diff --git a/src/math/lp/core_solver_pretty_printer_def.h b/src/math/lp/core_solver_pretty_printer_def.h
index 27aa6c75d..b8048b241 100644
--- a/src/math/lp/core_solver_pretty_printer_def.h
+++ b/src/math/lp/core_solver_pretty_printer_def.h
@@ -279,9 +279,9 @@ template <typename T, typename X> void core_solver_pretty_printer<T, X>::print()
         print_row(i);
     }
     m_out << std::endl;
-    if (m_core_solver.inf_set().size()) {
+    if (m_core_solver.inf_heap().size()) {
         m_out << "inf columns: ";
-        print_vector(m_core_solver.inf_set(), m_out);
+        print_vector(m_core_solver.inf_heap(), m_out);
         m_out << std::endl;
     }
 }
diff --git a/src/math/lp/lar_core_solver_def.h b/src/math/lp/lar_core_solver_def.h
index 550b6fe36..942c87b3b 100644
--- a/src/math/lp/lar_core_solver_def.h
+++ b/src/math/lp/lar_core_solver_def.h
@@ -85,8 +85,8 @@ unsigned lar_core_solver::get_number_of_non_ints() const {
 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;);
+    lp_assert(m_r_solver.inf_heap_is_correct());
+	TRACE("find_feas_stats", tout << "infeasibles = " << m_r_solver.inf_heap_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";);
@@ -117,11 +117,9 @@ void lar_core_solver::solve() {
     }
     lp_assert(r_basis_is_OK());
     lp_assert(m_r_solver.non_basic_columns_are_set_correctly());
-    lp_assert(m_r_solver.inf_set_is_correct());
-
-    TRACE("lar_solver", tout << m_r_solver.get_status() << "\n";);
-}
-
+    lp_assert(m_r_solver.inf_heap_is_correct());
 
+  TRACE("lar_solver", tout << m_r_solver.get_status() << "\n";);
 }
 
+} // namespace lp
diff --git a/src/math/lp/lar_solver.cpp b/src/math/lp/lar_solver.cpp
index 62712914c..5f544dff1 100644
--- a/src/math/lp/lar_solver.cpp
+++ b/src/math/lp/lar_solver.cpp
@@ -244,6 +244,14 @@ namespace lp {
             set.erase(j);
     }
 
+    void lar_solver::clean_popped_elements_for_heap(unsigned n, lpvar_heap& heap) {
+        vector<int> to_remove;
+        for (unsigned j : heap)
+            if (j >= n)
+                to_remove.push_back(j);
+        for (unsigned j : to_remove)
+            heap.erase(j);
+    }
     
 
     void lar_solver::pop(unsigned k) {
@@ -271,7 +279,7 @@ namespace lp {
 
         unsigned m = A_r().row_count();
         clean_popped_elements(m, m_rows_with_changed_bounds);
-        clean_inf_set_of_r_solver_after_pop();
+        clean_inf_heap_of_r_solver_after_pop();
         lp_assert(
             m_settings.simplex_strategy() == simplex_strategy_enum::undecided ||
             m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
@@ -328,7 +336,7 @@ namespace lp {
 
     void lar_solver::set_costs_to_zero(const lar_term& term) {
         auto& rslv = m_mpq_lar_core_solver.m_r_solver;
-        auto& jset = m_mpq_lar_core_solver.m_r_solver.inf_set(); // hijack this set that should be empty right now
+        auto& jset = m_mpq_lar_core_solver.m_r_solver.inf_heap(); // hijack this set that should be empty right now
         lp_assert(jset.empty());
 
         for (lar_term::ival p : term) {
@@ -674,9 +682,9 @@ namespace lp {
     void lar_solver::update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j) {
         if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
             if (costs_are_used()) {
-                bool was_infeas = m_mpq_lar_core_solver.m_r_solver.inf_set_contains(j);
+                bool was_infeas = m_mpq_lar_core_solver.m_r_solver.inf_heap_contains(j);
                 m_mpq_lar_core_solver.m_r_solver.track_column_feasibility(j);
-                if (was_infeas != m_mpq_lar_core_solver.m_r_solver.inf_set_contains(j))
+                if (was_infeas != m_mpq_lar_core_solver.m_r_solver.inf_heap_contains(j))
                     m_basic_columns_with_changed_cost.insert(j);
             }
             else {
@@ -1293,12 +1301,12 @@ namespace lp {
         lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
     }
 
