Merge pull request #6863 from Z3Prover/nl_branches

split free vars in nla

src/math/lp/lp_settings.h

@@ -115,6 +115,7 @@ struct statistics {
     unsigned m_hnf_cutter_calls;
     unsigned m_hnf_cuts;
     unsigned m_nla_calls;
+    unsigned m_nla_bounds;
     unsigned m_horner_calls;
     unsigned m_horner_conflicts;
     unsigned m_cross_nested_forms;
@@ -144,7 +145,7 @@ struct statistics {
         st.update("arith-grobner-conflicts", m_grobner_conflicts);
         st.update("arith-offset-eqs", m_offset_eqs);
         st.update("arith-fixed-eqs", m_fixed_eqs);
-
+        st.update("arith-nla-bounds", m_nla_bounds);
     }
 };
 

src/math/lp/nla_core.cpp

@@ -809,6 +809,7 @@ void core::print_stats(std::ostream& out) {
 
 void core::clear() {
     m_lemma_vec->clear();
+    m_literal_vec->clear();
 }
     
 void core::init_search() {
@@ -1501,12 +1502,28 @@ void core::check_bounded_divisions(vector<lemma>& l_vec) {
     m_lemma_vec = &l_vec;
     m_divisions.check_bounded_divisions();
 }
+// looking for a free variable inside of a monic to split
+void core::add_bounds() {
+    unsigned r = random(), sz = m_to_refine.size();
+    for (unsigned k = 0; k < sz; k++) {
+        lpvar i = m_to_refine[(k + r) % sz];
+        auto const& m = m_emons[i];
+        for (lpvar j : m.vars()) {
+            if (!var_is_free(j)) continue;
+            // split the free variable (j <= 0, or j > 0), and return
+            m_literal_vec->push_back(ineq(j, lp::lconstraint_kind::EQ, rational::zero()));  
+            ++lp_settings().stats().m_nla_bounds;
+            return;
+        }
+    }    
+}
 
-lbool core::check(vector<lemma>& l_vec) {
+lbool core::check(vector<ineq>& lits, vector<lemma>& l_vec) {
     lp_settings().stats().m_nla_calls++;
     TRACE("nla_solver", tout << "calls = " << lp_settings().stats().m_nla_calls << "\n";);
     lra.get_rid_of_inf_eps();
     m_lemma_vec =  &l_vec;
+    m_literal_vec = &lits;
     if (!(lra.get_status() == lp::lp_status::OPTIMAL || 
           lra.get_status() == lp::lp_status::FEASIBLE)) {
         TRACE("nla_solver", tout << "unknown because of the lra.m_status = " << lra.get_status() << "\n";);
@@ -1516,43 +1533,47 @@ lbool core::check(vector<lemma>& l_vec) {
     init_to_refine();
     patch_monomials();
     set_use_nra_model(false);    
-    if (m_to_refine.empty()) { return l_true; }   
+    if (m_to_refine.empty())
+        return l_true;    
     init_search();
 
     lbool ret = l_undef;
     bool run_grobner = need_run_grobner();
     bool run_horner = need_run_horner();
     bool run_bounded_nlsat = should_run_bounded_nlsat();
+    bool run_bounds = params().arith_nl_branching();    
 
-    if (l_vec.empty() && !done()) 
+    auto no_effect = [&]() { return !done() && l_vec.empty() && lits.empty(); };
+    
+    if (no_effect())
         m_monomial_bounds();
 
     if (l_vec.empty() && !done() && improve_bounds())
         return l_false;
     
-    if (l_vec.empty() && !done() && run_horner) 
+    {
-        m_horner.horner_lemmas();
+        std::function<void(void)> check1 = [&]() { if (no_effect() && run_horner) m_horner.horner_lemmas(); };
+        std::function<void(void)> check2 = [&]() { if (no_effect() && run_grobner) m_grobner(); };
+        std::function<void(void)> check3 = [&]() { if (no_effect() && run_bounds) add_bounds(); };
 
