diff --git a/src/math/lp/explanation.h b/src/math/lp/explanation.h
index d2e7edc33..b7f721a30 100644
--- a/src/math/lp/explanation.h
+++ b/src/math/lp/explanation.h
@@ -48,6 +48,15 @@ public:
         SASSERT(m_vector.empty());
         m_set.insert(j);
     }
+
+    void remove(constraint_index j) {
+        m_set.remove(j);
+        unsigned i = 0;
+        for (auto& p : m_vector) 
+            if (p.first != j)
+                m_vector[i++] = p;
+        m_vector.shrink(i);
+    }
     
     void add_expl(const explanation& e) {
         if (e.m_vector.empty()) {
diff --git a/src/math/lp/int_solver.cpp b/src/math/lp/int_solver.cpp
index 6c34ce16f..69a9a101c 100644
--- a/src/math/lp/int_solver.cpp
+++ b/src/math/lp/int_solver.cpp
@@ -17,51 +17,29 @@ namespace lp {
 int_solver::patcher::patcher(int_solver& lia):
     lia(lia),
     lra(lia.lra),
-    lrac(lia.lrac),
-    m_num_nbasic_patches(0),
-    m_patch_cost(0),
-    m_next_patch(0),
-    m_delay(0)
+    lrac(lia.lrac)
 {}
 
-bool int_solver::patcher::should_apply() {
-#if 1
-    return true;
-#else
-    if (m_delay == 0) {
-        return true;
-    }
-    --m_delay;
-    return false;
-#endif
-}
-
-lia_move int_solver::patcher::operator()() {
-    return patch_nbasic_columns();
-}
 
 lia_move int_solver::patcher::patch_nbasic_columns() {
     lia.settings().stats().m_patches++;
     lp_assert(lia.is_feasible());
-    m_num_nbasic_patches = 0;
-    m_patch_cost = 0;
-    for (unsigned j : lia.lrac.m_r_nbasis) {
-        patch_nbasic_column(j);
+    m_patch_success = 0;
+    m_patch_fail = 0;
+    unsigned num = lra.A_r().column_count();
+    for (unsigned v = 0; v < num; v++) {
+        if (lia.is_base(v))
+            continue;
+        patch_nbasic_column(v);
     }
+//        for (unsigned j : lia.lrac.m_r_nbasis) 
+//        patch_nbasic_column(j);
     lp_assert(lia.is_feasible());
+    verbose_stream() << "patch " << m_patch_success << " fails " << m_patch_fail << "\n";
     if (!lia.has_inf_int()) {
         lia.settings().stats().m_patches_success++;
-        m_delay = 0;
-        m_next_patch = 0;
         return lia_move::sat;
     }
-    if (m_patch_cost > 0 && m_num_nbasic_patches * 10 < m_patch_cost) {
-        m_delay = std::min(20u, m_next_patch++);
-    }
-    else {
-        m_delay = 0;
-        m_next_patch = 0;
-    }
     return lia_move::undef;
 }
 
@@ -71,10 +49,8 @@ void int_solver::patcher::patch_nbasic_column(unsigned j) {
     impq l, u;
     mpq m;
     bool has_free = lia.get_freedom_interval_for_column(j, inf_l, l, inf_u, u, m);
-    m_patch_cost += lra.A_r().number_of_non_zeroes_in_column(j);
-    if (!has_free) {
+    if (!has_free) 
         return;
-    }
     bool m_is_one = m.is_one();
     bool val_is_int = lia.value_is_int(j);
 
@@ -82,6 +58,7 @@ void int_solver::patcher::patch_nbasic_column(unsigned j) {
     if (val_is_int && (m_is_one || (val.x / m).is_int())) {
         return;
     }
+
     TRACE("patch_int",
           tout << "TARGET j" << j << " -> [";
           if (inf_l) tout << "-oo"; else tout << l;
@@ -89,9 +66,24 @@ void int_solver::patcher::patch_nbasic_column(unsigned j) {
           if (inf_u) tout << "oo"; else tout << u;
           tout << "]";
           tout << ", m: " << m << ", val: " << val << ", is_int: " << lra.column_is_int(j) << "\n";);
+
+#if 0
+    verbose_stream() << "path " << m << " ";
+    if (!inf_l) verbose_stream() << "infl " << l.x << " ";
+    if (!inf_u) verbose_stream() << "infu " << u.x << " ";
+    verbose_stream() << "\n";
     if (m.is_big() || (!inf_l && l.x.is_big()) || (!inf_u && u.x.is_big())) {
         return;
     }
+#endif
+
+    verbose_stream() << "TARGET v" << j << " -> [";
+    if (inf_l) verbose_stream() << "-oo"; else verbose_stream() << ceil(l.x);
+    verbose_stream() << ", ";
+    if (inf_u) verbose_stream() << "oo"; else verbose_stream() << floor(u.x);
+    verbose_stream() << "]";
+    verbose_stream() << ", m: " << m << ", val: " << val << ", is_int: " << lra.column_is_int(j) << "\n";
+
     if (!inf_l) {
         l = impq(m_is_one ? ceil(l) : m * ceil(l / m));
         if (inf_u || l <= u) {
@@ -99,7 +91,8 @@ void int_solver::patcher::patch_nbasic_column(unsigned j) {
             lra.set_value_for_nbasic_column(j, l);
         }
         else {
-            --m_num_nbasic_patches;
+            --m_patch_success;
+            ++m_patch_fail;
             TRACE("patch_int", tout << "not patching " << l << "\n";);
         }
     }
@@ -112,7 +105,7 @@ void int_solver::patcher::patch_nbasic_column(unsigned j) {
         lra.set_value_for_nbasic_column(j, impq(0));
         TRACE("patch_int", tout << "patching with 0\n";);
     }
-    ++m_num_nbasic_patches;
+    ++m_patch_success;
 }
 
 int_solver::int_solver(lar_solver& lar_slv) :
@@ -554,6 +547,7 @@ bool int_solver::shift_var(unsigned j, unsigned range) {
         return false;
     const impq & x = get_value(j);
     // x, the value of j column, might be shifted on a multiple of m
+
     if (inf_l && inf_u) {
         impq new_val = m * impq(random() % (range + 1)) + x;
         lra.set_value_for_nbasic_column(j, new_val);
@@ -570,6 +564,7 @@ bool int_solver::shift_var(unsigned j, unsigned range) {
     if (!inf_l && !inf_u && l >= u)
         return false;
 