-    void lar_solver::clean_inf_set_of_r_solver_after_pop() {
+    void lar_solver::clean_inf_heap_of_r_solver_after_pop() {
         vector<unsigned> became_feas;
-        clean_popped_elements(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.inf_set());
+        clean_popped_elements_for_heap(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.inf_heap());
         std::unordered_set<unsigned> basic_columns_with_changed_cost;
         m_inf_index_copy.reset();
-        for (auto j : m_mpq_lar_core_solver.m_r_solver.inf_set())
+        for (auto j : m_mpq_lar_core_solver.m_r_solver.inf_heap())
             m_inf_index_copy.push_back(j);
         for (auto j : m_inf_index_copy) {
             if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
@@ -1316,16 +1324,16 @@ namespace lp {
             lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis_heading[j] < 0);
             m_mpq_lar_core_solver.m_r_solver.m_d[j] -= m_mpq_lar_core_solver.m_r_solver.m_costs[j];
             m_mpq_lar_core_solver.m_r_solver.m_costs[j] = zero_of_type<mpq>();
-            m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_set(j);
+            m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_heap(j);
         }
         became_feas.clear();
-        for (unsigned j : m_mpq_lar_core_solver.m_r_solver.inf_set()) {
+        for (unsigned j : m_mpq_lar_core_solver.m_r_solver.inf_heap()) {
             lp_assert(m_mpq_lar_core_solver.m_r_heading[j] >= 0);
             if (m_mpq_lar_core_solver.m_r_solver.column_is_feasible(j))
                 became_feas.push_back(j);
         }
         for (unsigned j : became_feas)
-            m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_set(j);
+            m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_heap(j);
 
     }
 
@@ -1504,7 +1512,7 @@ namespace lp {
         m_mpq_lar_core_solver.m_r_x.resize(j + 1);
         m_mpq_lar_core_solver.m_r_lower_bounds.increase_size_by_one();
         m_mpq_lar_core_solver.m_r_upper_bounds.increase_size_by_one();
-        m_mpq_lar_core_solver.m_r_solver.inf_set_increase_size_by_one();
+        m_mpq_lar_core_solver.m_r_solver.inf_heap_increase_size_by_one();
         m_mpq_lar_core_solver.m_r_solver.m_costs.resize(j + 1);
         m_mpq_lar_core_solver.m_r_solver.m_d.resize(j + 1);
         lp_assert(m_mpq_lar_core_solver.m_r_heading.size() == j); // as A().column_count() on the entry to the method
diff --git a/src/math/lp/lar_solver.h b/src/math/lp/lar_solver.h
index 5b421d70d..f2017acd7 100644
--- a/src/math/lp/lar_solver.h
+++ b/src/math/lp/lar_solver.h
@@ -94,7 +94,7 @@ class lar_solver : public column_namer {
     // these are basic columns with the value changed, so the corresponding row in the tableau
     // does not sum to zero anymore
     u_set                                               m_incorrect_columns;
-    // copy of m_r_solver.inf_set()
+    // copy of m_r_solver.inf_heap()
     unsigned_vector                                     m_inf_index_copy;
     stacked_value<unsigned>                             m_term_count;
     vector<lar_term*>                                   m_terms;
@@ -178,7 +178,9 @@ class lar_solver : public column_namer {
             bp);
     }
     
