diff --git a/src/math/lp/horner.cpp b/src/math/lp/horner.cpp
index 0fe968098b9..82fb89b4ec3 100644
--- a/src/math/lp/horner.cpp
+++ b/src/math/lp/horner.cpp
@@ -48,8 +48,12 @@ bool horner::row_is_interesting(const T& row) const {
     c().clear_active_var_set();
     for (const auto& p : row) {
         lpvar j = p.var();
-        if (!c().is_monic_var(j))
+        if (!c().is_monic_var(j)) {
+            if (c().active_var_set_contains(j))
+                return true;
+            c().insert_to_active_var_set(j);
             continue;
+        }
         auto & m = c().emons()[j];
         
         for (lpvar k : m.vars()) {
diff --git a/src/math/lp/lar_solver.cpp b/src/math/lp/lar_solver.cpp
index 1c9254caf3c..bce1e9ef333 100644
--- a/src/math/lp/lar_solver.cpp
+++ b/src/math/lp/lar_solver.cpp
@@ -314,13 +314,6 @@ void lar_solver::fill_explanation_from_crossed_bounds_column(explanation & evide
     
 unsigned lar_solver::get_total_iterations() const { return m_mpq_lar_core_solver.m_r_solver.total_iterations(); }
 
-vector<unsigned> lar_solver::get_list_of_all_var_indices() const {
-    vector<unsigned> ret;
-    for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_heading.size(); j++)
-        ret.push_back(j);
-    return ret;
-}
-
 void lar_solver::push() {
     m_simplex_strategy = m_settings.simplex_strategy();
     m_simplex_strategy.push();
diff --git a/src/math/lp/lar_solver.h b/src/math/lp/lar_solver.h
index ae4d2df69f0..d20281a3bc4 100644
--- a/src/math/lp/lar_solver.h
+++ b/src/math/lp/lar_solver.h
@@ -269,7 +269,6 @@ class lar_solver : public column_namer {
         m_mpq_lar_core_solver.m_r_solver.update_x(j, v);
     }
 public:
-    vector<unsigned> get_list_of_all_var_indices() const;
     inline void set_column_value_test(unsigned j, const impq& v) {
         set_column_value(j, v);
     }
diff --git a/src/math/lp/lp_core_solver_base.cpp b/src/math/lp/lp_core_solver_base.cpp
index 1033fdf4f93..3a5a2020fa9 100644
--- a/src/math/lp/lp_core_solver_base.cpp
+++ b/src/math/lp/lp_core_solver_base.cpp
@@ -133,9 +133,6 @@ template void lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::init
 template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::A_mult_x_is_off_on_index(vector<unsigned int> const&) const;
 template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::find_x_by_solving();
 template void lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq> >::restore_x(unsigned int, lp::numeric_pair<lp::mpq> const&);
-template bool lp::lp_core_solver_base<double, double>::pivot_for_tableau_on_basis();
-template bool lp::lp_core_solver_base<lp::mpq, lp::mpq>::pivot_for_tableau_on_basis();
-template bool lp::lp_core_solver_base<lp::mpq, lp::numeric_pair<lp::mpq>>::pivot_for_tableau_on_basis();
 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<double, double>::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);
diff --git a/src/math/lp/lp_core_solver_base.h b/src/math/lp/lp_core_solver_base.h
index ddf2fd26c61..666a4c1a795 100644
--- a/src/math/lp/lp_core_solver_base.h
+++ b/src/math/lp/lp_core_solver_base.h
@@ -453,8 +453,6 @@ class lp_core_solver_base {
     void pivot_fixed_vars_from_basis();
     bool remove_from_basis(unsigned j);
     bool pivot_column_general(unsigned j, unsigned j_basic, indexed_vector<T> & w);
-    bool pivot_for_tableau_on_basis();
-    bool pivot_row_for_tableau_on_basis(unsigned row);
     void init_basic_part_of_basis_heading() {
         unsigned m = m_basis.size();
         for (unsigned i = 0; i < m; i++) {
diff --git a/src/math/lp/lp_core_solver_base_def.h b/src/math/lp/lp_core_solver_base_def.h
index e8adb0d7738..0880c69c21a 100644
--- a/src/math/lp/lp_core_solver_base_def.h
+++ b/src/math/lp/lp_core_solver_base_def.h
@@ -85,16 +85,6 @@ init() {
         init_factorization(m_factorization, m_A, m_basis, m_settings);
 }
 