+
     if (inf_u) {
         SASSERT(!inf_l);
         impq new_val = x + m * impq(random() % (range + 1));
@@ -640,9 +635,6 @@ int int_solver::select_int_infeasible_var() {
     unsigned n = 0;
     lar_core_solver & lcs = lra.m_mpq_lar_core_solver;
     unsigned prev_usage = 0; // to quiet down the compile
-    unsigned k = 0;
-    unsigned usage;
-    unsigned j;
 
     enum state { small_box, is_small_value,  any_value, not_found };
     state st = not_found;
@@ -650,11 +642,10 @@ int int_solver::select_int_infeasible_var() {
     // 1. small box
     // 2. small value
     // 3. any value
-    for (; k < lra.r_basis().size(); k++) {
-        j = lra.r_basis()[k];
+    for (unsigned j : lra.r_basis()) {
         if (!column_is_int_inf(j))
             continue;
-        usage = lra.usage_in_terms(j);
+        unsigned usage = lra.usage_in_terms(j);
         if (is_boxed(j) && (new_range = lcs.m_r_upper_bounds()[j].x - lcs.m_r_lower_bounds()[j].x - rational(2*usage)) <= small_value) {
             SASSERT(!is_fixed(j));
             if (st != small_box) {
@@ -688,12 +679,12 @@ int int_solver::select_int_infeasible_var() {
             continue;
         SASSERT(st == not_found || st == any_value);
         st = any_value;
-        if (n == 0 /*|| usage > prev_usage*/) {
+        if (n == 0 || usage > prev_usage) {
             result = j;
             prev_usage = usage;
             n = 1;
         } 
-        else if (usage > 0 && /*usage == prev_usage && */ (random() % (++n) == 0)) 
+        else if (usage > 0 && usage == prev_usage && (random() % (++n) == 0)) 
             result = j;
     }
     
diff --git a/src/math/lp/int_solver.h b/src/math/lp/int_solver.h
index 822e1cf1e..7f1807058 100644
--- a/src/math/lp/int_solver.h
+++ b/src/math/lp/int_solver.h
@@ -44,14 +44,12 @@ class int_solver {
         int_solver&         lia;
         lar_solver&         lra;
         lar_core_solver&    lrac;
-        unsigned            m_num_nbasic_patches;
-        unsigned            m_patch_cost;
-        unsigned            m_next_patch;
-        unsigned            m_delay;
+        unsigned            m_patch_success = 0;
+        unsigned            m_patch_fail = 0;
     public:
         patcher(int_solver& lia);
-        bool should_apply();
-        lia_move operator()();
+        bool should_apply() const { return true; }
+        lia_move operator()() { return patch_nbasic_columns(); }
         void patch_nbasic_column(unsigned j);
     private:
         lia_move patch_nbasic_columns();
diff --git a/src/math/lp/lar_core_solver_def.h b/src/math/lp/lar_core_solver_def.h
index 550b6fe36..9512cb397 100644
--- a/src/math/lp/lar_core_solver_def.h
+++ b/src/math/lp/lar_core_solver_def.h
@@ -86,12 +86,12 @@ void lar_core_solver::solve() {
     TRACE("lar_solver", tout << m_r_solver.get_status() << "\n";);
     lp_assert(m_r_solver.non_basic_columns_are_set_correctly());
     lp_assert(m_r_solver.inf_set_is_correct());
-	TRACE("find_feas_stats", tout << "infeasibles = " << m_r_solver.inf_set_size() << ", int_infs = " << get_number_of_non_ints() << std::endl;);
-	if (m_r_solver.current_x_is_feasible() && m_r_solver.m_look_for_feasible_solution_only) {
-            m_r_solver.set_status(lp_status::OPTIMAL);
-            TRACE("lar_solver", tout << m_r_solver.get_status() << "\n";);
-            return;
-	}
+    TRACE("find_feas_stats", tout << "infeasibles = " << m_r_solver.inf_set_size() << ", int_infs = " << get_number_of_non_ints() << std::endl;);
+    if (m_r_solver.current_x_is_feasible() && m_r_solver.m_look_for_feasible_solution_only) {
+        m_r_solver.set_status(lp_status::OPTIMAL);
+        TRACE("lar_solver", tout << m_r_solver.get_status() << "\n";);
+        return;
+    }
     ++settings().stats().m_need_to_solve_inf;
     lp_assert( r_basis_is_OK());
      
diff --git a/src/math/lp/lar_solver.cpp b/src/math/lp/lar_solver.cpp
index 0eb65e197..12033874d 100644
--- a/src/math/lp/lar_solver.cpp
+++ b/src/math/lp/lar_solver.cpp
@@ -41,7 +41,6 @@ namespace lp {
         for (auto t : m_terms)
             delete t;
     }
-
     
     bool lar_solver::sizes_are_correct() const {
         lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size());
@@ -50,7 +49,6 @@ namespace lp {
         return true;
     }
 
-
     std::ostream& lar_solver::print_implied_bound(const implied_bound& be, std::ostream& out) const {
         out << "implied bound\n";
         unsigned v = be.m_j;
@@ -1350,8 +1348,8 @@ namespace lp {
     }
 
     bool lar_solver::term_is_int(const vector<std::pair<mpq, unsigned int>>& coeffs) const {
-        for (auto const& p : coeffs)
-            if (!(column_is_int(p.second) && p.first.is_int()))
+        for (auto const& [coeff, v] : coeffs)
+            if (!(column_is_int(v) && coeff.is_int()))
                 return false;
         return true;
     }
@@ -1382,7 +1380,7 @@ namespace lp {
     // the lower/upper bound is not strict.
     // the LP obtained by making the bound strict is infeasible
     // -> the column has to be fixed
-    bool lar_solver::is_fixed_at_bound(column_index const& j) {
+    bool lar_solver::is_fixed_at_bound(column_index const& j, vector<std::tuple<explanation, column_index, bool, mpq>>& bounds) {
         if (column_is_fixed(j))
             return false;
         mpq val;
@@ -1391,50 +1389,56 @@ namespace lp {
         lp::lconstraint_kind k;
         if (column_has_upper_bound(j) &&
             get_upper_bound(j).x == val) {
-            verbose_stream() << "check upper " << j << "\n";
-            push();
-            if (column_is_int(j))
-                k = LE, val -= 1;
-            else
-                k = LT;
-            auto ci = mk_var_bound(j, k, val);
-            update_column_type_and_bound(j, k, val, ci);
+            push();   
+            k = column_is_int(j) ? LE : LT;
+            auto ci = mk_var_bound(j, k, column_is_int(j) ? val - 1 : val);
+            update_column_type_and_bound(j, k, column_is_int(j) ? val - 1 : val, ci);
             auto st = find_feasible_solution();
+            bool infeasible = st == lp_status::INFEASIBLE;
+            if (infeasible) {
+                explanation exp;
+                get_infeasibility_explanation(exp);
+                unsigned_vector cis;
+                exp.remove(ci);
+                verbose_stream() << "tight upper bound " << j << " " << val << "\n";
+                bounds.push_back({exp, j, true, val});
+            }
             pop(1);
-            return st == lp_status::INFEASIBLE;            
+            return infeasible;            
         }
         if (column_has_lower_bound(j) &&
             get_lower_bound(j).x == val) {
-            verbose_stream() << "check lower " << j << "\n";
             push();
-            if (column_is_int(j))
-                k = GE, val += 1;
-            else
-                k = GT;
-            auto ci = mk_var_bound(j, k, val);
-            update_column_type_and_bound(j, k, val, ci);
+            k = column_is_int(j) ? GE : GT;
+            auto ci = mk_var_bound(j, k, column_is_int(j) ? val + 1 : val);
+            update_column_type_and_bound(j, k, column_is_int(j) ? val + 1 : val, ci);
             auto st = find_feasible_solution();
+            bool infeasible = st == lp_status::INFEASIBLE;
+            if (infeasible) {
+                explanation exp;
+                get_infeasibility_explanation(exp);
+                exp.remove(ci);
+                verbose_stream() << "tight lower bound " << j << " " << val << "\n";
+                bounds.push_back({exp, j, false, val});
+            }
             pop(1);
-            return st == lp_status::INFEASIBLE;                        
+            return infeasible;
         }
         
         return false;
     }
 
-    bool lar_solver::has_fixed_at_bound() {
+    bool lar_solver::has_fixed_at_bound(vector<std::tuple<explanation, column_index, bool, mpq>>& bounds) {
         verbose_stream() << "has-fixed-at-bound\n";
-        unsigned num_fixed = 0;
         for (unsigned j = 0; j < A_r().m_columns.size(); ++j) {
             auto ci = column_index(j);
-            if (is_fixed_at_bound(ci)) {
-                ++num_fixed;
+            if (is_fixed_at_bound(ci, bounds)) 
                 verbose_stream() << "fixed " << j << "\n";
-            }
         }
-        verbose_stream() << "num fixed " << num_fixed << "\n";
-        if (num_fixed > 0)
+        verbose_stream() << "num fixed " << bounds.size() << "\n";
+        if (!bounds.empty())
             find_feasible_solution();
-        return num_fixed > 0;
+        return !bounds.empty();
     }
 