+    static void clean_popped_elements_for_heap(unsigned n, lpvar_heap& set);
     static void clean_popped_elements(unsigned n, u_set& set);
+    
     bool maximize_term_on_tableau(const lar_term & term,
                                   impq &term_max);
     bool costs_are_zeros_for_r_solver() const;
@@ -230,7 +232,7 @@ class lar_solver : public column_namer {
     void remove_last_column_from_basis_tableau(unsigned j);
     void remove_last_column_from_tableau();
     void pop_tableau();
-    void clean_inf_set_of_r_solver_after_pop();
+    void clean_inf_heap_of_r_solver_after_pop();
     inline bool column_value_is_integer(unsigned j) const { return get_column_value(j).is_int(); }
     bool model_is_int_feasible() const;
     
@@ -386,14 +388,15 @@ public:
         return tv::is_term(idx)?
             m_term_register.local_to_external(idx) : m_var_register.local_to_external(idx);
     }
+   
     bool column_corresponds_to_term(unsigned) const;
     inline unsigned row_count() const { return A_r().row_count(); }
     bool var_is_registered(var_index vj) const;
-    void clear_inf_set() {
-        m_mpq_lar_core_solver.m_r_solver.inf_set().clear();        
+    void clear_inf_heap() {
+        m_mpq_lar_core_solver.m_r_solver.inf_heap().clear();        
     }
-    inline void remove_column_from_inf_set(unsigned j) {
-        m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_set(j);
+    inline void remove_column_from_inf_heap(unsigned j) {
+        m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_heap(j);
     }
     template <typename ChangeReport>
     void change_basic_columns_dependend_on_a_given_nb_column_report(unsigned j,
diff --git a/src/math/lp/lp_core_solver_base.cpp b/src/math/lp/lp_core_solver_base.cpp
index f1ae95ea0..28f92d8e2 100644
--- a/src/math/lp/lp_core_solver_base.cpp
+++ b/src/math/lp/lp_core_solver_base.cpp
@@ -63,8 +63,8 @@ template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::colu
 template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq>>::pivot_column_tableau(unsigned int, unsigned int);
 template bool lp::lp_core_solver_base<lp::mpq, lp::mpq>::pivot_column_tableau(unsigned int, unsigned int);
 template void lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::transpose_rows_tableau(unsigned int, unsigned int);
-template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::inf_set_is_correct() const;
-template bool lp::lp_core_solver_base<lp::mpq, lp::mpq>::inf_set_is_correct() const;
+template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::inf_heap_is_correct() const;
+template bool lp::lp_core_solver_base<lp::mpq, lp::mpq>::inf_heap_is_correct() const;
 template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::remove_from_basis(unsigned int);
 
 
diff --git a/src/math/lp/lp_core_solver_base.h b/src/math/lp/lp_core_solver_base.h
index fb0c28507..f38587573 100644
--- a/src/math/lp/lp_core_solver_base.h
+++ b/src/math/lp/lp_core_solver_base.h
@@ -28,9 +28,13 @@ Revision History:
 #include "math/lp/permutation_matrix.h"
 #include "math/lp/column_namer.h"
 #include "math/lp/u_set.h"
-
+#include "util/heap.h"
 
