diff --git a/contrib/cmake/src/opt/CMakeLists.txt b/contrib/cmake/src/opt/CMakeLists.txt
index c50f8be52..e4166e3d4 100644
--- a/contrib/cmake/src/opt/CMakeLists.txt
+++ b/contrib/cmake/src/opt/CMakeLists.txt
@@ -8,7 +8,6 @@ z3_add_component(opt
     maxsls.cpp
     maxsmt.cpp
     mss.cpp
-    mus.cpp
     opt_cmds.cpp
     opt_context.cpp
     opt_pareto.cpp
diff --git a/contrib/cmake/src/solver/CMakeLists.txt b/contrib/cmake/src/solver/CMakeLists.txt
index 5e76c91ce..8142ca872 100644
--- a/contrib/cmake/src/solver/CMakeLists.txt
+++ b/contrib/cmake/src/solver/CMakeLists.txt
@@ -2,6 +2,7 @@ z3_add_component(solver
   SOURCES
     check_sat_result.cpp
     combined_solver.cpp
+    mus.cpp
     solver.cpp
     solver_na2as.cpp
     tactic2solver.cpp
diff --git a/src/opt/maxres.cpp b/src/opt/maxres.cpp
index 7c1fad80e..741bab4b5 100644
--- a/src/opt/maxres.cpp
+++ b/src/opt/maxres.cpp
@@ -119,7 +119,7 @@ public:
         maxsmt_solver_base(c, ws, soft),
         m_index(index), 
         m_B(m), m_asms(m), m_defs(m),
-        m_mus(c.get_solver(), m),
+        m_mus(c.get_solver()),
         m_mss(c.get_solver(), m),
         m_trail(m),
         m_st(st),
diff --git a/src/opt/mus.h b/src/opt/mus.h
deleted file mode 100644
index 8ca7ab91d..000000000
--- a/src/opt/mus.h
+++ /dev/null
@@ -1,55 +0,0 @@
-/*++
-Copyright (c) 2014 Microsoft Corporation
-
-Module Name:
-
-    mus.h
-
-Abstract:
-   
-    Basic MUS extraction
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2014-20-7
-
-Notes:
-
---*/
-#ifndef MUS_H_
-#define MUS_H_
-
-namespace opt {
-    class mus {
-        struct imp;
-        imp * m_imp;
-    public:
-        mus(solver& s, ast_manager& m);
-        ~mus();
-        /**
-           Add soft constraint.
-
-           Assume that the solver context enforces that 
-           cls is equivalent to a disjunction of args.
-           Assume also that cls is a literal.           
-        */
-        unsigned add_soft(expr* cls);
-        
-        lbool get_mus(unsigned_vector& mus);
-        
-        void reset();
-        
-        /**
-           Instrument MUS extraction to also provide the minimal
-           penalty model, if any is found.
-           The minimal penalty model has the least weight for the 
-           supplied soft constraints.
-         */
-        void set_soft(unsigned sz, expr* const* soft, rational const* weights);
-        rational get_best_model(model_ref& mdl);
-        
-    };
-
-};
-
-#endif
diff --git a/src/qe/qsat.cpp b/src/qe/qsat.cpp
index a9ca9e99d..4c6efdcd4 100644
--- a/src/qe/qsat.cpp
+++ b/src/qe/qsat.cpp
@@ -34,7 +34,9 @@ Notes:
 #include "expr_replacer.h"
 #include "th_rewriter.h"
 #include "model_evaluator.h"
-
+#include "smt_solver.h"
+#include "solver.h"
+#include "mus.h"
 
 namespace qe {
 
@@ -506,33 +508,58 @@ namespace qe {
     }
 
     class kernel {
-        smt_params   m_smtp;
-        smt::kernel  m_kernel;
+        ast_manager& m;
+        params_ref   m_params;
+        ref<solver>  m_solver;
         
     public:
         kernel(ast_manager& m):
-            m_kernel(m, m_smtp)
+            m(m),
+            m_solver(mk_smt_solver(m, m_params, symbol::null))
         {
-            m_smtp.m_model = true;
-            m_smtp.m_relevancy_lvl = 0;
-            m_smtp.m_case_split_strategy = CS_ACTIVITY_WITH_CACHE;
+            m_params.set_bool("model", true);
+            m_params.set_uint("relevancy_lvl", 0);
+            m_params.set_uint("case_split_strategy", CS_ACTIVITY_WITH_CACHE);
+            m_solver->updt_params(m_params);
         }
         