 
@@ -1613,6 +1617,18 @@ namespace lp {
         return ret;
     }
 
+    /**
+    * \brief ensure there is a column index corresponding to vi
+    * If vi is already a column, just return vi
+    * If vi is for a term, then create a row that uses the term.
+    */
+    var_index lar_solver::ensure_column(var_index vi) {
+        if (lp::tv::is_term(vi))
+            return to_column(vi);
+        else
+            return vi;
+    }
+
 
     void lar_solver::add_row_from_term_no_constraint(const lar_term* term, unsigned term_ext_index) {
         TRACE("dump_terms", print_term(*term, tout) << std::endl;);
diff --git a/src/math/lp/lar_solver.h b/src/math/lp/lar_solver.h
index 182ef0be3..762bae481 100644
--- a/src/math/lp/lar_solver.h
+++ b/src/math/lp/lar_solver.h
@@ -366,8 +366,8 @@ public:
                 }
     }
 
-    bool is_fixed_at_bound(column_index const& j);
-    bool has_fixed_at_bound();
+    bool is_fixed_at_bound(column_index const& j, vector<std::tuple<explanation, column_index, bool, mpq>>& bounds);
+    bool has_fixed_at_bound(vector<std::tuple<explanation, column_index, bool, mpq>>& bounds);
     
     bool is_fixed(column_index const& j) const { return column_is_fixed(j); }    
     inline column_index to_column_index(unsigned v) const { return column_index(external_to_column_index(v)); }
@@ -376,6 +376,7 @@ public:
     bool compare_values(var_index j, lconstraint_kind kind, const mpq & right_side);
     var_index add_term(const vector<std::pair<mpq, var_index>> & coeffs, unsigned ext_i);
     void register_existing_terms();
+    var_index ensure_column(var_index vi);
     constraint_index add_var_bound(var_index, lconstraint_kind, const mpq &);
     constraint_index add_var_bound_check_on_equal(var_index, lconstraint_kind, const mpq &, var_index&);
     
diff --git a/src/math/lp/lp_api.h b/src/math/lp/lp_api.h
index 2a4e5058d..483ac3c29 100644
--- a/src/math/lp/lp_api.h
+++ b/src/math/lp/lp_api.h
@@ -103,6 +103,7 @@ namespace lp_api {
         unsigned m_conflicts;
         unsigned m_bound_propagations1;
         unsigned m_bound_propagations2;
+        unsigned m_bound_axioms;
         unsigned m_assert_diseq;
         unsigned m_assert_eq;
         unsigned m_gomory_cuts;
@@ -113,21 +114,22 @@ namespace lp_api {
             memset(this, 0, sizeof(*this));
         }
         void collect_statistics(statistics& st) const {
-            st.update("arith-lower", m_assert_lower);
-            st.update("arith-upper", m_assert_upper);
-            st.update("arith-propagations", m_bounds_propagations);
-            st.update("arith-iterations", m_num_iterations);
-            st.update("arith-pivots", m_need_to_solve_inf);
-            st.update("arith-plateau-iterations", m_num_iterations_with_no_progress);
-            st.update("arith-fixed-eqs", m_fixed_eqs);
-            st.update("arith-conflicts", m_conflicts);
-            st.update("arith-bound-propagations-lp", m_bound_propagations1);
-            st.update("arith-bound-propagations-cheap", m_bound_propagations2);
-            st.update("arith-diseq", m_assert_diseq);
-            st.update("arith-eq",    m_assert_eq);
-            st.update("arith-gomory-cuts", m_gomory_cuts);
-            st.update("arith-assume-eqs", m_assume_eqs);
-            st.update("arith-branch", m_branch);
+            st.update("arith assert lower", m_assert_lower);
+            st.update("arith assert upper", m_assert_upper);
+            st.update("arith propagations", m_bounds_propagations);
+            st.update("arith iterations", m_num_iterations);
+            st.update("arith pivots", m_need_to_solve_inf);
+            st.update("arith plateau iterations", m_num_iterations_with_no_progress);
+            st.update("arith fixed eqs", m_fixed_eqs);
+            st.update("arith conflicts", m_conflicts);
+            st.update("arith bound propagations lp", m_bound_propagations1);
+            st.update("arith bound propagations cheap", m_bound_propagations2);
+            st.update("arith bound axioms", m_bound_axioms);
+            st.update("arith diseq", m_assert_diseq);
+            st.update("arith eq",    m_assert_eq);
+            st.update("arith gomory cuts", m_gomory_cuts);
+            st.update("arith assume eqs", m_assume_eqs);
+            st.update("arith branch", m_branch);
         }
     };
 
diff --git a/src/math/lp/lp_core_solver_base_def.h b/src/math/lp/lp_core_solver_base_def.h
index 8619c926e..587ac39a9 100644
--- a/src/math/lp/lp_core_solver_base_def.h
+++ b/src/math/lp/lp_core_solver_base_def.h
@@ -117,10 +117,10 @@ template <typename T, typename X> void lp_core_solver_base<T, X>::
 add_delta_to_entering(unsigned entering, const X& delta) {
     m_x[entering] += delta;
      
-        for (const auto & c : m_A.m_columns[entering]) {
-            unsigned i = c.var();
-            m_x[m_basis[i]] -= delta * m_A.get_val(c);
-        }
+    for (const auto & c : m_A.m_columns[entering]) {
+        unsigned i = c.var();
+        m_x[m_basis[i]] -= delta * m_A.get_val(c);
+    }
 }
 
 
@@ -295,7 +295,7 @@ divide_row_by_pivot(unsigned pivot_row, unsigned pivot_col) {
 }
 template <typename T, typename X> bool lp_core_solver_base<T, X>::
 pivot_column_tableau(unsigned j, unsigned piv_row_index) {
-	if (!divide_row_by_pivot(piv_row_index, j))
+    if (!divide_row_by_pivot(piv_row_index, j))
         return false;
     auto &column = m_A.m_columns[j];
     int pivot_col_cell_index = -1;
@@ -406,15 +406,16 @@ template <typename T, typename X>  void lp_core_solver_base<T, X>::transpose_row
 }
 // j is the new basic column, j_basic - the leaving column
 template <typename T, typename X> bool lp_core_solver_base<T, X>::pivot_column_general(unsigned j, unsigned j_basic, indexed_vector<T> & w) {
-	lp_assert(m_basis_heading[j] < 0);
-	lp_assert(m_basis_heading[j_basic] >= 0);
-	unsigned row_index = m_basis_heading[j_basic];
-	  // the tableau case
-	if (pivot_column_tableau(j, row_index))
-		change_basis(j, j_basic);
-	else return false;
-	
-	return true;
+    lp_assert(m_basis_heading[j] < 0);
+    lp_assert(m_basis_heading[j_basic] >= 0);
+    unsigned row_index = m_basis_heading[j_basic];
+    // the tableau case
+    if (pivot_column_tableau(j, row_index))
+        change_basis(j, j_basic);
+    else 
+        return false;
+    
+    return true;
 }
 