-template <typename T, typename X> bool lp_core_solver_base<T, X>::
-pivot_for_tableau_on_basis() {
-    m_d = m_costs; // we will be pivoting to m_d as well
-    unsigned m = m_A.row_count();
-    for (unsigned i = 0; i < m; i++)
-        if (!pivot_column_tableau(m_basis[i], i))
-            return false;
-    return true;
-}
-
 // i is the pivot row, and j is the pivot column
 template <typename T, typename X> void lp_core_solver_base<T, X>::
 pivot_to_reduced_costs_tableau(unsigned i, unsigned j) {
diff --git a/src/math/lp/nla_basics_lemmas.cpp b/src/math/lp/nla_basics_lemmas.cpp
index 60910892231..567258b8136 100644
--- a/src/math/lp/nla_basics_lemmas.cpp
+++ b/src/math/lp/nla_basics_lemmas.cpp
@@ -91,7 +91,7 @@ void basics::basic_sign_lemma_model_based_one_mon(const monic& m, int product_si
         TRACE("nla_solver_bl", tout << "zero product sign: " << pp_mon(_(), m)<< "\n"; );
         generate_zero_lemmas(m);
     } else {
-        add_empty_lemma();
+        add_lemma();
         for(lpvar j: m.vars()) {
             negate_strict_sign(j);
         }
@@ -158,7 +158,7 @@ bool basics::basic_sign_lemma(bool derived) {
 // the value of the i-th monic has to be equal to the value of the k-th monic modulo sign
 // but it is not the case in the model
 void basics::generate_sign_lemma(const monic& m, const monic& n, const rational& sign) {
-    add_empty_lemma();
+    add_lemma();
     TRACE("nla_solver",
           tout << "m = " << pp_mon_with_vars(_(), m);
           tout << "n = " << pp_mon_with_vars(_(), n);
@@ -186,7 +186,7 @@ lpvar basics::find_best_zero(const monic& m, unsigned_vector & fixed_zeros) cons
     return zero_j;    
 }
 void basics::add_trival_zero_lemma(lpvar zero_j, const monic& m) {
-    add_empty_lemma();
+    add_lemma();
     c().mk_ineq(zero_j, llc::NE);
     c().mk_ineq(m.var(), llc::EQ);
     TRACE("nla_solver", c().print_lemma(tout););            
@@ -194,7 +194,7 @@ void basics::add_trival_zero_lemma(lpvar zero_j, const monic& m) {
 void basics::generate_strict_case_zero_lemma(const monic& m, unsigned zero_j, int sign_of_zj) {
     TRACE("nla_solver_bl", tout << "sign_of_zj = " << sign_of_zj << "\n";);
     // we know all the signs
-    add_empty_lemma();
+    add_lemma();
     c().mk_ineq(zero_j, (sign_of_zj == 1? llc::GT : llc::LT));
     for (unsigned j : m.vars()){
         if (j != zero_j) {
@@ -205,7 +205,7 @@ void basics::generate_strict_case_zero_lemma(const monic& m, unsigned zero_j, in
     TRACE("nla_solver", c().print_lemma(tout););
 }
 void basics::add_fixed_zero_lemma(const monic& m, lpvar j) {
-    add_empty_lemma();
+    add_lemma();
     c().explain_fixed_var(j);
     c().mk_ineq(m.var(), llc::EQ);
     TRACE("nla_solver", c().print_lemma(tout););
@@ -234,7 +234,7 @@ bool basics::basic_lemma_for_mon_zero(const monic& rm, const factorization& f) {
     return true;
 #if 0
     TRACE("nla_solver", c().trace_print_monic_and_factorization(rm, f, tout););
-    add_empty_lemma();
+    add_lemma();
     c().explain_fixed_var(var(rm));
     std::unordered_set<lpvar> processed;
     for (auto j : f) {
@@ -315,7 +315,7 @@ bool basics::basic_lemma_for_mon_non_zero_derived(const monic& rm, const factori
     if (zero_j == -1) {
         return false;
     } 
-    add_empty_lemma();
+    add_lemma();
     c().explain_fixed_var(zero_j);
     c().explain_var_separated_from_zero(var(rm));
     explain(rm);
@@ -364,7 +364,7 @@ bool basics::basic_lemma_for_mon_neutral_monic_to_factor_derived(const monic& rm
         return false;
     } 
 