-    if (l_vec.empty() && !done() && run_grobner) 
+        std::pair<unsigned, std::function<void(void)>> checks[] =
-        m_grobner();                
+            { {1, check1},
-
+              {1, check2},
-    if (l_vec.empty() && !done()) 
+              {1, check3} };
+        check_weighted(3, checks);
+        if (!l_vec.empty() || !lits.empty())
+            return l_false;
+    }
+                
+    if (no_effect()) 
         m_basics.basic_lemma(true); 
 
-    if (l_vec.empty() && !done()) 
+    if (no_effect()) 
         m_basics.basic_lemma(false);
 
-    if (l_vec.empty() && !done())
+    if (no_effect()) 
         m_divisions.check();
     
-#if 0
-    if (l_vec.empty() && !done() && !run_horner) 
-        m_horner.horner_lemmas();
-
-    if (l_vec.empty() && !done() && !run_grobner) 
-        m_grobner();                    
-#endif
-
     if (!conflict_found() && !done() && run_bounded_nlsat)
         ret = bounded_nlsat();
 
@@ -1636,8 +1657,9 @@ bool core::no_lemmas_hold() const {
 }
     
 lbool core::test_check(vector<lemma>& l) {
+    vector<ineq> lits;
     lra.set_status(lp::lp_status::OPTIMAL);
-    return check(l);
+    return check(lits, l);
 }
 
 std::ostream& core::print_terms(std::ostream& out) const {

src/math/lp/nla_core.h

@@ -85,6 +85,7 @@ class core {
     smt_params_helper        m_params;
     std::function<bool(lpvar)> m_relevant;
     vector<lemma> *          m_lemma_vec;
+    vector<ineq> *           m_literal_vec = nullptr;
     indexed_uint_set                m_to_refine;
     tangents                 m_tangents;
     basics                   m_basics;
@@ -110,7 +111,7 @@ class core {
     monic const*             m_patched_monic = nullptr;      
 
     void check_weighted(unsigned sz, std::pair<unsigned, std::function<void(void)>>* checks);
-
+    void add_bounds();
     // try to improve bounds for variables in monomials.
     bool improve_bounds();
 
@@ -384,7 +385,7 @@ public:
 
     bool  conflict_found() const;
     
-    lbool check(vector<lemma>& l_vec);
+    lbool check(vector<ineq>& ineqs, vector<lemma>& l_vec);
     lbool check_power(lpvar r, lpvar x, lpvar y, vector<lemma>& l_vec);
     void check_bounded_divisions(vector<lemma>&);
 

src/math/lp/nla_solver.cpp

@@ -42,8 +42,8 @@ namespace nla {
     
     bool solver::need_check() { return m_core->has_relevant_monomial(); }
     
-    lbool solver::check(vector<lemma>& l) {
+    lbool solver::check(vector<ineq>& lits, vector<lemma>& lemmas) {
-        return m_core->check(l);
+        return m_core->check(lits, lemmas);
     }
     
     void solver::push(){

src/math/lp/nla_solver.h

@@ -36,7 +36,7 @@ namespace nla {
         void push();
         void pop(unsigned scopes);
         bool need_check();
-        lbool check(vector<lemma>&);
+        lbool check(vector<ineq>& lits, vector<lemma>&);
         lbool check_power(lpvar r, lpvar x, lpvar y, vector<lemma>&);
         bool is_monic_var(lpvar) const;
         bool influences_nl_var(lpvar) const;