 
diff --git a/src/math/lp/lp_primal_core_solver_tableau_def.h b/src/math/lp/lp_primal_core_solver_tableau_def.h
index 898abb152..7ae8624af 100644
--- a/src/math/lp/lp_primal_core_solver_tableau_def.h
+++ b/src/math/lp/lp_primal_core_solver_tableau_def.h
@@ -59,6 +59,7 @@ template <typename T, typename X> void lp_primal_core_solver<T, X>::advance_on_e
     }
     unsigned j_nz = this->m_m() + 1; // this number is greater than the max column size
     std::list<unsigned>::iterator entering_iter = m_non_basis_list.end();
+    unsigned n = 0;
     for (auto non_basis_iter = m_non_basis_list.begin(); number_of_benefitial_columns_to_go_over && non_basis_iter != m_non_basis_list.end(); ++non_basis_iter) {
         unsigned j = *non_basis_iter;
         if (!column_is_benefitial_for_entering_basis(j))
@@ -71,8 +72,9 @@ template <typename T, typename X> void lp_primal_core_solver<T, X>::advance_on_e
             entering_iter = non_basis_iter;
             if (number_of_benefitial_columns_to_go_over)
                 number_of_benefitial_columns_to_go_over--;
+            n = 1;
         }
-        else if (t == j_nz && this->m_settings.random_next() % 2 == 0) {
+        else if (t == j_nz && this->m_settings.random_next() % (++n) == 0) {
             entering_iter = non_basis_iter;
         }
     }// while (number_of_benefitial_columns_to_go_over && initial_offset_in_non_basis != offset_in_nb);
diff --git a/src/smt/params/smt_params.cpp b/src/smt/params/smt_params.cpp
index 3c63e2fff..1666d0946 100644
--- a/src/smt/params/smt_params.cpp
+++ b/src/smt/params/smt_params.cpp
@@ -246,7 +246,7 @@ void smt_params::setup_QF_LRA(static_features const& st) {
     m_phase_selection       = PS_THEORY;
     if (!st.m_cnf) {
         m_restart_strategy      = RS_GEOMETRIC;
-        m_arith_stronger_lemmas = false;
+        m_arith_relax_bounds = false;
         m_restart_adaptive      = false;
     }
     m_arith_small_lemma_size = 32;
@@ -288,7 +288,7 @@ void smt_params::setup_QF_LIA(static_features const& st) {
     }
     if (st.m_num_bin_clauses + st.m_num_units == st.m_num_clauses && st.m_cnf && st.m_arith_k_sum > rational(100000)) {
         m_arith_bound_prop      = bound_prop_mode::BP_NONE;
-        m_arith_stronger_lemmas = false;
+        m_arith_relax_bounds    = false;
     }
 }
 
diff --git a/src/smt/params/theory_arith_params.cpp b/src/smt/params/theory_arith_params.cpp
index 7f3f1ca23..4dea7a5bb 100644
--- a/src/smt/params/theory_arith_params.cpp
+++ b/src/smt/params/theory_arith_params.cpp
@@ -52,7 +52,7 @@ void theory_arith_params::display(std::ostream & out) const {
     DISPLAY_PARAM(m_arith_blands_rule_threshold);
     DISPLAY_PARAM(m_arith_propagate_eqs);
     DISPLAY_PARAM((unsigned)m_arith_bound_prop);
-    DISPLAY_PARAM(m_arith_stronger_lemmas);
+    DISPLAY_PARAM(m_arith_relax_bounds);
     DISPLAY_PARAM(m_arith_skip_rows_with_big_coeffs);
     DISPLAY_PARAM(m_arith_max_lemma_size);
     DISPLAY_PARAM(m_arith_small_lemma_size);
diff --git a/src/smt/params/theory_arith_params.h b/src/smt/params/theory_arith_params.h
index 526cb6f09..738dbe7d7 100644
--- a/src/smt/params/theory_arith_params.h
+++ b/src/smt/params/theory_arith_params.h
@@ -58,7 +58,7 @@ struct theory_arith_params {
     unsigned                m_arith_blands_rule_threshold = 1000;
     bool                    m_arith_propagate_eqs = true;
     bound_prop_mode         m_arith_bound_prop = bound_prop_mode::BP_REFINE;
-    bool                    m_arith_stronger_lemmas = true;
+    bool                    m_arith_relax_bounds = true;
     bool                    m_arith_skip_rows_with_big_coeffs = true;
     unsigned                m_arith_max_lemma_size = 128; 
     unsigned                m_arith_small_lemma_size = 16;
diff --git a/src/smt/theory_arith.h b/src/smt/theory_arith.h
index 92aa4baec..7bc73b508 100644
--- a/src/smt/theory_arith.h
+++ b/src/smt/theory_arith.h
@@ -43,7 +43,7 @@ namespace smt {
     struct theory_arith_stats {
         unsigned m_conflicts, m_add_rows, m_pivots, m_diseq_cs, m_gomory_cuts, m_branches, m_gcd_tests, m_gcd_conflicts, m_patches, m_patches_succ;
         unsigned m_assert_lower, m_assert_upper, m_assert_diseq, m_core2th_eqs, m_core2th_diseqs;
-        unsigned m_th2core_eqs, m_th2core_diseqs, m_bound_props, m_offset_eqs, m_fixed_eqs, m_offline_eqs;
+        unsigned m_th2core_eqs, m_th2core_diseqs, m_bound_props, m_bound_axioms, m_offset_eqs, m_fixed_eqs, m_offline_eqs;
         unsigned m_max_min; 
         unsigned m_assume_eqs;
         unsigned m_gb_simplify, m_gb_superpose, m_gb_compute_basis, m_gb_num_processed;
@@ -541,7 +541,7 @@ namespace smt {
         double adaptive_assertion_threshold() const { return m_params.m_arith_adaptive_assertion_threshold; }
         unsigned max_lemma_size() const { return m_params.m_arith_max_lemma_size; }
         unsigned small_lemma_size() const { return m_params.m_arith_small_lemma_size; }
-        bool relax_bounds() const { return m_params.m_arith_stronger_lemmas; }
+        bool relax_bounds() const { return m_params.m_arith_relax_bounds; }
         bool skip_big_coeffs() const { return m_params.m_arith_skip_rows_with_big_coeffs; }
         bool process_atoms() const;
         unsigned get_num_conflicts() const { return m_num_conflicts; }
diff --git a/src/smt/theory_arith_aux.h b/src/smt/theory_arith_aux.h
index 470ea5f7b..5d31f0657 100644
--- a/src/smt/theory_arith_aux.h
+++ b/src/smt/theory_arith_aux.h
@@ -2141,6 +2141,8 @@ namespace smt {
 
         if (candidates.empty())
             return;
+
+        verbose_stream() << "candidates " << candidates.size() << "\n";
         m_tmp_var_set.reset();
         m_tmp_var_set2.reset();
         for (theory_var v : candidates) {
diff --git a/src/smt/theory_arith_core.h b/src/smt/theory_arith_core.h
index 159758c80..0eddd1273 100644
--- a/src/smt/theory_arith_core.h
+++ b/src/smt/theory_arith_core.h
@@ -1148,6 +1148,7 @@ namespace smt {
                 mk_clause(~l1, l2, 3, coeffs);
             }
         }
+        ++m_stats.m_bound_axioms;
     }
 
