diff --git a/src/ast/rewriter/arith_rewriter.cpp b/src/ast/rewriter/arith_rewriter.cpp
index 6d2e9dae1..18556b71b 100644
--- a/src/ast/rewriter/arith_rewriter.cpp
+++ b/src/ast/rewriter/arith_rewriter.cpp
@@ -755,6 +755,13 @@ br_status arith_rewriter::mk_mod_core(expr * arg1, expr * arg2, expr_ref & resul
         return BR_DONE;
     }
 
+    if (arg1 == arg2 && !m_util.is_numeral(arg2)) {
+        expr_ref zero(m_util.mk_int(0), m()), abs(m());
+        mk_abs_core(arg2, abs);
+        result = m().mk_ite(m().mk_eq(arg2, zero), m_util.mk_mod(zero, zero), abs);
+        return BR_DONE;
+    }
+
     // mod is idempotent on non-zero modulus.
     expr* t1, *t2;
     if (m_util.is_mod(arg1, t1, t2) && t2 == arg2 && m_util.is_numeral(arg2, v2, is_int) && is_int && !v2.is_zero()) {
diff --git a/src/qe/nlqsat.cpp b/src/qe/nlqsat.cpp
index 4f041cc41..0f2437982 100644
--- a/src/qe/nlqsat.cpp
+++ b/src/qe/nlqsat.cpp
@@ -18,22 +18,22 @@ Revision History:
 
 --*/
 
-#include "qe/nlqsat.h"
-#include "nlsat/nlsat_solver.h"
-#include "nlsat/nlsat_explain.h"
-#include "nlsat/nlsat_assignment.h"
-#include "qe/qsat.h"
-#include "ast/rewriter/quant_hoist.h"
-#include "nlsat/tactic/goal2nlsat.h"
-#include "ast/expr2var.h"
 #include "util/uint_set.h"
+#include "ast/expr2var.h"
 #include "ast/ast_util.h"
-#include "tactic/core/tseitin_cnf_tactic.h"
 #include "ast/rewriter/expr_safe_replace.h"
 #include "ast/ast_pp.h"
 #include "ast/for_each_expr.h"
 #include "ast/rewriter/rewriter.h"
 #include "ast/rewriter/rewriter_def.h"
+#include "ast/rewriter/quant_hoist.h"
+#include "qe/nlqsat.h"
+#include "qe/qsat.h"
+#include "nlsat/nlsat_solver.h"
+#include "nlsat/nlsat_explain.h"
+#include "nlsat/nlsat_assignment.h"
+#include "nlsat/tactic/goal2nlsat.h"
+#include "tactic/core/tseitin_cnf_tactic.h"
 
 
 namespace qe {
@@ -292,8 +292,8 @@ namespace qe {
             nlsat::var_vector vs;
             m_solver.vars(l, vs);
             TRACE("qe", m_solver.display(tout, l); tout << "\n";);
-            for (unsigned i = 0; i < vs.size(); ++i) {
-                level.merge(m_rvar2level[vs[i]]);
+            for (unsigned v : vs) {
+                level.merge(m_rvar2level[v]);                
             }
             set_level(l.var(), level);
             return level;
@@ -438,9 +438,10 @@ namespace qe {
         class div_rewriter_cfg : public default_rewriter_cfg {
             ast_manager&  m;
             arith_util    a;
+            expr_ref      m_zero;
             vector<div>   m_divs;
         public:
-            div_rewriter_cfg(nlqsat& s): m(s.m), a(s.m) {}
+            div_rewriter_cfg(nlqsat& s): m(s.m), a(s.m), m_zero(a.mk_real(0), m) {}
             ~div_rewriter_cfg() {}
             br_status reduce_app(func_decl* f, unsigned sz, expr* const* args, expr_ref& result, proof_ref& pr) {
                 if (is_decl_of(f, a.get_family_id(), OP_DIV) && sz == 2 && !a.is_numeral(args[1])) {                    
@@ -448,6 +449,11 @@ namespace qe {
                     m_divs.push_back(div(m, args[0], args[1], to_app(result)));
                     return BR_DONE;
                 }
+                if (is_decl_of(f, a.get_family_id(), OP_DIV_0) && sz == 1 && !a.is_numeral(args[0])) {                    
+                    result = m.mk_fresh_const("div", a.mk_real());
+                    m_divs.push_back(div(m, args[0], m_zero, to_app(result)));
+                    return BR_DONE;
+                }
                 return BR_FAILED;
             }
             vector<div> const& divs() const { return m_divs; }
@@ -497,7 +503,11 @@ namespace qe {
                 if (a.is_power(n, n1, n2) && a.is_numeral(n2, r) && r.is_unsigned()) {
                     return;
                 }
-                if (a.is_div(n, n1, n2) && s.m_mode == qsat_t) {
+                if (a.is_div(n) && s.m_mode == qsat_t) {
+                    m_has_divs = true;
+                    return;
+                }
+                if (a.is_div0(n) && s.m_mode == qsat_t) {
                     m_has_divs = true;
                     return;
                 }
@@ -539,7 +549,7 @@ namespace qe {
             app_ref_vector pvars(m);
             expr_ref_vector paxioms(m);
             purify(fml, pvars, paxioms);            
-            if (pvars.empty()) {
+            if (paxioms.empty()) {
                 return;
             }
             expr_ref ante = mk_and(paxioms);
@@ -552,6 +562,7 @@ namespace qe {
             }
         }
 