src/sat/smt/arith_solver.cpp

@@ -1410,30 +1410,43 @@ namespace arith {
         m_lemma = l; //todo avoid the copy
         m_explanation = l.expl();
         literal_vector core;
-        for (auto const& ineq : m_lemma.ineqs()) {
+        for (auto const& ineq : m_lemma.ineqs()) 
-            bool is_lower = true, pos = true, is_eq = false;
+            core.push_back(mk_ineq_literal(ineq));
-            switch (ineq.cmp()) {
-            case lp::LE: is_lower = false; pos = false; break;
-            case lp::LT: is_lower = true;  pos = true;  break;
-            case lp::GE: is_lower = true;  pos = false; break;
-            case lp::GT: is_lower = false; pos = true;  break;
-            case lp::EQ: is_eq = true;     pos = false; break;
-            case lp::NE: is_eq = true;     pos = true;  break;
-            default: UNREACHABLE();
-            }
-            TRACE("arith", tout << "is_lower: " << is_lower << " pos " << pos << "\n";);
-            // TBD utility: lp::lar_term term = mk_term(ineq.m_poly);
-            // then term is used instead of ineq.m_term
-            sat::literal lit;
-            if (is_eq) 
-                lit = mk_eq(ineq.term(), ineq.rs());
-            else 
-                lit = ctx.expr2literal(mk_bound(ineq.term(), ineq.rs(), is_lower));
-            core.push_back(pos ? lit : ~lit);
-        }
         set_conflict_or_lemma(hint_type::nla_h, core, false);
     }
 
+    void solver::assume_literals() {
+        for (auto const& ineq : m_nla_literals) {
+            auto lit = mk_ineq_literal(ineq);
+            ctx.mark_relevant(lit);
+            s().set_phase(lit);
+        }
+    }
+    
+    sat::literal solver::mk_ineq_literal(nla::ineq const& ineq) {
+        bool is_lower = true, pos = true, is_eq = false;
+        switch (ineq.cmp()) {
+        case lp::LE: is_lower = false; pos = false; break;
+        case lp::LT: is_lower = true;  pos = true;  break;
+        case lp::GE: is_lower = true;  pos = false; break;
+        case lp::GT: is_lower = false; pos = true;  break;
+        case lp::EQ: is_eq = true;     pos = false; break;
+        case lp::NE: is_eq = true;     pos = true;  break;
+        default: UNREACHABLE();
+        }
+        TRACE("arith", tout << "is_lower: " << is_lower << " pos " << pos << "\n";);
+        // TBD utility: lp::lar_term term = mk_term(ineq.m_poly);
+        // then term is used instead of ineq.m_term
+        sat::literal lit;
+        if (is_eq) 
+            lit = mk_eq(ineq.term(), ineq.rs());
+        else 
+            lit = ctx.expr2literal(mk_bound(ineq.term(), ineq.rs(), is_lower));
+
+        return pos ? lit : ~lit;                                            
+    }
+
+
     lbool solver::check_nla() {
         if (!m.inc()) {
             TRACE("arith", tout << "canceled\n";);
@@ -1446,9 +1459,10 @@ namespace arith {
             return l_true;
 
         m_a1 = nullptr; m_a2 = nullptr;
-        lbool r = m_nla->check(m_nla_lemma_vector);
+        lbool r = m_nla->check(m_nla_literals, m_nla_lemma_vector);
         switch (r) {
-        case l_false: 
+        case l_false:
+            assume_literals();
             for (const nla::lemma& l : m_nla_lemma_vector)
                 false_case_of_check_nla(l);
             break;

src/sat/smt/arith_solver.h

@@ -249,6 +249,7 @@ namespace arith {
         // lemmas
         lp::explanation     m_explanation;
         vector<nla::lemma>  m_nla_lemma_vector;
+        vector<nla::ineq>   m_nla_literals;
         literal_vector      m_core, m_core2;
         vector<rational>    m_coeffs;
         svector<enode_pair> m_eqs;
@@ -463,6 +464,8 @@ namespace arith {
         void set_evidence(lp::constraint_index idx);
         void assign(literal lit, literal_vector const& core, svector<enode_pair> const& eqs, euf::th_proof_hint const* pma);
 