-    add_empty_lemma();
+    add_lemma();
     // mon_var = 0
     if (mon_var_is_sep_from_zero)
          c().explain_var_separated_from_zero(mon_var);
@@ -426,7 +426,7 @@ bool basics::proportion_lemma_derived(const monic& rm, const factorization& fact
 }
 // if there are no zero factors then |m| >= |m[factor_index]|
 void basics::generate_pl_on_mon(const monic& m, unsigned factor_index) {
-    add_empty_lemma();
+    add_lemma();
     unsigned mon_var = m.var();
     rational mv = val(mon_var);
     rational sm = rational(nla::rat_sign(mv));
@@ -457,7 +457,7 @@ void basics::generate_pl(const monic& m, const factorization& fc, int factor_ind
         generate_pl_on_mon(m, factor_index);
         return;
     }
-    add_empty_lemma();
+    add_lemma();
     int fi = 0;
     rational mv = var_val(m);
     rational sm = rational(nla::rat_sign(mv));
@@ -506,7 +506,7 @@ bool basics::factorization_has_real(const factorization& f) const {
 void basics::basic_lemma_for_mon_zero_model_based(const monic& rm, const factorization& f) {        
     TRACE("nla_solver",  c().trace_print_monic_and_factorization(rm, f, tout););
     SASSERT(var_val(rm).is_zero()&& ! c().rm_check(rm));
-    add_empty_lemma();
+    add_lemma();
     if (!is_separated_from_zero(f)) {
         c().mk_ineq(var(rm), llc::NE);        
         for (auto j : f) {
@@ -577,7 +577,7 @@ bool basics::basic_lemma_for_mon_neutral_monic_to_factor_model_based_fm(const mo
         return false;
     } 
 
-    add_empty_lemma();
+    add_lemma();
     // mon_var = 0
     c().mk_ineq(mon_var, llc::EQ);
         
@@ -625,7 +625,7 @@ bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based_fm(co
         }
     }
         
-    add_empty_lemma();
+    add_lemma();
     for (auto j : m.vars()){
         if (not_one == j) continue;
         c().mk_ineq(j, llc::NE, val(j));   
@@ -678,7 +678,7 @@ bool basics::basic_lemma_for_mon_neutral_monic_to_factor_model_based(const monic
         return false;
     } 
 
-    add_empty_lemma();
+    add_lemma();
     // mon_var = 0
     c().mk_ineq(mon_var, llc::EQ);
         
@@ -753,7 +753,7 @@ bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(const
 
     TRACE("nla_solver_bl", tout << "not_one = " << not_one << "\n";);
         
-    add_empty_lemma();
+    add_lemma();
 
     for (auto j : f){
         lpvar var_j = var(j);
@@ -788,7 +788,7 @@ void basics::basic_lemma_for_mon_non_zero_model_based_mf(const factorization& f)
     }
 
     if (zero_j == -1) { return; } 
-    add_empty_lemma();
+    add_lemma();
     c().mk_ineq(zero_j, llc::NE);
     c().mk_ineq(f.mon().var(), llc::EQ);
     TRACE("nla_solver", c().print_lemma(tout););
diff --git a/src/math/lp/nla_common.cpp b/src/math/lp/nla_common.cpp
index 770e782c225..548ce80f5a3 100644
--- a/src/math/lp/nla_common.cpp
+++ b/src/math/lp/nla_common.cpp
@@ -41,7 +41,7 @@ rational common::mul_val(monic const& m) const { return c().mul_val(m); }
 template <typename T> lpvar common::var(T const& t) const { return c().var(t); }
 template lpvar common::var<factor>(factor const& t) const;
 template lpvar common::var<monic>(monic const& t) const;
-void common::add_empty_lemma() { c().add_empty_lemma(); }
+void common::add_lemma() { c().add_lemma(); }
 template <typename T> bool common::canonize_sign(const T& t) const {
     return c().canonize_sign(t);
 }
diff --git a/src/math/lp/nla_common.h b/src/math/lp/nla_common.h
index 682b50578fd..9e40d763f51 100644
--- a/src/math/lp/nla_common.h
+++ b/src/math/lp/nla_common.h
@@ -63,7 +63,7 @@ struct common {
     bool done() const;
     template <typename T> void explain(const T&);
     void explain(lpvar);
-    void add_empty_lemma();
+    void add_lemma();
     template <typename T> bool canonize_sign(const T&) const;
     void mk_ineq(lp::lar_term& t, llc cmp, const rational& rs);
     void mk_ineq(const rational& a, lpvar j, const rational& b, lpvar k, llc cmp, const rational& rs);
diff --git a/src/math/lp/nla_core.cpp b/src/math/lp/nla_core.cpp
index 1a4a7a0431c..70491d251b2 100644
--- a/src/math/lp/nla_core.cpp
+++ b/src/math/lp/nla_core.cpp
@@ -1243,7 +1243,7 @@ rational core::val(const factorization& f) const {
     return r;
 }
 
