diff --git a/src/math/lp/nla_mul_saturate.cpp b/src/math/lp/nla_mul_saturate.cpp
deleted file mode 100644
index e41f4491d..000000000
--- a/src/math/lp/nla_mul_saturate.cpp
+++ /dev/null
@@ -1,383 +0,0 @@
-/*++
-  Copyright (c) 2025 Microsoft Corporation
-
-  given a monic m = x * y * z ... with evaluation val(m) != val(x) * val(y) * val(z) ...
-
-  saturate constraints with respect to m
-  in other words, if a constraint contains x*y + p >= 0, 
-  then include the constraint z >= 0 => x*y*z + z*p >= 0
-  assuming current value of z is non-negative.
-  Check if the system with new constraints is LP feasible.
-  If it is not, then produce a lemma that explains the infeasibility.
-
-  Strategy 1: The lemma is in terms of the original constraints and bounds.
-  Strategy 2: Attempt to eliminate new monomials from the lemma by relying on Farkas multipliers.
-              If it succeeds to eliminate new monomials we have a lemma that is a linear 
-              combination of existing variables. 
-  Strategy 3: The lemma uses the new constraints.
-
-  --*/
-
-#include "math/lp/nla_core.h"
-#include "math/lp/nla_coi.h"
-#include "math/lp/nla_mul_saturate.h"
-
-
-namespace nla {
-
-    mul_saturate::mul_saturate(core* core) : common(core), m_coi(*core) {}
-
-    lbool mul_saturate::saturate() {
-        lp::explanation ex;
-        init_solver();
-        add_multiply_constraints();
-        lbool r = solve(ex);
-        if (r == l_false)
-            add_lemma(ex);
-        return r;
-    }
-
-    void mul_saturate::init_solver() {
-        local_solver = alloc(lp::lar_solver);
-        m_vars2mon.reset();
-        m_mon2vars.reset();
-        m_values.reset();
-        m_coi.init();
-        init_vars();
-    }
-
-    void mul_saturate::init_vars() {
-        auto const& lra = c().lra_solver();
-        auto sz = lra.number_of_vars();
-        for (unsigned v = 0; v < sz; ++v) {
-            unsigned w;
-            if (m_coi.mons().contains(v))
-                init_monomial(v);
-            else 
-                m_values.push_back(c().val(v));
-            if (m_coi.terms().contains(v)) {
-                auto const& t = lra.get_term(v);
-                // Assumption: variables in coefficients are always declared before term variable.
-                SASSERT(all_of(t, [&](auto p) { return p.j() < v; }));
-                w = local_solver->add_term(t.coeffs_as_vector(), v);
-            } 
-            else
-                w = local_solver->add_var(v, lra.var_is_int(v));
-
-            VERIFY(w == v);
-            if (lra.column_has_lower_bound(v)) {
-                auto lo_dep = lra.get_column_lower_bound_witness(v);
-                auto lo_bound = lra.get_lower_bound(v);
-                auto k = lo_bound.y > 0 ? lp::lconstraint_kind::GT : lp::lconstraint_kind::GE;
-                auto ci = local_solver->add_var_bound(v, k, lo_bound.x);
-            }
-            if (lra.column_has_upper_bound(v)) {
-                auto hi_dep = lra.get_column_upper_bound_witness(v);
-                auto hi_bound = lra.get_upper_bound(v);
-                auto k = hi_bound.y < 0 ? lp::lconstraint_kind::LT : lp::lconstraint_kind::LE;
-                auto ci = local_solver->add_var_bound(v, k, hi_bound.x);
-                m_ci2dep.setx(ci, hi_dep, nullptr);
-            }
-        }
-    }
-
-    void mul_saturate::init_monomial(unsigned mon_var) {
-        auto& mon = c().emons()[mon_var];
-        svector<lpvar> vars(mon.vars());
-        std::sort(vars.begin(), vars.end());
-        m_vars2mon.insert(vars, mon_var);
-        m_mon2vars.insert(mon_var, vars);
-        rational p(1);
-        for (auto v : vars)
-            p *= m_values[v];
-        m_values.push_back(p);
-    }
-
-    void mul_saturate::add_lemma(lp::explanation const& ex1) {
-        auto& lra = c().lra_solver();
-        lp::explanation ex2;
-        for (auto p : ex1) {
-            lp::constraint_index src_ci;
-            if (!m_new_mul_constraints.find(p.ci(), src_ci))
-                src_ci = p.ci();
-            auto dep = m_ci2dep.get(src_ci, nullptr);
-            local_solver->push_explanation(dep, ex2);
-        }
-        for (auto [v, sign, dep] : m_var_signs) {            