-        smt::kernel& k() { return m_kernel; }
-        smt::kernel const& k() const { return m_kernel; }
         
+        solver& s() { return *m_solver; }
+        solver const& s() const { return *m_solver; }
+
+        void reset() {
+            m_solver = mk_smt_solver(m, m_params, symbol::null);
+        }
         void assert_expr(expr* e) {
-            m_kernel.assert_expr(e);
+            m_solver->assert_expr(e);
         }
         
+        ptr_vector<expr> m_core;
+
         void get_core(expr_ref_vector& core) {
-            unsigned sz = m_kernel.get_unsat_core_size();
             core.reset();
-            for (unsigned i = 0; i < sz; ++i) {
-                core.push_back(m_kernel.get_unsat_core_expr(i));
+            m_core.reset();
+            m_solver->get_unsat_core(m_core);
+            core.append(m_core.size(), m_core.c_ptr());
+
+#if 0
+
+            mus mus(*m_solver);
+            for (unsigned i = 0; i < m_core.size(); ++i) {
+                VERIFY(i == mus.add_soft(m_core[i]));
             }
+            unsigned_vector mus2;
+            core.reset();
+            if (mus.get_mus(mus2) != l_undef) {
+                for (unsigned i = 0; i < mus2.size(); ++i) {
+                    core.push_back(m_core[mus2[i]]);
+                }
+            }
+            std::cout << m_core.size() << " => " << core.size() << "\n";
+#endif
+
             TRACE("qe", tout << "core: " << core << "\n";
-                  m_kernel.display(tout);
+                  m_solver->display(tout);
                   tout << "\n";
                   );
         }
@@ -586,13 +613,13 @@ namespace qe {
                 expr_ref_vector asms(m_asms);
                 m_pred_abs.get_assumptions(m_model.get(), asms);
                 TRACE("qe", tout << asms << "\n";);
-                smt::kernel& k = get_kernel(m_level).k();
-                lbool res = k.check(asms);
+                solver& s = get_kernel(m_level).s();
+                lbool res = s.check_sat(asms);
                 switch (res) {
                 case l_true:
-                    k.get_model(m_model);
+                    s.get_model(m_model);
                     SASSERT(validate_model(asms));
-                    TRACE("qe", k.display(tout); display(tout << "\n", *m_model.get()); display(tout, asms); );
+                    TRACE("qe", s.display(tout); display(tout << "\n", *m_model.get()); display(tout, asms); );
                     push();
                     break;
                 case l_false:
@@ -655,8 +682,8 @@ namespace qe {
         
         void reset() {
             m_st.reset();        
-            m_fa.k().collect_statistics(m_st);
-            m_ex.k().collect_statistics(m_st);        
+            m_fa.s().collect_statistics(m_st);
+            m_ex.s().collect_statistics(m_st);        
             m_pred_abs.collect_statistics(m_st);
             m_level = 0;
             m_answer.reset();
@@ -664,8 +691,8 @@ namespace qe {
             m_pred_abs.reset();
             m_vars.reset();
             m_model = 0;
-            m_fa.k().reset();
-            m_ex.k().reset();        
+            m_fa.reset();
+            m_ex.reset();        
             m_free_vars.reset();
         }    
         
@@ -964,10 +991,12 @@ namespace qe {
 
         bool validate_core(expr_ref_vector const& core) {
             TRACE("qe", tout << "Validate core\n";);
-            smt::kernel& k = get_kernel(m_level).k();
+            solver& s = get_kernel(m_level).s();
             expr_ref_vector fmls(m);
             fmls.append(core.size(), core.c_ptr());
-            fmls.append(k.size(), k.get_formulas());
+            for (unsigned i = 0; i < s.get_num_assertions(); ++i) {
+                fmls.push_back(s.get_assertion(i));
+            }
             return check_fmls(fmls) || m.canceled();
         }
 