     template<typename Ext>
@@ -1489,6 +1490,19 @@ namespace smt {
         unsigned old_idx = m_final_check_idx;
         final_check_status result = FC_DONE;
         final_check_status ok;
+
+        //display(verbose_stream());
+        //exit(0);
+
+
+        if (false)
+        {
+            verbose_stream() << "final\n";
+            ::statistics stats;
+            collect_statistics(stats);
+            stats.display(verbose_stream());
+        }
+
         do {
             if (ctx.get_cancel_flag()) {
                 return FC_GIVEUP;
@@ -2812,10 +2826,11 @@ namespace smt {
     template<typename Ext>
     void theory_arith<Ext>::explain_bound(row const & r, int idx, bool is_lower, inf_numeral & delta, antecedents& ante) {
         SASSERT(delta >= inf_numeral::zero());
-        TRACE("arith_conflict", tout << "relax: " << relax_bounds() << " lits: " << ante.lits().size() << " eqs: " << ante.eqs().size() << " idx: " << idx << "\n";);
         if (!relax_bounds() && (!ante.lits().empty() || !ante.eqs().empty())) {
             return;
         }
+
+
         row_entry const & entry = r[idx];
         numeral           coeff = entry.m_coeff;
         if (relax_bounds()) {
@@ -2835,6 +2850,7 @@ namespace smt {
                 if (!b->has_justification()) {
                     continue;
                 }
+
                 if (!relax_bounds() || delta.is_zero()) {
                     TRACE("propagate_bounds", tout << "push justification: v" << it->m_var << "\n";);
                     b->push_justification(ante, it->m_coeff, coeffs_enabled());
diff --git a/src/smt/theory_arith_int.h b/src/smt/theory_arith_int.h
index c9bc9f31a..496d27614 100644
--- a/src/smt/theory_arith_int.h
+++ b/src/smt/theory_arith_int.h
@@ -219,7 +219,7 @@ namespace smt {
         {
             std::function<expr*(void)> fn = [&]() { return m.mk_or(bound, m.mk_not(bound)); };
             scoped_trace_stream _sts(*this, fn);
-            IF_VERBOSE(10, verbose_stream() << "branch " << bound << "\n");
+            IF_VERBOSE(4, verbose_stream() << "branch " << bound << "\n");
             TRACE("arith_int", tout << mk_bounded_pp(bound, m) << "\n";);
             ctx.internalize(bound, true);
             ctx.mark_as_relevant(bound.get());
@@ -670,13 +670,14 @@ namespace smt {
         TRACE("gomory_cut", tout << "new cut:\n" << bound << "\n"; ante.display(tout););
         literal l     = null_literal;
         context & ctx = get_context();
+        ctx.get_rewriter()(bound);
         {
             std::function<expr*(void)> fn = [&]() { return bound; };
             scoped_trace_stream _sts(*this, fn);
             ctx.internalize(bound, true);
         }
         l = ctx.get_literal(bound);
-        IF_VERBOSE(10, verbose_stream() << "cut " << bound << "\n");
+        IF_VERBOSE(4, verbose_stream() << "cut " << bound << "\n");
         ctx.mark_as_relevant(l);
         auto js = ctx.mk_justification(
             gomory_cut_justification(
@@ -906,6 +907,7 @@ namespace smt {
         bool inf_l, inf_u;
         inf_numeral l, u;
         numeral m;
+        unsigned num_patched = 0, num_not_patched = 0;
         for (theory_var v = 0; v < num; v++) {
             if (!is_non_base(v)) 
                 continue;
@@ -915,6 +917,7 @@ namespace smt {
             // check whether value of v is already a multiple of m.
             if ((get_value(v).get_rational() / m).is_int())
                 continue;
+
             TRACE("patch_int",
                   tout << "TARGET v" << v << " -> [";
                   if (inf_l) tout << "-oo"; else tout << ceil(l);
@@ -922,6 +925,15 @@ namespace smt {
                   if (inf_u) tout << "oo"; else tout << floor(u);
                   tout << "]";
                   tout << ", m: " << m << ", val: " << get_value(v) << ", is_int: " << is_int(v) << "\n";);
+
+
+            verbose_stream() << "TARGET v" << v << " -> [";
+            if (inf_l) verbose_stream() << "-oo"; else verbose_stream() << ceil(l);
+            verbose_stream() << ", ";
+            if (inf_u) verbose_stream() << "oo"; else verbose_stream() << floor(u);
+            verbose_stream() << "]";
+            verbose_stream() << ", m: " << m << ", val: " << get_value(v) << ", is_int: " << is_int(v) << "\n";
+
             if (!inf_l)
                 l = ceil(l);
             if (!inf_u)
@@ -932,8 +944,11 @@ namespace smt {
                 if (!inf_u)
                     u = m*floor(u/m);
             }
-            if (!inf_l && !inf_u && l > u)
+            if (!inf_l && !inf_u && l > u) {
+                ++num_not_patched;
                 continue; // cannot patch
+            }
+            ++num_patched;
             if (!inf_l)
                 set_value(v, l);
             else if (!inf_u)
@@ -942,6 +957,7 @@ namespace smt {
                 set_value(v, inf_numeral(0));
         }
         SASSERT(m_to_patch.empty());
+        verbose_stream() << "patched " << num_patched << " not patched " << num_not_patched << "\n";
     }
 
     /**
diff --git a/src/smt/theory_arith_pp.h b/src/smt/theory_arith_pp.h
index b0d43bc00..a7d2efa63 100644
--- a/src/smt/theory_arith_pp.h
+++ b/src/smt/theory_arith_pp.h
@@ -33,13 +33,14 @@ namespace smt {
         st.update("arith assert upper", m_stats.m_assert_upper);
         st.update("arith assert diseq", m_stats.m_assert_diseq);
         st.update("arith bound prop", m_stats.m_bound_props);
+        st.update("arith bound axioms", m_stats.m_bound_axioms);
         st.update("arith fixed eqs", m_stats.m_fixed_eqs);
         st.update("arith assume eqs", m_stats.m_assume_eqs);
         st.update("arith offset eqs", m_stats.m_offset_eqs);
         st.update("arith gcd tests", m_stats.m_gcd_tests);
         st.update("arith gcd conflicts", m_stats.m_gcd_conflicts);
-        st.update("arith ineq splits", m_stats.m_branches);
         st.update("arith gomory cuts", m_stats.m_gomory_cuts);
+        st.update("arith branch", m_stats.m_branches);
         st.update("arith branch int", m_stats.m_branch_infeasible_int);
         st.update("arith branch var", m_stats.m_branch_infeasible_var);
         st.update("arith patches", m_stats.m_patches);
diff --git a/src/smt/theory_diff_logic_def.h b/src/smt/theory_diff_logic_def.h
index 807eb6cb6..ce3c1e3e7 100644
--- a/src/smt/theory_diff_logic_def.h
+++ b/src/smt/theory_diff_logic_def.h
@@ -695,7 +695,7 @@ void theory_diff_logic<Ext>::new_edge(dl_var src, dl_var dst, unsigned num_edges
 template<typename Ext>
 void theory_diff_logic<Ext>::set_neg_cycle_conflict() {
     m_nc_functor.reset();
-    m_graph.traverse_neg_cycle2(m_params.m_arith_stronger_lemmas, m_nc_functor);
+    m_graph.traverse_neg_cycle2(m_params.m_arith_relax_bounds, m_nc_functor);
     inc_conflicts();
     literal_vector const& lits = m_nc_functor.get_lits();
     TRACE("arith_conflict", 
diff --git a/src/smt/theory_lra.cpp b/src/smt/theory_lra.cpp
index c6bd12f03..9f94df354 100644
--- a/src/smt/theory_lra.cpp
+++ b/src/smt/theory_lra.cpp
@@ -127,6 +127,7 @@ class theory_lra::imp {
         ptr_vector<expr>&    to_ensure_enode() { return m_st.m_to_ensure_enode; }            
         ptr_vector<expr>&    to_ensure_var() { return m_st.m_to_ensure_var; }            
         void push(expr* e, rational c) { m_st.m_terms.push_back(e); m_st.m_coeffs.push_back(c); }
+        void add(theory_var v, rational const& c) { vars().push_back(v); coeffs().push_back(c); }
         void set_back(unsigned i) { 
             if (terms().size() == i + 1) return;
             terms()[i] = terms().back(); 
@@ -335,17 +336,204 @@ class theory_lra::imp {
 