-            if (!dep) {
-                verbose_stream() << "TODO explain non-implied bound\n";
-                continue;
-            }
-            local_solver->push_explanation(dep, ex2);
-        }
-        lemma_builder new_lemma(c(), "stellensatz");
-        new_lemma &= ex2;
-        IF_VERBOSE(1, verbose_stream() << "unsat \n" << new_lemma << "\n");
-        TRACE(arith, tout << "unsat\n" << new_lemma << "\n");
-    }
-
-    lbool mul_saturate::solve(lp::explanation& ex) {
-        for (auto const& [new_ci, old_ci] : m_new_mul_constraints)
-            local_solver->activate(new_ci);
-        auto st = local_solver->solve();
-        lbool r = l_undef;
-        if (st == lp::lp_status::INFEASIBLE) {
-            local_solver->get_infeasibility_explanation(ex);
-            r = l_false;
-        }
-        if (st == lp::lp_status::OPTIMAL || st == lp::lp_status::FEASIBLE) {
-            // TODO: check model just in case it got lucky.
-            IF_VERBOSE(1, verbose_stream() << "saturation is LP feasible, maybe it is a model of the NLA problem\n");
-        }
-        IF_VERBOSE(0, display(verbose_stream()));
-        return r;
-    }
-
-    // record new monomials that are created and recursively down-saturate with respect to these.
-    // this is a simplistic pass
-    void mul_saturate::add_multiply_constraints() {
-        m_new_mul_constraints.reset();
-        m_seen_vars.reset();
-        m_var_signs.reset();
-        m_to_refine.reset();
-        vector<svector<lp::constraint_index>> var2cs;
-
-        for (auto ci : local_solver->constraints().indices()) {
-            auto const& con = local_solver->constraints()[ci];
-            for (auto [coeff, v] : con.coeffs()) {
-                if (v >= var2cs.size())
-                    var2cs.resize(v + 1);
-                var2cs[v].push_back(ci);
-            }
-
-            // insert monomials to be refined
-            insert_monomials_from_constraint(ci);            
-        }
-
-        for (unsigned it = 0; it < m_to_refine.size(); ++it) {
-            auto j = m_to_refine[it];
-            verbose_stream() << "refining " << j << " := " << m_mon2vars[j] << "\n";
-            auto vars = m_mon2vars[j];
-            for (auto v : vars) {
-                if (v >= var2cs.size())
-                    continue;
-                auto cs = var2cs[v];
-                for (auto ci : cs) {
-                    for (auto [coeff, u] : local_solver->constraints()[ci].coeffs()) {
-                        if (u == v)
-                            add_multiply_constraint(ci, j, v);
-                    }                    
-                }
-            }
-        }
-        IF_VERBOSE(0,
-                   c().lra_solver().display(verbose_stream() << "original\n");
-                   c().display(verbose_stream());
-                   display(verbose_stream() << "saturated\n"));
-    }
-
-    // multiply by remaining vars
-    void mul_saturate::add_multiply_constraint(lp::constraint_index old_ci, lp::lpvar mi, lpvar x) {
-        lp::lar_base_constraint const& con = local_solver->constraints()[old_ci];
-        auto &lra = c().lra_solver();
-        auto const& lhs = con.coeffs();
-        auto const& rhs = con.rhs();
-        auto k = con.kind();
-        if (k == lp::lconstraint_kind::NE || k == lp::lconstraint_kind::EQ)
-            return;  // not supported
-        auto sign = false;
-        svector<lpvar> vars;
-        bool first = true;
-        for (auto v : c().emon(mi).vars()) {
-            if (v != x || !first)
-                vars.push_back(v);
-            else
-                first = false;
-        }
-        // compute sign of vars
-        for (auto v : vars) {
-            if (m_seen_vars.contains(v))
-                continue;
-            m_seen_vars.insert(v);
-            // retrieve bounds of v
-            // if v has positive lower bound add as positive
-            // if v has negative upper bound add as negative
-            // otherwise, soft-fail (for now unsound)
-            // proper signs of variables from old tableau should be extracted using lra_solver()
-            // instead of local_solver.