@@ -985,10 +1014,14 @@ namespace qe {
 
         bool validate_model(expr_ref_vector const& asms) {
             TRACE("qe", tout << "Validate model\n";);
-            smt::kernel& k = get_kernel(m_level).k();
+            solver& s = get_kernel(m_level).s();
+            expr_ref_vector fmls(m);
+            for (unsigned i = 0; i < s.get_num_assertions(); ++i) {
+                fmls.push_back(s.get_assertion(i));
+            }
             return 
                 validate_model(*m_model, asms.size(), asms.c_ptr()) &&
-                validate_model(*m_model, k.size(), k.get_formulas());
+                validate_model(*m_model, fmls.size(), fmls.c_ptr());
         }
 
         bool validate_model(model& mdl, unsigned sz, expr* const* fmls) {
@@ -1161,9 +1194,9 @@ namespace qe {
                 break;
             case l_undef:
                 result.push_back(in.get());
-                std::string s = m_ex.k().last_failure_as_string();
-                if (s == "ok") {
-                    s = m_fa.k().last_failure_as_string();
+                std::string s = m_ex.s().reason_unknown();
+                if (s == "ok" || s == "unknown") {
+                    s = m_fa.s().reason_unknown();
                 }
                 throw tactic_exception(s.c_str()); 
             }        
@@ -1171,8 +1204,8 @@ namespace qe {
         
         void collect_statistics(statistics & st) const {
             st.copy(m_st);
-            m_fa.k().collect_statistics(st);
-            m_ex.k().collect_statistics(st);        
+            m_fa.s().collect_statistics(st);
+            m_ex.s().collect_statistics(st);        
             m_pred_abs.collect_statistics(st);
             st.update("qsat num rounds", m_stats.m_num_rounds); 
             m_pred_abs.collect_statistics(st);
@@ -1180,8 +1213,8 @@ namespace qe {
         
         void reset_statistics() {
             m_stats.reset();
-            m_fa.k().reset_statistics();
-            m_ex.k().reset_statistics();      
+            m_fa.reset();
+            m_ex.reset();
         }
         
         void cleanup() {
@@ -1223,9 +1256,9 @@ namespace qe {
                 UNREACHABLE();
                 break;
             case l_undef:
-                std::string s = m_ex.k().last_failure_as_string();
+                std::string s = m_ex.s().reason_unknown();
                 if (s == "ok") {
-                    s = m_fa.k().last_failure_as_string();
+                    s = m_fa.s().reason_unknown();
                 }
 
                 throw tactic_exception(s.c_str()); 
diff --git a/src/solver/check_sat_result.h b/src/solver/check_sat_result.h
index e6586d492..b981b3119 100644
--- a/src/solver/check_sat_result.h
+++ b/src/solver/check_sat_result.h
@@ -54,6 +54,7 @@ public:
     virtual void set_reason_unknown(char const* msg) = 0;
     virtual void get_labels(svector<symbol> & r) = 0;
     virtual ast_manager& get_manager() = 0;
+
 };
 
 /**
diff --git a/src/opt/mus.cpp b/src/solver/mus.cpp
similarity index 55%
rename from src/opt/mus.cpp
rename to src/solver/mus.cpp
index aa8446256..ebdffca13 100644
--- a/src/opt/mus.cpp
+++ b/src/solver/mus.cpp
@@ -19,14 +19,11 @@ Notes:
 --*/
 
 #include "solver.h"
-#include "smt_literal.h"
 #include "mus.h"
 #include "ast_pp.h"
 #include "ast_util.h"
+#include "uint_set.h"
 
-using namespace opt;
-
-// 
 
 struct mus::imp {
     solver&                  m_s;
@@ -38,15 +35,14 @@ struct mus::imp {
     vector<rational>         m_weights;
     rational                 m_weight;
 
-    imp(solver& s, ast_manager& m): 
-        m_s(s), m(m), m_cls2expr(m),  m_soft(m)
+    imp(solver& s): 
+        m_s(s), m(s.get_manager()), m_cls2expr(m),  m_soft(m)
     {}
 
     void reset() {
         m_cls2expr.reset();
         m_expr2cls.reset();
-    }
-            
+    }            
     
     unsigned add_soft(expr* cls) {
         SASSERT(is_uninterp_const(cls) || 
@@ -55,7 +51,7 @@ struct mus::imp {
         m_expr2cls.insert(cls, idx);
         m_cls2expr.push_back(cls);
         TRACE("opt", tout << idx << ": " << mk_pp(cls, m) << "\n";
-        display_vec(tout, m_cls2expr););
+              display_vec(tout, m_cls2expr););
         return idx;
     }
     