-void core::add_empty_lemma() {
+void core::add_lemma() {
     m_lemma_vec->push_back(lemma()); 
 }
     
@@ -1656,7 +1656,7 @@ bool core::check_pdd_eq(const dd::solver::equation* e) {
         return false;
     eval.get_interval<dd::w_dep::with_deps>(e->poly(), i_wd);  
     std::function<void (const lp::explanation&)> f = [this](const lp::explanation& e) {
-        add_empty_lemma();
+        add_lemma();
         current_expl().add(e);
     };
     if (di.check_interval_for_conflict_on_zero(i_wd, e->dep(), f)) {
diff --git a/src/math/lp/nla_core.h b/src/math/lp/nla_core.h
index 7027727e9d2..5b370c49d07 100644
--- a/src/math/lp/nla_core.h
+++ b/src/math/lp/nla_core.h
@@ -161,7 +161,7 @@ class core {
     svector<lpvar> sorted_rvars(const factor& f) const;
     bool done() const;
 
-    void add_empty_lemma();
+    void add_lemma();
     // the value of the factor is equal to the value of the variable multiplied
     // by the canonize_sign
     bool canonize_sign(const factor& f) const;
diff --git a/src/math/lp/nla_intervals.cpp b/src/math/lp/nla_intervals.cpp
index 53917390b64..a9019b7ac4e 100644
--- a/src/math/lp/nla_intervals.cpp
+++ b/src/math/lp/nla_intervals.cpp
@@ -84,7 +84,7 @@ bool intervals::check_nex(const nex* n, u_dependency* initial_deps) {
     m_core->lp_settings().stats().m_cross_nested_forms++;
     scoped_dep_interval i(get_dep_intervals());
     std::function<void (const lp::explanation&)> f = [this](const lp::explanation& e) {
-                                                         m_core->add_empty_lemma();
+                                                         m_core->add_lemma();
                                                          m_core->current_expl().add(e);
                                                      };
     if (!interval_of_expr<e_with_deps::without_deps>(n, 1, i, f)) {
diff --git a/src/math/lp/nla_monotone_lemmas.cpp b/src/math/lp/nla_monotone_lemmas.cpp
index d7e507b8095..8114732e27c 100644
--- a/src/math/lp/nla_monotone_lemmas.cpp
+++ b/src/math/lp/nla_monotone_lemmas.cpp
@@ -48,7 +48,7 @@ void monotone::monotonicity_lemma(monic const& m) {
 void monotone::monotonicity_lemma_gt(const monic& m, const rational& prod_val) {
     TRACE("nla_solver", tout << "prod_val = " << prod_val << "\n";
           tout << "m = "; c().print_monic_with_vars(m, tout););
-    add_empty_lemma();
+    add_lemma();
     for (lpvar j : m.vars()) {
         c().add_abs_bound(j, llc::GT);
     }
@@ -64,7 +64,7 @@ void monotone::monotonicity_lemma_gt(const monic& m, const rational& prod_val) {
     \/_i |m[i]| < |val(m[i])} or |m| >= |product_i val(m[i])|
 */
 void monotone::monotonicity_lemma_lt(const monic& m, const rational& prod_val) {
-    add_empty_lemma();
+    add_lemma();
     for (lpvar j : m.vars()) {
         c().add_abs_bound(j, llc::LT);
     }
diff --git a/src/math/lp/nla_order_lemmas.cpp b/src/math/lp/nla_order_lemmas.cpp
index 91aabae6e4a..54dda5d65e0 100644
--- a/src/math/lp/nla_order_lemmas.cpp
+++ b/src/math/lp/nla_order_lemmas.cpp
@@ -92,7 +92,7 @@ void order::order_lemma_on_binomial(const monic& ac) {
 void order::order_lemma_on_binomial_sign(const monic& xy, lpvar x, lpvar y, int sign) {
     SASSERT(!_().mon_has_zero(xy.vars()));
     int sy = rat_sign(val(y));
-    add_empty_lemma();
+    add_lemma();
     mk_ineq(y,                     sy == 1      ? llc::LE : llc::GE); // negate sy
     mk_ineq(x,                     sy*sign == 1 ? llc::GT : llc::LT , val(x)); 
     mk_ineq(xy.var(), - val(x), y, sign == 1    ? llc::LE : llc::GE);
@@ -175,7 +175,7 @@ void order::generate_mon_ol(const monic& ac,
     SASSERT(ab_cmp != llc::LT || (var_val(ac) >= var_val(bd) && val(a)*c_sign < val(b)*d_sign));
     SASSERT(ab_cmp != llc::GT || (var_val(ac) <= var_val(bd) && val(a)*c_sign > val(b)*d_sign));
     