-            // TODO is to also add case where lower or upper bound is zero and then the sign
-            // of the inequality is relaxed if it is strict.
-            if (lra.number_of_vars() > v && lra.column_has_lower_bound(v) && lra.get_lower_bound(v).is_pos()) {
-                m_var_signs.push_back({v, false, lra.get_column_lower_bound_witness(v)});
-            } 
-            else if (lra.number_of_vars() > v && lra.column_has_upper_bound(v) && lra.get_upper_bound(v).is_neg()) {
-                m_var_signs.push_back({v, true, lra.get_column_upper_bound_witness(v)});
-                sign = !sign;
-            } 
-            else if (m_values[v].is_neg()) {
-                m_var_signs.push_back({v, true, nullptr});
-                sign = !sign;
-            } 
-            else if (m_values[v].is_pos()) {
-                m_var_signs.push_back({v, false, nullptr});
-            } 
-            else {
-                IF_VERBOSE(0, verbose_stream() << "not separated from 0\n");
-                return;
-            }
-        }
-        lp::lar_term new_lhs;
-        rational new_rhs(rhs), term_value(0);
-        for (auto const & [coeff, v] : lhs) {
-            unsigned old_sz = vars.size();
-            if (m_mon2vars.contains(v))
-                vars.append(m_mon2vars[v]);
-            else
-                vars.push_back(v);
-            lpvar new_monic_var = add_monomial(vars);
-            new_lhs.add_monomial(coeff, new_monic_var);
-            term_value += coeff * m_values[new_monic_var];
-            vars.shrink(old_sz);
-        }
-        if (rhs != 0) {
-            lpvar new_monic_var = add_monomial(vars);
-            new_lhs.add_monomial(-rhs, new_monic_var);
-            term_value -= rhs * m_values[new_monic_var];
-            new_rhs = 0;
-        }
-
-        if (sign) {
-            switch (k) {
-            case lp::lconstraint_kind::LE:
-                k = lp::lconstraint_kind::GE;
-                break;
-            case lp::lconstraint_kind::LT:
-                k = lp::lconstraint_kind::GT;
-                break;
-            case lp::lconstraint_kind::GE:
-                k = lp::lconstraint_kind::LE;
-                break;
-            case lp::lconstraint_kind::GT:
-                k = lp::lconstraint_kind::LT;
-                break;
-            default:
-                break;
-            }
-        }
-        display_constraint(verbose_stream(), old_ci) << " -> ";
-        display_constraint(verbose_stream(), new_lhs.coeffs_as_vector(), k, new_rhs) << "\n";
-        auto ti = local_solver->add_term(new_lhs.coeffs_as_vector(), local_solver->number_of_vars());
-        auto new_ci = local_solver->add_var_bound(ti, k, new_rhs);
-        insert_monomials_from_constraint(new_ci);
-        m_values.push_back(term_value);
-        SASSERT(m_values.size() - 1 == ti);
-        m_new_mul_constraints.insert(new_ci, old_ci);
-    }
-
-    lpvar mul_saturate::add_monomial(svector<lpvar> const& vars) {
-        lpvar v;
-        if (vars.size() == 1)
-            return vars[0];
-        svector<lpvar> _vars(vars);
-        std::sort(_vars.begin(), _vars.end());
-        if (m_vars2mon.find(_vars, v))
-            return v;
-
-        v = add_var(is_int(vars));
-        m_vars2mon.insert(_vars, v);
-        m_mon2vars.insert(v, _vars);
-        rational p(1);
-        for (auto v : vars)
-            p *= m_values[v];
-        m_values.push_back(p);
-        SASSERT(m_values.size() - 1 == v);
-        return v;
-    }
-
-    bool mul_saturate::is_int(svector<lp::lpvar> const& vars) const {
-        auto const& lra = m_core.lra;
-        return all_of(vars, [&](lpvar v) { return lra.var_is_int(v); });
-    }
-
-    lpvar mul_saturate::add_var(bool is_int) {
-        auto v = local_solver->number_of_vars();
-        auto w = local_solver->add_var(v, is_int);
-        VERIFY(v == w);
-        return w;
-    }
-
-    void mul_saturate::insert_monomials_from_constraint(lp::constraint_index ci) {
-        if (constraint_is_true(ci))
-            return;
-        auto const& con = local_solver->constraints()[ci];