@@ -70,11 +66,16 @@ struct mus::imp {
             mus.push_back(core.back());
             return l_true;
         }
+
         mus.reset();
+        if (core.size() > 64) {
+            return qx(mus);
+        }
+
         expr_ref_vector assumptions(m);
         ptr_vector<expr> core_exprs;
         while (!core.empty()) { 
-            IF_VERBOSE(2, verbose_stream() << "(opt.mus reducing core: " << core.size() << " new core: " << mus.size() << ")\n";);
+            IF_VERBOSE(12, verbose_stream() << "(opt.mus reducing core: " << core.size() << " new core: " << mus.size() << ")\n";);
             unsigned cls_id = core.back();
             TRACE("opt", 
                   display_vec(tout << "core:  ", core);
@@ -84,11 +85,12 @@ struct mus::imp {
             expr* cls = m_cls2expr[cls_id].get();
             expr_ref not_cls(m);
             not_cls = mk_not(m, cls);
-            unsigned sz = assumptions.size();
-            assumptions.push_back(not_cls);
-            add_core(core, assumptions);
-            lbool is_sat = m_s.check_sat(assumptions.size(), assumptions.c_ptr());
-            assumptions.resize(sz);
+            lbool is_sat = l_undef;
+            {
+                scoped_append _sa(*this, assumptions, core);
+                assumptions.push_back(not_cls);
+                is_sat = m_s.check_sat(assumptions);
+            }
             switch (is_sat) {
             case l_undef: 
                 return is_sat;
@@ -132,6 +134,30 @@ struct mus::imp {
         return l_true;
     }
 
+    class scoped_append {
+        expr_ref_vector& m_fmls;
+        unsigned         m_size;
+    public:
+        scoped_append(imp& imp, expr_ref_vector& fmls1, unsigned_vector const& fmls2):
+            m_fmls(fmls1),
+            m_size(fmls1.size()) {
+            for (unsigned i = 0; i < fmls2.size(); ++i) {
+                fmls1.push_back(imp.m_cls2expr[fmls2[i]].get());
+            }            
+        }
+        scoped_append(imp& imp, expr_ref_vector& fmls1, uint_set const& fmls2):
+            m_fmls(fmls1),
+            m_size(fmls1.size()) {
+            uint_set::iterator it = fmls2.begin(), end = fmls2.end();
+            for (; it != end; ++it) {
+                fmls1.push_back(imp.m_cls2expr[*it].get());
+            }            
+        }
+        ~scoped_append() {
+            m_fmls.shrink(m_size);
+        }
+    };
+
     void add_core(unsigned_vector const& core, expr_ref_vector& assumptions) {
         for (unsigned i = 0; i < core.size(); ++i) {
             assumptions.push_back(m_cls2expr[core[i]].get());
@@ -193,10 +219,110 @@ struct mus::imp {
     }
 