 namespace lp {
+struct lpvar_lt {
+  bool operator()(lpvar v1, lpvar v2) const { return v1 < v2; }
+};
+typedef heap<lpvar_lt> lpvar_heap;
 template <typename T, typename X>
 X dot_product(const vector<T> & a, const vector<X> & b) {
     lp_assert(a.size() == b.size());
@@ -51,24 +55,24 @@ private:
 public:
     bool current_x_is_feasible() const {
         TRACE("feas",
-              if (m_inf_set.size()) {
-                  tout << "column " << *m_inf_set.begin() << " is infeasible" << std::endl;
-                  print_column_info(*m_inf_set.begin(), tout);
+              if (m_inf_heap.size()) {
+                  tout << "column " << *m_inf_heap.begin() << " is infeasible" << std::endl;
+                  print_column_info(*m_inf_heap.begin(), tout);
               } else {
                   tout << "x is feasible\n";
               }
               );
-        return m_inf_set.size() == 0;
+        return m_inf_heap.empty();
     }
-    bool current_x_is_infeasible() const { return m_inf_set.size() != 0; }
+    bool current_x_is_infeasible() const { return m_inf_heap.size() != 0; }
 private:
-    u_set m_inf_set;
+    lpvar_heap m_inf_heap;
 public:
-    const u_set& inf_set() const { return m_inf_set; }
-    u_set& inf_set() { return m_inf_set; }
-    void inf_set_increase_size_by_one() { m_inf_set.increase_size_by_one(); }
-    bool inf_set_contains(unsigned j) const { return m_inf_set.contains(j); }
-    unsigned inf_set_size() const { return m_inf_set.size(); }    
+    const lpvar_heap& inf_heap() const { return m_inf_heap; }
+    lpvar_heap& inf_heap() { return m_inf_heap; }
+    void inf_heap_increase_size_by_one() { m_inf_heap.reserve(m_inf_heap.size() + 1); }
+    bool inf_heap_contains(unsigned j) const { return m_inf_heap.contains(j); }
+    unsigned inf_heap_size() const { return m_inf_heap.size(); }    
     indexed_vector<T>     m_pivot_row; // this is the real pivot row of the simplex tableu
     static_matrix<T, X> & m_A; // the matrix A
     // vector<X> const &           m_b; // the right side
@@ -255,7 +259,7 @@ public:
 
     bool calc_current_x_is_feasible_include_non_basis() const;
 
-    bool inf_set_is_correct() const;
+    bool inf_heap_is_correct() const;
     
     bool column_is_dual_feasible(unsigned j) const;
 
@@ -526,8 +530,8 @@ public:
         swap(m_basis_heading, m_basis[i], m_basis[ii]);
     }
 
-    bool column_is_in_inf_set(unsigned j) const {
-        return m_inf_set.contains(j);
+    bool column_is_in_inf_heap(unsigned j) const {
+        return m_inf_heap.contains(j);
     }
 
     bool column_is_base(unsigned j) const {
@@ -560,29 +564,26 @@ public:
    
     void track_column_feasibility(unsigned j) {
         if (column_is_feasible(j))
-            remove_column_from_inf_set(j);
+            remove_column_from_inf_heap(j);
         else
-            insert_column_into_inf_set(j);
+            insert_column_into_inf_heap(j);
     }
-    void insert_column_into_inf_set(unsigned j) {
+    void insert_column_into_inf_heap(unsigned j) {
         TRACE("lar_solver", tout << "j = " << j << "\n";);
-        m_inf_set.insert(j);
+		if (!m_inf_heap.contains(j))
+	        m_inf_heap.insert(j);
         lp_assert(!column_is_feasible(j));
     }
-    void remove_column_from_inf_set(unsigned j) {
+    void remove_column_from_inf_heap(unsigned j) {
         TRACE("lar_solver", tout << "j = " << j << "\n";);
-        m_inf_set.erase(j);
+		if (m_inf_heap.contains(j))
+        	m_inf_heap.erase(j);
         lp_assert(column_is_feasible(j));
     }
 