     }
 
+
+    bool internalize_term2(app* term) {
+        TRACE("arith_internalize", tout << "internalising term:\n" << mk_pp(term, m) << "\n";);
+        theory_var v = internalize_term_core(term);
+        TRACE("arith_internalize", tout << "theory_var: " << v << "\n";);
+        return v != null_theory_var;
+    }
+
+    theory_var internalize_add(app* n) {
+        TRACE("add_bug", tout << "n: " << mk_pp(n, m) << "\n";);
+        CTRACE("internalize_add_bug", n->get_num_args() == 2 && n->get_arg(0) == n->get_arg(1), tout << "n: " << mk_pp(n, m) << "\n";);
+        SASSERT(a.is_add(n));
+        scoped_internalize_state st(*this);
+        for (expr* arg : *n) 
+            internalize_internal_monomial(to_app(arg), st);
+        
+        enode* e = mk_enode(n);
+        theory_var v = e->get_th_var(get_id());
+        if (v == null_theory_var) 
+            v = internalize_linearized_def(n, st);        
+        return v;
+    }
+
+    void internalize_internal_monomial(app* arg, scoped_internalize_state& st) {
+        expr* arg1, * arg2;
+        rational val, val2;
+
+        if (ctx().e_internalized(arg)) {
+            enode* e = ctx().get_enode(arg);
+            if (th.is_attached_to_var(e)) {
+                // there is already a theory variable (i.e., name) for arg.
+                st.add(e->get_th_var(get_id()), rational::one());
+                return;
+            }
+        }
+
+        if (a.is_extended_numeral(arg, val)) 
+            st.add(internalize_numeral(arg, val), rational::one());        
+        else if (a.is_mul(arg, arg1, arg2)) {
+            if (a.is_extended_numeral(arg2, val)) 
+                std::swap(arg1, arg2);
+            if (a.is_extended_numeral(arg1, val)) {
+                st.add(internalize_term_core(to_app(arg2)), val);
+                if (reflect(arg)) {
+                    internalize_term_core(to_app(arg1));
+                    mk_enode(arg);
+                }                
+                return;
+            }
+        }
+        st.add(internalize_term_core(arg), rational::one());
+    }
+
+    theory_var internalize_numeral(app* n, rational const& val) {
+
+        if (ctx().e_internalized(n))
+            return mk_var(n);
+
+        enode* e = mk_enode(n);
+        theory_var v = mk_var(n);
+        lpvar vi = get_lpvar(v);
+        if (vi == UINT_MAX) {
+            vi = lp().add_var(v, a.is_int(n));
+            add_def_constraint_and_equality(vi, lp::GE, val);
+            add_def_constraint_and_equality(vi, lp::LE, val);
+            register_fixed_var(v, val);
+        }
+        return v;
+    }
+
+    /**
+         \brief Internalize the terms of the form (* c (* t1 ... tn)) and (* t1 ... tn).
+        Return an alias for the term.
+     */
+    theory_var internalize_mul1(app* arg) {
+        rational val;
+        TRACE("arith", tout << arg->get_num_args() << " " << mk_pp(arg, m) << "\n";);
+        SASSERT(a.is_mul(arg));
+        expr* arg0 = arg->get_arg(0);
+        expr* arg1 = arg->get_arg(1);
+        if (a.is_numeral(arg1)) 
+            std::swap(arg0, arg1);
+        
+        if (a.is_numeral(arg0, val) && !a.is_numeral(arg1) && arg->get_num_args() == 2) {
+            if (val.is_zero()) 
+                return internalize_numeral(arg, val);
+            scoped_internalize_state st(*this);
+            if (reflect(arg))
+                internalize_term_core(to_app(arg0));
+            st.add(internalize_mul_core(to_app(arg1)), val);
+            mk_enode(arg);
+            return internalize_linearized_def(arg, st);
+        }
+        else 
+            return internalize_mul_core(arg);        
+    }
+
+    theory_var internalize_mul_core(app* t) {
+        TRACE("internalize_mul_core", tout << "internalizing...\n" << mk_pp(t, m) << "\n";);
+        if (!a.is_mul(t))
+            return internalize_term_core(t);
+        for (expr* arg : *t) {
+            theory_var v = internalize_term_core(to_app(arg));
+            if (v == null_theory_var) 
+                mk_var(to_app(arg));            
+        }
+        enode* e = mk_enode(t);
+        theory_var v = e->get_th_var(get_id());
+        if (v == null_theory_var) 
+            v = mk_var(t);        
+        return v;
+    }
+
+    /**
+     * \brief Internalize the given term and return an alias for it.
+     *  Return null_theory_var if the term was not implemented by the theory yet.
+     */
+
+    theory_var internalize_term_core(app* n) {
+        TRACE("arith_internalize_detail", tout << "internalize_term_core:\n" << mk_pp(n, m) << "\n";);
+        if (ctx().e_internalized(n)) {
+            enode* e = ctx().get_enode(n);
+            if (th.is_attached_to_var(e))
+                return e->get_th_var(get_id());
+        }
+
+        SASSERT(!a.is_uminus(n));
+
+        rational val;
+
+        if (a.is_add(n))
+            return internalize_add(n);
+        else if (a.is_extended_numeral(n, val))
+            return internalize_numeral(n, val);
+        else if (a.is_mul(n))
+            return internalize_mul1(n);
+        else if (a.is_arith_expr(n))
+            NOT_IMPLEMENTED_YET();
+#if 0
+
+        else if (a.is_div(n))
+            return internalize_div(n);
+        else if (a.is_idiv(n))
+            return internalize_idiv(n);
+        else if (a.is_mod(n))
+            return internalize_mod(n);
+        else if (a.is_rem(n))
+            return internalize_rem(n);
+        else if (a.is_to_real(n))
+            return internalize_to_real(n);
+        else if (a.is_to_int(n))
+            return internalize_to_int(n);
+
+        else if (a.is_sub(n))
+            return internalize_sub(n);
+        if (a.is_power(n)) {
+            // unsupported
+            found_unsupported_op(n);
+            return mk_binary_op(n);
+        }
+        if (a.is_irrational_algebraic_numeral(n)) {
+            // unsupported
+            found_unsupported_op(n);
+            enode* e = mk_enode(n);
+            return mk_var(e);
+        }
+        if (a.get_family_id() == n->get_family_id()) {
+            if (!a.is_div0(n) && !a.is_mod0(n) && !a.is_idiv0(n) && !a.is_rem0(n))
+                found_unsupported_op(n);
+            if (ctx().e_internalized(n))
+                return expr2var(n);
+            for (expr* arg : *n)
+                ctx().internalize(arg, false);
+            return mk_var(mk_enode(n));
+    }
+
+#endif
+
+        TRACE("arith_internalize_detail", tout << "before:\n" << mk_pp(n, m) << "\n";);
+        if (!ctx().e_internalized(n))
+            ctx().internalize(n, false);
+        TRACE("arith_internalize_detail", tout << "after:\n" << mk_pp(n, m) << "\n";);
+        enode* e = ctx().get_enode(n);
+        if (!th.is_attached_to_var(e))
+            return mk_var(n);
+        else
+            return e->get_th_var(get_id());
+    }
+
+
+
+
+
     void linearize_term(expr* term, scoped_internalize_state& st) {
         st.push(term, rational::one());
         linearize(st);
     } 
-        
-    void linearize_ineq(expr* lhs, expr* rhs, scoped_internalize_state& st) {
-        st.push(lhs, rational::one());
-        st.push(rhs, rational::minus_one());
-        linearize(st);
-    }
-        
+                
     void linearize(scoped_internalize_state& st) { 
         expr_ref_vector & terms = st.terms();
         svector<theory_var>& vars = st.vars();
@@ -371,6 +559,7 @@ class theory_lra::imp {
                     st.push(to_app(n)->get_arg(i), -coeffs[index]);
                 }
             }
+#if 1
             else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n1, r)) {
                 coeffs[index] *= r;
                 terms[index] = n2;
@@ -381,6 +570,29 @@ class theory_lra::imp {
                 terms[index] = n1;
                 st.to_ensure_enode().push_back(n2);
             }
+#else
+            else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n1, r)) {
+                internalize_args(n2);
+                VERIFY(internalize_term(to_app(n2)));
+                theory_var v = mk_var(n2);
+                coeffs[vars.size()] = r * coeffs[index];
+                vars.push_back(v);
+                get_lpvar(v);
+                verbose_stream() << v << "\n";
+                st.to_ensure_enode().push_back(n1);
+                ++index;
+            }
+            else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n2, r)) {
+                VERIFY(internalize_term(to_app(n1)));
+                theory_var v = mk_var(n1);
+                coeffs[vars.size()] = r * coeffs[index];
+                vars.push_back(v);
+                get_lpvar(v);
+                verbose_stream() << v << "\n";
+                st.to_ensure_enode().push_back(n2);
+                ++index;
+            }
+#endif
             else if (a.is_mul(n)) {
                 theory_var v = internalize_mul(to_app(n));
                 coeffs[vars.size()] = coeffs[index];
@@ -663,8 +875,10 @@ class theory_lra::imp {
         for (unsigned i = 0; i < vars.size(); ++i) {
             theory_var var = vars[i];
             rational const& r = m_columns[var];
-            if (!r.is_zero()) {
-                m_left_side.push_back(std::make_pair(r, register_theory_var_in_lar_solver(var)));
+            if (!r.is_zero()) {          
+                auto vi = register_theory_var_in_lar_solver(var);
+                vi = lp().ensure_column(vi);
+                m_left_side.push_back({ r, vi });
                 m_columns[var].reset();                    
             }
         }
@@ -672,12 +886,7 @@ class theory_lra::imp {
     }
         