-        for (auto [coeff, v] : con.coeffs()) 
-            if (c().is_monic_var(v))
-                m_to_refine.insert(v);        
-    }
-
-    bool mul_saturate::constraint_is_true(lp::constraint_index ci) {
-        auto const& con = local_solver->constraints()[ci];
-        auto lhs = -con.rhs();
-        for (auto const& [coeff, v] : con.coeffs())
-            lhs += coeff * m_values[v];
-        switch (con.kind()) {
-            case lp::lconstraint_kind::GT:
-                return lhs > 0;
-            case lp::lconstraint_kind::GE:
-                return lhs >= 0;
-            case lp::lconstraint_kind::LE:
-                return lhs <= 0;
-            case lp::lconstraint_kind::LT:
-                return lhs < 0;
-            case lp::lconstraint_kind::EQ:
-                return lhs == 0;
-            case lp::lconstraint_kind::NE:
-                return lhs != 0;
-            default:
-                UNREACHABLE();
-                return false;        
-        }
-    }
-
-    std::ostream& mul_saturate::display(std::ostream& out) const {
-        local_solver->display(out);
-        for (auto const& [vars, v] : m_vars2mon) {
-            out << "j" << v << " := ";
-            display_product(out, vars);
-            out << "\n";
-        }
-        return out;
-    }
-
-    std::ostream& mul_saturate::display_product(std::ostream& out, svector<lpvar> const& vars) const {
-        bool first = true;
-        for (auto v : vars) {
-            if (first)
-                first = false;
-            else
-                out << " * ";
-            out << "j" << v;
-        }
-        return out;
-    }
-
-    std::ostream& mul_saturate::display_constraint(std::ostream& out, lp::constraint_index ci) const {
-        auto const& con = local_solver->constraints()[ci];
-        return display_constraint(out, con.coeffs(), con.kind(), con.rhs());
-    }
-
-    std::ostream& mul_saturate::display_constraint(std::ostream& out, 
-        vector<std::pair<rational, lpvar>> const& lhs,
-        lp::lconstraint_kind k, rational const& rhs) const {
-        bool first = true;
-        for (auto [coeff, v] : lhs) {
-            c().display_coeff(out, first, coeff);
-            first = false;
-            if (m_mon2vars.contains(v))
-                display_product(out, m_mon2vars[v]);
-            else
-                out << "j" << v;
-        }
-        return out << " " << k << " " << rhs;
-    }
-}
diff --git a/src/math/lp/nla_mul_saturate.h b/src/math/lp/nla_mul_saturate.h
deleted file mode 100644
index 0c5e09e1f..000000000
--- a/src/math/lp/nla_mul_saturate.h
+++ /dev/null
@@ -1,69 +0,0 @@
-/*++
-  Copyright (c) 2025 Microsoft Corporation
-
-  --*/
-#pragma once
-
-#include "math/lp/nla_coi.h"
-
-namespace nla {
-
-    class core;
-    class lar_solver;    
-    class mul_saturate : common {
-
-        struct var_sign {
-            lpvar v = lp::null_lpvar;
-            bool is_neg = false;
-            u_dependency* dep = nullptr;
-        };
-        coi m_coi;
-        // source of multiplication constraint
-        u_map<lp::constraint_index> m_new_mul_constraints;
-        svector<var_sign> m_var_signs;
-        tracked_uint_set m_seen_vars;
-        indexed_uint_set m_to_refine;
-        scoped_ptr<lp::lar_solver> local_solver;
-        ptr_vector<u_dependency> m_ci2dep;
-        vector<rational> m_values;
-        struct eq {
-            bool operator()(unsigned_vector const& a, unsigned_vector const& b) const {
-                return a == b;
-            }
-        };
-        map<unsigned_vector, unsigned, svector_hash<unsigned_hash>, eq> m_vars2mon;
-        u_map<unsigned_vector> m_mon2vars;
-
-        // initialization
-        void init_solver();
-        void init_vars();
-        void init_monomial(unsigned mon_var);
-
-        bool constraint_is_true(lp::constraint_index ci);
-        void insert_monomials_from_constraint(lp::constraint_index ci);
-
-        // additional variables and monomials and constraints
-        lpvar add_monomial(svector<lp::lpvar> const& vars);