-    void resize_inf_set(unsigned size) {
+    void clear_inf_heap() {
         TRACE("lar_solver",);
-        m_inf_set.resize(size);
-    }
-
-    void clear_inf_set() {
-        TRACE("lar_solver",);
-        m_inf_set.clear();
+        m_inf_heap.clear();
     }
     
     bool costs_on_nbasis_are_zeros() const {
diff --git a/src/math/lp/lp_core_solver_base_def.h b/src/math/lp/lp_core_solver_base_def.h
index 8619c926e..319966091 100644
--- a/src/math/lp/lp_core_solver_base_def.h
+++ b/src/math/lp/lp_core_solver_base_def.h
@@ -42,7 +42,7 @@ lp_core_solver_base(static_matrix<T, X> & A,
     m_total_iterations(0),
     m_iters_with_no_cost_growing(0),
     m_status(lp_status::FEASIBLE),
-    m_inf_set(A.column_count()),
+    m_inf_heap(std::max(static_cast<unsigned>(1024), A.column_count())),
     m_pivot_row(A.column_count()),
     m_A(A),
     m_basis(basis),
@@ -250,9 +250,9 @@ template <typename T, typename X> bool lp_core_solver_base<T, X>::calc_current_x
     return true;
 }
 
-template <typename T, typename X> bool lp_core_solver_base<T, X>::inf_set_is_correct() const {
+template <typename T, typename X> bool lp_core_solver_base<T, X>::inf_heap_is_correct() const {
     for (unsigned j = 0; j < this->m_n(); j++) {
-        bool belongs_to_set = m_inf_set.contains(j);
+        bool belongs_to_set = m_inf_heap.contains(j);
         bool is_feas = column_is_feasible(j);
         if (is_feas == belongs_to_set) {
             TRACE("lp_core", tout << "incorrectly set column in inf set "; print_column_info(j, tout) << "\n";);
diff --git a/src/math/lp/lp_primal_core_solver.h b/src/math/lp/lp_primal_core_solver.h
index 207428985..b2e402c08 100644
--- a/src/math/lp/lp_primal_core_solver.h
+++ b/src/math/lp/lp_primal_core_solver.h
@@ -33,6 +33,8 @@ Revision History:
 #include <sstream>
 #include <string>
 #include <unordered_map>
+#include "util/heap.h"
+
 namespace lp {
 
 // This core solver solves (Ax=b, lower_bound_values \leq x \leq
@@ -152,19 +154,28 @@ public:
     UNREACHABLE(); // unreachable
     return false;
   }
-
-  unsigned get_number_of_basic_vars_that_might_become_inf(
-      unsigned j) const { // consider looking at the signs here: todo
+/**
+ * Return the number of base non-free variables depending on the column j,
+ * different from bj,
+ * but take the min with the (bound+1).
+ * This function is used to select the pivot variable.
+*/
+  unsigned get_num_of_not_free_basic_dependent_vars(
+      unsigned j, unsigned bound, unsigned bj) const { // consider looking at the signs here: todo
     unsigned r = 0;
     for (const auto &cc : this->m_A.m_columns[j]) {
-      unsigned k = this->m_basis[cc.var()];
-      if (this->m_column_types[k] != column_type::free_column)
-        r++;
+      unsigned basic_for_row = this->m_basis[cc.var()];
+      if (basic_for_row == bj)
+        continue;
+        
+     // std::cout << this->m_A.m_rows[cc.var()] << std::endl;
+      if (this->m_column_types[basic_for_row] != column_type::free_column)         
+         if (r++ > bound) return r;      
     }
     return r;
   }
 
-  int find_beneficial_column_in_row_tableau_rows_bland_mode(int i, T &a_ent) {
+  int find_beneficial_entering_in_row_tableau_rows_bland_mode(int i, T &a_ent) {
     int j = -1;
     unsigned bj = this->m_basis[i];
     bool bj_needs_to_grow = needs_to_grow(bj);
@@ -190,15 +201,15 @@ public:
     return j;
   }
 