     bool all_zeros(vector<rational> const& v) const {
-        for (rational const& r : v) {
-            if (!r.is_zero()) {
-                return false;
-            }
-        }
-        return true;
+        return all_of(v, [](rational const& r) { return r.is_zero(); });
     }
         
     void add_eq_constraint(lp::constraint_index index, enode* n1, enode* n2) {
@@ -850,8 +1059,9 @@ class theory_lra::imp {
         else if (is_zero(st) && a.is_numeral(term)) {
             return lp().local_to_external(get_zero(a.is_int(term)));
         }
-        else {
+        else {            
             init_left_side(st);
+
             lpvar vi = get_lpvar(v);
             if (vi == UINT_MAX) {
                 if (m_left_side.empty()) {
@@ -862,8 +1072,10 @@ class theory_lra::imp {
                     return v;
                 }
                 if (!st.offset().is_zero()) {
-                    m_left_side.push_back(std::make_pair(st.offset(), get_one(a.is_int(term))));
+                    verbose_stream() << "Offset row " << st.offset() << "\n";
+                    m_left_side.push_back({ st.offset(), get_one(a.is_int(term)) });
                 }
+                
                 if (m_left_side.empty()) {
                     vi = lp().add_var(v, a.is_int(term));
                     add_def_constraint_and_equality(vi, lp::GE, rational(0));
@@ -872,7 +1084,7 @@ class theory_lra::imp {
                 else {
                     vi = lp().add_term(m_left_side, v);
                     SASSERT(lp::tv::is_term(vi));
-                    TRACE("arith_verbose", 
+                    TRACE("arith_init", 
                           tout << "v" << v << " := " << mk_pp(term, m) 
                           << " slack: " << vi << " scopes: " << m_scopes.size() << "\n";
                           lp().print_term(lp().get_term(lp::tv::raw(vi)), tout) << "\n";);
@@ -963,19 +1175,19 @@ public:
         m_bool_var2bound.erase(bv);
         ctx().set_var_theory(bv, get_id());
         if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n2, r) && is_app(n1)) {
-            v = internalize_def(to_app(n1));
+            v = internalize_term_core(to_app(n1));
             k = lp_api::upper_t;
         }
         else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n2, r) && is_app(n1)) {
-            v = internalize_def(to_app(n1));
+            v = internalize_term_core(to_app(n1));
             k = lp_api::lower_t;
         }  
         else if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n1, r) && is_app(n2)) {
-            v = internalize_def(to_app(n2));
+            v = internalize_term_core(to_app(n2));
             k = lp_api::lower_t;
         }
         else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n1, r) && is_app(n2)) {
-            v = internalize_def(to_app(n2));
+            v = internalize_term_core(to_app(n2));
             k = lp_api::upper_t;
         }
         else if (a.is_is_int(atom)) {
@@ -1007,7 +1219,8 @@ public:
             // skip
         }
         else {
-            internalize_def(term);
+            internalize_term2(term);
+ //           internalize_def(term);
         }
         return true;
     }
@@ -1098,6 +1311,8 @@ public:
         if (num_scopes == 0) {
             return;
         }
+        m_has_popped = true;
+
         unsigned old_size = m_scopes.size() - num_scopes;
         del_bounds(m_scopes[old_size].m_bounds_lim);
         m_asserted_atoms.shrink(m_scopes[old_size].m_asserted_atoms_lim);
@@ -1499,6 +1714,8 @@ public:
     void random_update() {
         if (m_nla && m_nla->need_check())
             return;
+        if (!m_liberal_final_check)
+            return;
         m_tmp_var_set.clear();
         m_tmp_var_set.resize(th.get_num_vars());
         m_model_eqs.reset();
@@ -1536,7 +1753,9 @@ public:
                       tout << "v" << v << " ";
               tout << "\n"; );
         if (!vars.empty()) {
+            verbose_stream() << "random update " << vars.size() << "\n";
             lp().random_update(vars.size(), vars.data());
+            m_changed_assignment = true;
         }
     }
 