-        bool is_int(svector<lp::lpvar> const& vars) const;
-        lpvar add_var(bool is_int);
-        void add_multiply_constraints();
-        void add_multiply_constraint(lp::constraint_index con_id, lp::lpvar mi, lpvar x);
-
-        // solving
-        lbool solve(lp::explanation& ex);
-
-        // lemmas
-        void add_lemma(lp::explanation const& ex);
-
-        std::ostream& display(std::ostream& out) const;
-        std::ostream& display_product(std::ostream& out, svector<lpvar> const& vars) const;
-        std::ostream& display_constraint(std::ostream& out, lp::constraint_index ci) const;
-        std::ostream& display_constraint(std::ostream& out, vector<std::pair<rational, lpvar>> const& lhs,
-                                         lp::lconstraint_kind k, rational const& rhs) const;
-
-    public:
-        mul_saturate(core* core);
-        lbool saturate();
-    };
-
-}
diff --git a/src/math/lp/nla_stellensatz.cpp b/src/math/lp/nla_stellensatz.cpp
index e0b7a8c89..2b4b0161e 100644
--- a/src/math/lp/nla_stellensatz.cpp
+++ b/src/math/lp/nla_stellensatz.cpp
@@ -46,8 +46,6 @@ namespace nla {
         UNREACHABLE();
         return k1;
     }
-
-
     
     lpvar stellensatz::monomial_factory::mk_monomial(lp::lar_solver &lra, svector<lpvar> const &vars) {
         lpvar v = lp::null_lpvar;
@@ -112,6 +110,7 @@ namespace nla {
         m_constraints.reset();
         m_monomial_factory.reset();
         m_coi.init();
+        m_constraint_index.reset();
         init_vars();
         init_occurs();
     }
@@ -204,8 +203,13 @@ namespace nla {
             k = lp::lconstraint_kind::GE;
             p += rational(1);
         }
+        lp::constraint_index ci = lp::null_ci;
+        if (m_constraint_index.find({p.index(), k}, ci))
+            return ci;
+        ci = m_constraints.size();
         m_constraints.push_back({p, k, j });
-        return m_constraints.size() - 1;
+        m_constraint_index.insert({p.index(), k}, ci);
+        return ci;
     }
 
     // initialize active set of constraints that evaluate to false in the current model
@@ -327,7 +331,7 @@ namespace nla {
                     ci_a = multiply(ci, add_constraint(g_p, lp::lconstraint_kind::GT, aj));
 
                 auto new_ci = add(ci_a, ci_b);
-                if (m_constraints[new_ci].p.degree() < 3)
+                if (m_constraints[new_ci].p.degree() <= 3)
                     init_occurs(new_ci);        
                 TRACE(arith, tout << "eliminate j" << x << ":\n"; 
                     display_constraint(tout << "ci: ", ci) << "\n";
@@ -349,7 +353,7 @@ namespace nla {
                         c().lra_solver().settings().stats().m_nla_stellensatz++;
                         return l_false;
                     }
-                    if (m_constraints[new_ci].p.degree() < 3) {
+                    if (m_constraints[new_ci].p.degree() <= 3 && !m_constraints[new_ci].p.free_vars().contains(x)) {
                         uint_set new_tabu(tabu), fv;
                         for (auto v : new_p.free_vars())
                             fv.insert(v);
diff --git a/src/math/lp/nla_stellensatz.h b/src/math/lp/nla_stellensatz.h
index 0b2ad01b6..c51851a2a 100644
--- a/src/math/lp/nla_stellensatz.h
+++ b/src/math/lp/nla_stellensatz.h
@@ -109,6 +109,22 @@ namespace nla {
         vector<constraint> m_constraints;
         monomial_factory m_monomial_factory;
 
+        struct constraint_key {
+            unsigned pdd;
+            lp::lconstraint_kind k;
+            struct eq {
+                bool operator()(constraint_key const &a, constraint_key const &b) const {
+                    return a.pdd == b.pdd && a.k == b.k;
+                }
+            };
+            struct hash {
+                unsigned operator()(constraint_key const &c) const {
+                    return hash_u_u(c.pdd, static_cast<unsigned>(c.k));
+                }            
+            };
+        };
+        map<constraint_key, lp::constraint_index, constraint_key::hash, constraint_key::eq> m_constraint_index;
+
 
         dd::pdd to_pdd(lpvar v);
         void init_monomial(unsigned mon_var);