-  int find_beneficial_column_in_row_tableau_rows(int i, T &a_ent) {
+  int find_beneficial_entering_tableau_rows(int i, T &a_ent) {
     if (m_bland_mode_tableau)
-      return find_beneficial_column_in_row_tableau_rows_bland_mode(i, a_ent);
+      return find_beneficial_entering_in_row_tableau_rows_bland_mode(i, a_ent);
     // a short row produces short infeasibility explanation and benefits at
     // least one pivot operation
     int choice = -1;
     int nchoices = 0;
-    unsigned num_of_non_free_basics = 1000000;
-    unsigned len = 100000000;
+    unsigned min_non_free_so_far = -1;
+    unsigned best_col_sz = -1;
     unsigned bj = this->m_basis[i];
     bool bj_needs_to_grow = needs_to_grow(bj);
     for (unsigned k = 0; k < this->m_A.m_rows[i].size(); k++) {
@@ -213,17 +224,18 @@ public:
         if (!monoid_can_increase(rc))
           continue;
       }
-      unsigned damage = get_number_of_basic_vars_that_might_become_inf(j);
-      if (damage < num_of_non_free_basics) {
-        num_of_non_free_basics = damage;
-        len = this->m_A.m_columns[j].size();
+      unsigned not_free = get_num_of_not_free_basic_dependent_vars(j, min_non_free_so_far, bj);
+      unsigned col_sz = this->m_A.m_columns[j].size();
+      if (not_free < min_non_free_so_far || (not_free == min_non_free_so_far && col_sz < best_col_sz)) {
+        min_non_free_so_far = not_free;
+        best_col_sz = this->m_A.m_columns[j].size();
         choice = k;
         nchoices = 1;
-      } else if (damage == num_of_non_free_basics &&
-                 this->m_A.m_columns[j].size() <= len &&
-                 (this->m_settings.random_next() % (++nchoices))) {
-        choice = k;
-        len = this->m_A.m_columns[j].size();
+      } else if (not_free == min_non_free_so_far &&
+                 col_sz == best_col_sz) {
+        if (this->m_settings.random_next(++nchoices) == 0){         
+          choice = k;          
+        }
       }
     }
 
@@ -282,7 +294,7 @@ public:
       unsigned j, vector<unsigned> &leavings, T m, X &t,
       T &abs_of_d_of_leaving);
 
-  X get_max_bound(vector<X> &b);
+ 
 
 #ifdef Z3DEBUG
   void check_Ax_equal_b();
@@ -291,14 +303,6 @@ public:
   void check_correctness();
 #endif
 
-  // from page 183 of Istvan Maros's book
-  // the basis structures have not changed yet
-  void update_reduced_costs_from_pivot_row(unsigned entering, unsigned leaving);
-
-  // return 0 if the reduced cost at entering is close enough to the refreshed
-  // 1 if it is way off, and 2 if it is unprofitable
-  int refresh_reduced_cost_at_entering_and_check_that_it_is_off(
-      unsigned entering);
 
   void backup_and_normalize_costs();
 
@@ -356,15 +360,13 @@ public:
   }
 
   int find_smallest_inf_column() {
-    int j = -1;
-    for (unsigned k : this->inf_set()) {
-      if (k < static_cast<unsigned>(j)) {
-        j = k;
-      }
-    }
-    return j;
+    if (this->inf_heap().empty())
+      return -1;
+    return this->inf_heap().min_value();
   }
 
+  
+
   const X &get_val_for_leaving(unsigned j) const {
     lp_assert(!this->column_is_feasible(j));
     switch (this->m_column_types[j]) {
@@ -405,7 +407,7 @@ public:
       }
     }
     T a_ent;
-    int entering = find_beneficial_column_in_row_tableau_rows(
+    int entering = find_beneficial_entering_tableau_rows(
         this->m_basis_heading[leaving], a_ent);
     if (entering == -1) {
       this->set_status(lp_status::INFEASIBLE);
@@ -414,7 +416,7 @@ public:
     const X &new_val_for_leaving = get_val_for_leaving(leaving);
     X theta = (this->m_x[leaving] - new_val_for_leaving) / a_ent;
     this->m_x[leaving] = new_val_for_leaving;
-    this->remove_column_from_inf_set(leaving);
+    this->remove_column_from_inf_heap(leaving);
     advance_on_entering_and_leaving_tableau_rows(entering, leaving, theta);
     if (this->current_x_is_feasible())
       this->set_status(lp_status::OPTIMAL);
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..0c4f6216e 100644
--- a/src/math/lp/lp_primal_core_solver_tableau_def.h
+++ b/src/math/lp/lp_primal_core_solver_tableau_def.h
@@ -30,7 +30,7 @@ template <typename T, typename X> void lp_primal_core_solver<T, X>::one_iteratio
     else {
         advance_on_entering_tableau(entering);
     }
-    lp_assert(this->inf_set_is_correct());
+    lp_assert(this->inf_heap_is_correct());
 }
 