@@ -1552,8 +1771,9 @@ public:
         unsigned old_sz = m_assume_eq_candidates.size();
         unsigned num_candidates = 0;
         int start = ctx().get_random_value();
-        for (theory_var i = 0; i < sz; ++i) {
+        for (int i = 0; i < sz; ++i) {
             theory_var v = (i + start) % sz;
+
             enode* n1 = get_enode(v);
             if (!th.is_relevant_and_shared(n1)) {                    
                 continue;
@@ -1646,10 +1866,84 @@ public:
         return FC_GIVEUP;
     }
 
+    bool m_has_propagated_fixed = false;
+    bool m_has_popped = false;
+
+    bool propagate_fixed() {
+        m_has_propagated_fixed = false;
+        vector<std::tuple<lp::explanation, lp::column_index, bool, lp::mpq>> bounds;
+        if (!lp().has_fixed_at_bound(bounds)) 
+            return false;
+        // verbose_stream() << "scope " << ctx().get_scope_level() << "\n";
+        for (auto const& [exp, j, lower, b] : bounds) {
+            auto t = lp().column2tv(j);
+            expr_ref trm(m);
+            if (t.is_term())
+                trm = term2expr(lp().get_term(t));
+            else
+                trm = var2expr(t.id());
+            
+            expr* v = a.mk_numeral(b, a.is_int(trm));
+            expr* bound = lower ? a.mk_ge(trm, v) : a.mk_le(trm, v);
+            literal lit = mk_literal(bound);
+            reset_evidence();
+            for (auto ev : exp)
+                set_evidence(ev.ci(), m_core, m_eqs);
+            //verbose_stream() << "assign " << lit << " " << mk_pp(bound, m) << " " << ctx().get_assignment(lit) << "\n";
+            ctx().mark_as_relevant(bound);
+            //ctx().display(verbose_stream());
+            assign(lit, m_core, m_eqs, m_params);      
+            /// verbose_stream() << "propagate " << lit << "\n";
+            //exit(0);
+        }
+        m_has_propagated_fixed = true;
+        m_has_popped = false;
+        return true;
+    }
+
     unsigned m_final_check_idx = 0;
     distribution m_dist { 0 };
-    
+
+    bool m_liberal_final_check = false;
+    bool m_changed_assignment = false;
+
     final_check_status final_check_eh() {
+        TRACE("arith_eq_adapter_info", m_arith_eq_adapter.display_already_processed(tout););
+        TRACE("arith", display(tout););
+
+        if (propagate_core())
+            return FC_CONTINUE;
+        if (delayed_assume_eqs())
+            return FC_CONTINUE;
+        m_liberal_final_check = true;
+        m_changed_assignment = false;
+        ctx().push_trail(value_trail<unsigned>(m_final_check_idx));
+        final_check_status result = final_check_core();
+        if (result != FC_DONE)
+            return result;
+        if (!m_changed_assignment)
+            return FC_DONE;
+        m_liberal_final_check = false;
+        m_changed_assignment = false;
+        result = final_check_core();
+        TRACE("arith", tout << "result: " << result << "\n";);
+        return result;
+    }
+    
+    final_check_status final_check_core() {
+
+
+        if (false)
+        {
+            verbose_stream() << "final\n";
+            ::statistics stats;
+            collect_statistics(stats);
+            stats.display(verbose_stream());
+        }
+#if 0
+        if (!m_has_propagated_fixed && propagate_fixed())
+            return FC_CONTINUE;
+#endif
         if (propagate_core())
             return FC_CONTINUE;
         m_model_is_initialized = false;
@@ -1661,13 +1955,11 @@ public:
         }
         bool giveup = false;
         final_check_status st = FC_DONE;
-        m_final_check_idx = 0; // remove to experiment.
         unsigned old_idx = m_final_check_idx;
         switch (is_sat) {
         case l_true:
             TRACE("arith", display(tout));
 
-            // if (lp().has_fixed_at_bound()) // explain and propagate.
 
 #if 0
             m_dist.reset();
@@ -1691,6 +1983,7 @@ public:
                     st = check_lia();
                     break;
                 default:
+                    verbose_stream() << idx << "\n";
                     UNREACHABLE();
                     break;                    
                 }
@@ -1713,11 +2006,11 @@ public:
                 
                 switch (m_final_check_idx) {
                 case 0:
-                    if (assume_eqs()) 
-                        st = FC_CONTINUE;                    
+                    st = check_lia();
                     break;
                 case 1:
-                    st = check_lia();
+                    if (assume_eqs()) 
+                        st = FC_CONTINUE;                    
                     break;
                 case 2:
                     st = check_nla();
@@ -2171,7 +2464,7 @@ public:
     }
     
     bool can_propagate_core() {
-        return m_asserted_atoms.size() > m_asserted_qhead || m_new_def;
+        return m_asserted_atoms.size() > m_asserted_qhead || m_new_def || (m_has_propagated_fixed && m_has_popped);
     }
 
     bool propagate() {
@@ -2181,8 +2474,9 @@ public:
     bool propagate_core() {
         m_model_is_initialized = false;
         flush_bound_axioms();
-        if (!can_propagate_core())
+        if (!can_propagate_core()) 
             return false;
+        
         m_new_def = false;        
         while (m_asserted_qhead < m_asserted_atoms.size() && !ctx().inconsistent() && m.inc()) {
             auto [bv, is_true] = m_asserted_atoms[m_asserted_qhead];
@@ -2196,6 +2490,10 @@ public:
                 assert_bound(bv, is_true, *b);
             ++m_asserted_qhead;
         }
+
+        if (false && m_has_propagated_fixed && m_has_popped && propagate_fixed())
+            return true;
+
         if (ctx().inconsistent()) {
             m_bv_to_propagate.reset();
             return true;
@@ -2603,6 +2901,7 @@ public:
                 mk_clause(~l1, l2, 3, coeffs);
             }
         }        
+        ++m_stats.m_bound_axioms;
     }
 
     typedef lp_bounds::iterator iterator;
@@ -3305,6 +3604,13 @@ public:
               tout << "\n";
               display_evidence(tout, m_explanation);
               display(tout << "is-conflict: " << is_conflict << "\n"););
+
+        TRACE("arith_conflict",
+              display_evidence(tout, m_explanation);
+              for (auto lit : m_core)
+                  ctx().display_literal_verbose(tout, lit);
+              );
+
         for (auto ev : m_explanation) 
             set_evidence(ev.ci(), m_core, m_eqs);
         
diff --git a/src/smt/theory_utvpi_def.h b/src/smt/theory_utvpi_def.h
index d4c6d684c..7932b2e54 100644
--- a/src/smt/theory_utvpi_def.h
+++ b/src/smt/theory_utvpi_def.h
@@ -507,7 +507,7 @@ namespace smt {
         TRACE("utvpi", a.display(*this, tout); tout << "\n";);       
         int edge_id = a.get_asserted_edge();
         if (!enable_edge(edge_id)) {
-            m_graph.traverse_neg_cycle2(m_params.m_arith_stronger_lemmas, m_nc_functor);
+            m_graph.traverse_neg_cycle2(m_params.m_arith_relax_bounds, m_nc_functor);
             set_conflict();
             return false;
         }