 
+    lbool qx(unsigned_vector& mus) {
+        uint_set core, support;
+        for (unsigned i = 0; i < m_cls2expr.size(); ++i) {
+            core.insert(i);
+        }
+        lbool is_sat = qx(core, support, false);
+        if (is_sat == l_true) {
+            uint_set::iterator it = core.begin(), end = core.end();
+            mus.reset();
+            for (; it != end; ++it) {
+                mus.push_back(*it);
+            }
+        }
+        return is_sat;
+    }
+
+    lbool qx(uint_set& assignment, uint_set& support, bool has_support) {
+        lbool is_sat = l_true;
+#if 0
+        if (s.m_config.m_minimize_core_partial && s.m_stats.m_restart - m_restart > m_max_restarts) {
+            IF_VERBOSE(1, verbose_stream() << "(sat restart budget exceeded)\n";);
+            return l_true;
+        }
+#endif
+        if (has_support) {
+            expr_ref_vector asms(m);
+            scoped_append _sa(*this, asms, support);
+            is_sat = m_s.check_sat(asms);
+            switch (is_sat) {
+            case l_false: {
+                uint_set core; 
+                get_core(core);
+                support &= core;
+                assignment.reset();
+                return l_true;
+            }
+            case l_undef:
+                return l_undef;
+            case l_true:
+                update_model();
+                break;
+            default:
+                break;
+            }
+        }
+        if (assignment.num_elems() == 1) {
+            return l_true;
+        }
+        uint_set assign2;
+        split(assignment, assign2);
+        support |= assignment;
+        is_sat = qx(assign2, support, !assignment.empty());        
+        unsplit(support, assignment);
+        if (is_sat != l_true) return is_sat;
+        support |= assign2;
+        is_sat = qx(assignment, support, !assign2.empty());
+        assignment |= assign2;
+        unsplit(support, assign2);
+        return is_sat;
+    }
+
+    void get_core(uint_set& core) {
+        ptr_vector<expr> core_exprs;
+        m_s.get_unsat_core(core_exprs);
+        for (unsigned i = 0; i < core_exprs.size(); ++i) {
+            expr* cls = core_exprs[i];
+            core.insert(m_expr2cls.find(cls));
+        }
+    }
+
+    void unsplit(uint_set& A, uint_set& B) {
+        uint_set A1, B1;
+        uint_set::iterator it = A.begin(), end = A.end();
+        for (; it != end; ++it) {
+            if (B.contains(*it)) {
+                B1.insert(*it);
+            }
+            else {
+                A1.insert(*it);
+            }
+        }
+        A = A1;
+        B = B1;
+    }
+
+    void split(uint_set& lits1, uint_set& lits2) {
+        unsigned half = lits1.num_elems()/2;
+        uint_set lits3;
+        uint_set::iterator it = lits1.begin(), end = lits1.end();
+        for (unsigned i = 0; it != end; ++it, ++i) {
+            if (i < half) {
+                lits3.insert(*it);
+            }
+            else {
+                lits2.insert(*it);
+            }
+        }
+        lits1 = lits3;
+    }
+
 };
 
-mus::mus(solver& s, ast_manager& m) {
-    m_imp = alloc(imp, s, m);
+mus::mus(solver& s) {
+    m_imp = alloc(imp, s);
 }
 
 mus::~mus() {
diff --git a/src/solver/mus.h b/src/solver/mus.h
new file mode 100644
index 000000000..d66049030
--- /dev/null
+++ b/src/solver/mus.h
@@ -0,0 +1,54 @@
+/*++
+Copyright (c) 2014 Microsoft Corporation
+
+Module Name:
+
+    mus.h
+
+Abstract:
+   
+    Basic MUS extraction
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2014-20-7
+
+Notes:
+
+--*/
+#ifndef MUS_H_
+#define MUS_H_
+
+class mus {
+    struct imp;
+    imp * m_imp;
+ public:
+    mus(solver& s);
+    ~mus();
+    /**
+       Add soft constraint.
+       
+       Assume that the solver context enforces that 
+       cls is equivalent to a disjunction of args.
+       Assume also that cls is a literal.           
+    */
+    unsigned add_soft(expr* cls);
+    
+    lbool get_mus(unsigned_vector& mus);
+    
+    void reset();
+    
+    /**
+       Instrument MUS extraction to also provide the minimal
+       penalty model, if any is found.
+       The minimal penalty model has the least weight for the 
+       supplied soft constraints.
+    */
+    void set_soft(unsigned sz, expr* const* soft, rational const* weights);
+
+    rational get_best_model(model_ref& mdl);
+    
+};
+
+
+#endif
diff --git a/src/solver/solver.h b/src/solver/solver.h
index 5a1514795..0b2578968 100644
--- a/src/solver/solver.h
+++ b/src/solver/solver.h
@@ -108,6 +108,10 @@ public:
     */
     virtual lbool check_sat(unsigned num_assumptions, expr * const * assumptions) = 0;
 
+    lbool check_sat(expr_ref_vector const& asms) { return check_sat(asms.size(), asms.c_ptr()); }
+    
+    lbool check_sat(app_ref_vector const& asms) { return check_sat(asms.size(), (expr* const*)asms.c_ptr()); }
+
 
     /**
        \brief Set a progress callback procedure that is invoked by this solver during check_sat.