 template <typename T, typename X> void lp_primal_core_solver<T, X>::advance_on_entering_tableau(int entering) {
@@ -256,7 +256,7 @@ template <typename T, typename X> void lp_primal_core_solver<T, X>::init_run_tab
         this->m_basis_sort_counter = 0; // to initiate the sort of the basis
         //  this->set_total_iterations(0);
         this->iters_with_no_cost_growing() = 0;
-		lp_assert(this->inf_set_is_correct());
+		lp_assert(this->inf_heap_is_correct());
         if (this->current_x_is_feasible() && this->m_look_for_feasible_solution_only)
             return;
         if (this->m_settings.backup_costs)
diff --git a/src/math/lp/lp_settings.h b/src/math/lp/lp_settings.h
index c213333e0..727bc3531 100644
--- a/src/math/lp/lp_settings.h
+++ b/src/math/lp/lp_settings.h
@@ -218,6 +218,8 @@ public:
     unsigned hnf_cut_period() const { return m_hnf_cut_period; }
     void set_hnf_cut_period(unsigned period) { m_hnf_cut_period = period;  }
     unsigned random_next() { return m_rand(); }
+    unsigned random_next(unsigned u ) { return m_rand(u); }
+    
     void set_random_seed(unsigned s) { m_rand.set_seed(s); }
 
     bool bound_progation() const { 
diff --git a/src/math/lp/nla_core.cpp b/src/math/lp/nla_core.cpp
index 4d1cc6edb..4380b940b 100644
--- a/src/math/lp/nla_core.cpp
+++ b/src/math/lp/nla_core.cpp
@@ -1436,7 +1436,7 @@ void core::patch_monomials() {
     } else {
         m_lar_solver.pop();
         restore_tableau();
-        m_lar_solver.clear_inf_set();
+        m_lar_solver.clear_inf_heap();
     }
     SASSERT(m_lar_solver.ax_is_correct());
 }
diff --git a/src/math/lp/nla_tangent_lemmas.cpp b/src/math/lp/nla_tangent_lemmas.cpp
index 299d8031f..4ba9eeccc 100644
--- a/src/math/lp/nla_tangent_lemmas.cpp
+++ b/src/math/lp/nla_tangent_lemmas.cpp
@@ -75,8 +75,8 @@ private:
         c().negate_relation(lemma, m_jy, m_y.rat_sign()*pl.y);
 #if Z3DEBUG
         SASSERT(c().val(m_x) == m_xy.x && c().val(m_y) == m_xy.y);
-        int mult_sign = nla::rat_sign(pl.x - m_xy.x)*nla::rat_sign(pl.y - m_xy.y);
-        SASSERT((mult_sign == 1) == m_below);
+        // int mult_sign = nla::rat_sign(pl.x - m_xy.x)*nla::rat_sign(pl.y - m_xy.y);
+        SASSERT((nla::rat_sign(pl.x - m_xy.x)*nla::rat_sign(pl.y - m_xy.y) == 1) == m_below);
         // If "mult_sign is 1"  then (a - x)(b-y) > 0 and ab - bx - ay + xy > 0
         // or -ab + bx + ay < xy or -ay - bx + xy > -ab
         // val(j) stands for xy. So, finally we have  -ay - bx + j > - ab