+
         void reset() {
             //m_solver.reset();
             m_asms.reset();
@@ -618,10 +629,12 @@ namespace qe {
             app_ref_vector vars(m);
             bool is_forall = false;   
             pred_abs abs(m);
+
             abs.get_free_vars(fml, vars);
             insert_set(m_free_vars, vars);
             qvars.push_back(vars); 
             vars.reset();  
+
             if (m_mode == elim_t) {
                 is_forall = true;
                 hoist.pull_quantifier(is_forall, fml, vars);
@@ -638,6 +651,7 @@ namespace qe {
                 qvars.push_back(vars);
             }
             while (!vars.empty());
+            SASSERT(qvars.size() >= 2);
             SASSERT(qvars.back().empty()); 
 
             ackermanize_div(is_forall, qvars, fml);
diff --git a/src/qe/qsat.cpp b/src/qe/qsat.cpp
index abd396818..713ecfe77 100644
--- a/src/qe/qsat.cpp
+++ b/src/qe/qsat.cpp
@@ -20,23 +20,23 @@ Notes:
 
 --*/
 
-#include "smt/smt_kernel.h"
-#include "qe/qe_mbp.h"
-#include "smt/params/smt_params.h"
+#include "ast/expr_abstract.h"
 #include "ast/ast_util.h"
 #include "ast/rewriter/quant_hoist.h"
 #include "ast/ast_pp.h"
-#include "model/model_v2_pp.h"
-#include "qe/qsat.h"
-#include "ast/expr_abstract.h"
-#include "qe/qe.h"
-#include "ast/rewriter/label_rewriter.h"
-#include "ast/rewriter/expr_replacer.h"
 #include "ast/rewriter/th_rewriter.h"
+#include "ast/rewriter/expr_replacer.h"
+#include "model/model_v2_pp.h"
 #include "model/model_evaluator.h"
+#include "smt/smt_kernel.h"
+#include "smt/params/smt_params.h"
 #include "smt/smt_solver.h"
 #include "solver/solver.h"
 #include "solver/mus.h"
+#include "qe/qsat.h"
+#include "qe/qe_mbp.h"
+#include "qe/qe.h"
+#include "ast/rewriter/label_rewriter.h"
 
 namespace qe {
 
diff --git a/src/tactic/portfolio/smt_strategic_solver.cpp b/src/tactic/portfolio/smt_strategic_solver.cpp
index fe1cf5260..bde9e0e98 100644
--- a/src/tactic/portfolio/smt_strategic_solver.cpp
+++ b/src/tactic/portfolio/smt_strategic_solver.cpp
@@ -31,14 +31,15 @@ Notes:
 #include "tactic/smtlogics/qfaufbv_tactic.h"
 #include "tactic/smtlogics/qfufbv_tactic.h"
 #include "tactic/smtlogics/qfidl_tactic.h"
+#include "tactic/smtlogics/nra_tactic.h"
 #include "tactic/portfolio/default_tactic.h"
+#include "tactic/portfolio/fd_solver.h"
 #include "tactic/ufbv/ufbv_tactic.h"
 #include "tactic/fpa/qffp_tactic.h"
 #include "tactic/smtlogics/qfufnra_tactic.h"
 #include "muz/fp/horn_tactic.h"
 #include "smt/smt_solver.h"
 #include "sat/sat_solver/inc_sat_solver.h"
-#include "tactic/portfolio/fd_solver.h"
 #include "ast/rewriter/bv_rewriter.h"
 #include "solver/solver2tactic.h"
 
@@ -78,6 +79,8 @@ tactic * mk_tactic_for_logic(ast_manager & m, params_ref const & p, symbol const
         return mk_uflra_tactic(m, p);
     else if (logic=="LRA")
         return mk_lra_tactic(m, p);
+    else if (logic=="NRA")
+        return mk_nra_tactic(m, p);
     else if (logic=="LIA")
         return mk_lia_tactic(m, p);
     else if (logic=="UFBV")