-    add_empty_lemma();
+    add_lemma();
     mk_ineq(c_sign, c, llc::LE);
     explain(c); // this explains c == +- d
     mk_ineq(c_sign, a, -d_sign * b.rat_sign(), b.var(), negate(ab_cmp));
@@ -261,7 +261,7 @@ void order::generate_ol_eq(const monic& ac,
                         const monic& bc,
                         const factor& b)                        {
     
-    add_empty_lemma();
+    add_lemma();
 #if 0
     IF_VERBOSE(0, verbose_stream() << var_val(ac) << "(" << mul_val(ac) << "): " << ac 
                << " " << ab_cmp << " " << var_val(bc) << "(" << mul_val(bc) << "): " << bc << "\n"
@@ -287,7 +287,7 @@ void order::generate_ol(const monic& ac,
                         const monic& bc,
                         const factor& b)                        {
     
-    add_empty_lemma();
+    add_lemma();
 #if 0
     IF_VERBOSE(0, verbose_stream() << var_val(ac) << "(" << mul_val(ac) << "): " << ac 
                << " " << ab_cmp << " " << var_val(bc) << "(" << mul_val(bc) << "): " << bc << "\n"
@@ -339,7 +339,7 @@ bool order::order_lemma_on_ac_and_bc_and_factors(const monic& ac,
 */
 void order::order_lemma_on_ab_gt(const monic& m, const rational& sign, lpvar a, lpvar b) {
     SASSERT(sign * var_val(m) > val(a) * val(b));
-    add_empty_lemma();
+    add_lemma();
     if (val(a).is_pos()) {
         TRACE("nla_solver", tout << "a is pos\n";);
         //negate a > 0
@@ -369,7 +369,7 @@ void order::order_lemma_on_ab_lt(const monic& m, const rational& sign, lpvar a,
     TRACE("nla_solver", tout << "sign = " << sign << ", m = "; c().print_monic(m, tout) << ", a = "; c().print_var(a, tout) <<
           ", b = "; c().print_var(b, tout) << "\n";);
     SASSERT(sign * var_val(m) < val(a) * val(b));
-    add_empty_lemma();
+    add_lemma();
     if (val(a).is_pos()) {
         //negate a > 0
         mk_ineq(a, llc::LE);
diff --git a/src/math/lp/nla_tangent_lemmas.cpp b/src/math/lp/nla_tangent_lemmas.cpp
index aa6d7c9d6dd..f8901640cdf 100644
--- a/src/math/lp/nla_tangent_lemmas.cpp
+++ b/src/math/lp/nla_tangent_lemmas.cpp
@@ -75,7 +75,7 @@ struct imp {
 
 
     void generate_tang_plane(const point & pl) {
-        c().add_empty_lemma();
+        c().add_lemma();
         c().negate_relation(m_jx, m_x.rat_sign()*pl.x);
         c().negate_relation(m_jy, m_y.rat_sign()*pl.y);
 #if Z3DEBUG
@@ -95,12 +95,12 @@ struct imp {
     }
     
     void generate_two_tang_lines() {
-        m_tang.add_empty_lemma();
+        m_tang.add_lemma();
         // Should be  v = val(m_x)*val(m_y), and val(factor) = factor.rat_sign()*var(factor.var())
         c().mk_ineq(m_jx, llc::NE, c().val(m_jx));
         c().mk_ineq(m_j,  - m_y.rat_sign() * m_xy.x,  m_jy, llc::EQ);
         
-        m_tang.add_empty_lemma();
+        m_tang.add_lemma();
         c().mk_ineq(m_jy, llc::NE, c().val(m_jy));
         c().mk_ineq(m_j, - m_x.rat_sign() * m_xy.y, m_jx, llc::EQ);
     }
diff --git a/src/test/lp/lp.cpp b/src/test/lp/lp.cpp
index 93d1c9d86df..e40232a81fe 100644
--- a/src/test/lp/lp.cpp
+++ b/src/test/lp/lp.cpp
@@ -2683,7 +2683,10 @@ void run_lar_solver(argument_parser & args_parser, lar_solver * solver, mps_read
             return;
         }
         std::cout << "checking randomize" << std::endl;
-        vector<var_index> all_vars = solver->get_list_of_all_var_indices();
+        vector<var_index> all_vars;
+        for (unsigned j = 0; j < solver->number_of_vars(); j++)
+            all_vars.push_back(j);
+        
         unsigned m = all_vars.size();
         if (m > 100)
             m = 100;