+        void assume_literals();
+        sat::literal mk_ineq_literal(nla::ineq const& ineq);
         void false_case_of_check_nla(const nla::lemma& l);        
         void dbg_finalize_model(model& mdl);
 

src/smt/theory_lra.cpp

@@ -1979,44 +1979,55 @@ public:
     }
 
     nla::lemma m_lemma;
- 
+
+    literal mk_literal(nla::ineq const& ineq) {
+        bool is_lower = true, pos = true, is_eq = false;
+        switch (ineq.cmp()) {
+        case lp::LE: is_lower = false; pos = false;  break;
+        case lp::LT: is_lower = true;  pos = true; break;
+        case lp::GE: is_lower = true;  pos = false;  break;
+        case lp::GT: is_lower = false; pos = true; break;
+        case lp::EQ: is_eq = true; pos = false; break;
+        case lp::NE: is_eq = true; pos = true; break;
+        default: UNREACHABLE();
+        }
+        TRACE("arith", tout << "is_lower: " << is_lower << " pos " << pos << "\n";);
+        app_ref atom(m);
+        // TBD utility: lp::lar_term term = mk_term(ineq.m_poly);
+        // then term is used instead of ineq.m_term
+        if (is_eq) 
+            atom = mk_eq(ineq.term(), ineq.rs());
+        else 
+            // create term >= 0 (or term <= 0)
+            atom = mk_bound(ineq.term(), ineq.rs(), is_lower);
+        return literal(ctx().get_bool_var(atom), pos);
+    }
+
     void false_case_of_check_nla(const nla::lemma & l) {
         m_lemma = l; //todo avoid the copy
         m_explanation = l.expl();
         literal_vector core;
         for (auto const& ineq : m_lemma.ineqs()) {
-            bool is_lower = true, pos = true, is_eq = false;
+            auto lit = mk_literal(ineq);
-            switch (ineq.cmp()) {
-            case lp::LE: is_lower = false; pos = false;  break;
-            case lp::LT: is_lower = true;  pos = true; break;
-            case lp::GE: is_lower = true;  pos = false;  break;
-            case lp::GT: is_lower = false; pos = true; break;
-            case lp::EQ: is_eq = true; pos = false; break;
-            case lp::NE: is_eq = true; pos = true; break;
-            default: UNREACHABLE();
-            }
-            TRACE("arith", tout << "is_lower: " << is_lower << " pos " << pos << "\n";);
-            app_ref atom(m);
-            // TBD utility: lp::lar_term term = mk_term(ineq.m_poly);
-            // then term is used instead of ineq.m_term
-            if (is_eq) {
-                atom = mk_eq(ineq.term(), ineq.rs());
-            }
-            else {
-                // create term >= 0 (or term <= 0)
-                atom = mk_bound(ineq.term(), ineq.rs(), is_lower);
-            }
-            literal lit(ctx().get_bool_var(atom), pos);
             core.push_back(~lit);
         }
         set_conflict_or_lemma(core, false);
     }
+
+    void assume_literal(nla::ineq const& i) {
+        auto lit = mk_literal(i);
+        ctx().mark_as_relevant(lit);
+        ctx().set_true_first_flag(lit.var());
+    }
     
     final_check_status check_nla_continue() {
         m_a1 = nullptr; m_a2 = nullptr;
-        lbool r = m_nla->check(m_nla_lemma_vector);
+        lbool r = m_nla->check(m_nla_literals, m_nla_lemma_vector);
+
         switch (r) {
-        case l_false: 
+        case l_false:
+            for (const nla::ineq& i : m_nla_literals)
+                assume_literal(i); 
             for (const nla::lemma & l : m_nla_lemma_vector) 
                 false_case_of_check_nla(l);
             return FC_CONTINUE;
@@ -3173,6 +3184,7 @@ public:
  
     lp::explanation     m_explanation;
     vector<nla::lemma>  m_nla_lemma_vector;
+    vector<nla::ineq>       m_nla_literals;
     literal_vector      m_core;
     svector<enode_pair> m_eqs;
     vector<parameter>   m_params;