++i) {
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delta_cost += seq[i];
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}
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if (cost + delta_cost < m_min_cost) {
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m_min_cost = cost + delta_cost;
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m_min_base = m_base;
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m_min_base.push_back(delta_cost + rational::one());
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}
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for (unsigned i = 0; i < sizeof(primes)/sizeof(*primes); ++i) {
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vector<rational> seq1;
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rational p(primes[i]);
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rational rest = carry_in;
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// create seq1
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for (unsigned j = 0; j < seq.size(); ++j) {
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rest += seq[j] % p;
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if (seq[j] >= p) {
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seq1.push_back(div(seq[j], p));
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}
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}
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m_base.push_back(p);
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create_basis(seq1, div(rest, p), cost + rest);
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m_base.pop_back();
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}
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}
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bool create_basis() {
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m_base.reset();
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m_min_cost = rational(INT_MAX);
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m_min_base.reset();
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rational cost(0);
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create_basis(m_coeffs, rational::zero(), cost);
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m_base = m_min_base;
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TRACE("pb",
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tout << "Base: ";
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for (unsigned i = 0; i < m_base.size(); ++i) {
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tout << m_base[i] << " ";
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}
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tout << "\n";);
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return
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!m_base.empty() &&
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m_base.back().is_unsigned() &&
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m_base.back().get_unsigned() <= 20*m_base.size();
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}
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/**
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\brief Check if 'out mod n >= lim'.
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*/
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expr_ref mod_ge(ptr_vector<expr> const& out, unsigned n, unsigned lim) {
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TRACE("pb", for (unsigned i = 0; i < out.size(); ++i) tout << mk_pp(out[i], m) << " "; tout << "\n";
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tout << "n:" << n << " lim: " << lim << "\n";);
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if (lim == n) {
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return expr_ref(m.mk_false(), m);
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}
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if (lim == 0) {
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return expr_ref(m.mk_true(), m);
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}
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SASSERT(0 < lim && lim < n);
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expr_ref_vector ors(m);
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for (unsigned j = 0; j + lim - 1 < out.size(); j += n) {
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expr_ref tmp(m);
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tmp = out[j + lim - 1];
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if (j + n < out.size()) {
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tmp = m.mk_and(tmp, m.mk_not(out[j + n]));
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}
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ors.push_back(tmp);
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}
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return ::mk_or(ors);
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}
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bool mk_ge(unsigned sz, expr * const* args, rational bound, expr_ref& result) {
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if (!create_basis()) return false;
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if (!bound.is_unsigned()) return false;
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vector<rational> coeffs(m_coeffs);
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result = m.mk_true();
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expr_ref_vector carry(m), new_carry(m);
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for (unsigned i = 0; i < m_base.size(); ++i) {
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rational b_i = m_base[i];
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unsigned B = b_i.get_unsigned();
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unsigned d_i = (bound % b_i).get_unsigned();
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bound = div(bound, b_i);
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for (unsigned j = 0; j < coeffs.size(); ++j) {
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rational c = coeffs[j] % b_i;
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SASSERT(c.is_unsigned());
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for (unsigned k = 0; k < c.get_unsigned(); ++k) {
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carry.push_back(args[j]);
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}
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coeffs[j] = div(coeffs[j], b_i);
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}
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TRACE("pb", tout << "Carry: " << carry << "\n";
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for (unsigned j = 0; j < coeffs.size(); ++j) tout << coeffs[j] << " ";
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tout << "\n";
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);
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ptr_vector<expr> out;
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m_sort.sorting(carry.size(), carry.c_ptr(), out);
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expr_ref gt = mod_ge(out, B, d_i + 1);
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expr_ref ge = mod_ge(out, B, d_i);
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result = mk_or(gt, mk_and(ge, result));
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TRACE("pb", tout << result << "\n";);
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new_carry.reset();
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for (unsigned j = B - 1; j < out.size(); j += B) {
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new_carry.push_back(out[j]);
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}
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carry.reset();
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carry.append(new_carry);
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}
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TRACE("pb", tout << result << "\n";);
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return true;
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}
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expr_ref mk_and(expr_ref& a, expr_ref& b) {
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if (m.is_true(a)) return b;
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if (m.is_true(b)) return a;
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if (m.is_false(a)) return a;
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if (m.is_false(b)) return b;
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return expr_ref(m.mk_and(a, b), m);
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}
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expr_ref mk_or(expr_ref& a, expr_ref& b) {
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if (m.is_true(a)) return a;
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if (m.is_true(b)) return b;
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if (m.is_false(a)) return b;
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if (m.is_false(b)) return a;
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return expr_ref(m.mk_or(a, b), m);
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}
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bool mk_le(unsigned sz, expr * const* args, rational const& k, expr_ref& result) {
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expr_ref_vector args1(m);
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rational bound(-k);
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for (unsigned i = 0; i < sz; ++i) {
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args1.push_back(mk_not(args[i]));
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bound += m_coeffs[i];
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}
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return mk_ge(sz, args1.c_ptr(), bound, result);
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}
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bool mk_eq(unsigned sz, expr * const* args, rational const& k, expr_ref& result) {
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expr_ref r1(m), r2(m);
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if (mk_ge(sz, args, k, r1) && mk_le(sz, args, k, r2)) {
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result = m.mk_and(r1, r2);
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return true;
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}
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else {
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return false;
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}
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}
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expr_ref mk_bv(func_decl * f, unsigned sz, expr * const* args) {
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decl_kind kind = f->get_decl_kind();
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rational k = pb.get_k(f);
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@ -403,7 +579,7 @@ struct pb2bv_rewriter::imp {
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}
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void mk_clause(unsigned n, literal const* lits) {
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m_imp.m_lemmas.push_back(mk_or(m, n, lits));
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m_imp.m_lemmas.push_back(::mk_or(m, n, lits));
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}
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void keep_cardinality_constraints(bool f) {
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