diff --git a/src/muz/rel/udoc_relation.cpp b/src/muz/rel/udoc_relation.cpp
index d3c1f929d..4d1fdf1d2 100644
--- a/src/muz/rel/udoc_relation.cpp
+++ b/src/muz/rel/udoc_relation.cpp
@@ -1264,6 +1264,21 @@ namespace datalog {
         return check_kind(t)?alloc(filter_proj_fn, get(t), get_ast_manager(), condition, removed_col_cnt, removed_cols):0;
     }
 
+    relation_join_fn * udoc_plugin::mk_join_project_fn(
+        relation_base const& t1, relation_base const& t2,
+        unsigned joined_col_cnt, const unsigned * cols1, const unsigned * cols2, 
+        unsigned removed_col_cnt, const unsigned * removed_cols) {    
+        if (check_kind(t1) && check_kind(t2)) 
+            return 0;
+#if 0
+            return alloc(join_proj_fn, get(t1), ge(t2), 
+                         joined_col_cnt, cols1, cols2, 
+                         removed_col_cnt, removed_cols);   
+#endif     
+        else
+            return 0;
+    }
+
 
 
 
diff --git a/src/muz/rel/udoc_relation.h b/src/muz/rel/udoc_relation.h
index f040e4745..596a1f0dd 100644
--- a/src/muz/rel/udoc_relation.h
+++ b/src/muz/rel/udoc_relation.h
@@ -81,6 +81,7 @@ namespace datalog {
     class udoc_plugin : public relation_plugin {
         friend class udoc_relation;
         class join_fn;
+        class join_project_fn;
         class project_fn;
         class union_fn;
         class rename_fn;
@@ -138,6 +139,11 @@ namespace datalog {
         virtual relation_transformer_fn * mk_filter_interpreted_and_project_fn(
             const relation_base & t, app * condition,
             unsigned removed_col_cnt, const unsigned * removed_cols);
+        virtual relation_join_fn * mk_join_project_fn(
+            relation_base const& t1, relation_base const& t2,
+            unsigned joined_col_cnt, const unsigned * cols1, const unsigned * cols2, 
+            unsigned removed_col_cnt, const unsigned * removed_cols);
+             
         void disable_fast_pass() { m_disable_fast_pass = true; }
     };
 };
diff --git a/src/opt/inc_sat_solver.cpp b/src/opt/inc_sat_solver.cpp
index 5eecf42d7..1c450bbef 100644
--- a/src/opt/inc_sat_solver.cpp
+++ b/src/opt/inc_sat_solver.cpp
@@ -316,6 +316,7 @@ private:
         for (; it != end; ++it) {
             asms.push_back(it->m_value);
         }
+        //IF_VERBOSE(0, verbose_stream() << asms << "\n";);
     }
 
     void extract_core(dep2asm_t& dep2asm) {
@@ -341,7 +342,7 @@ private:
         m_core.reset();
         for (unsigned i = 0; i < core.size(); ++i) {
             expr* e;
-            VERIFY (asm2dep.find(core[i].index(), e));
+            VERIFY(asm2dep.find(core[i].index(), e));
             m_core.push_back(e);
         }
 
@@ -397,6 +398,14 @@ private:
         SASSERT(m_model);
         // IF_VERBOSE(0, model_smt2_pp(verbose_stream(), m, *(m_model.get()), 0););
 
+        DEBUG_CODE(
+            for (unsigned i = 0; i < m_fmls.size(); ++i) {
+                expr_ref tmp(m);
+                VERIFY(m_model->eval(m_fmls[i].get(), tmp));                
+                CTRACE("opt", !m.is_true(tmp),
+                       tout << "Evaluation failed: " << mk_pp(m_fmls[i].get(), m) << "\n";);
+                SASSERT(m.is_true(tmp));
+            });
     }
 };
 
diff --git a/src/opt/maxres.cpp b/src/opt/maxres.cpp
index 86c0efb8f..63397664a 100644
--- a/src/opt/maxres.cpp
+++ b/src/opt/maxres.cpp
@@ -64,6 +64,7 @@ Notes:
 #include "pb_decl_plugin.h"
 #include "opt_params.hpp"
 #include "ast_util.h"
+#include "smt_solver.h"
 
 using namespace opt;
 
@@ -150,6 +151,7 @@ public:
     }
 
     void new_assumption(expr* e, rational const& w) {
+        IF_VERBOSE(3, verbose_stream() << "new assumption " << mk_pp(e, m) << " " << w << "\n";);
         TRACE("opt", tout << "insert: " << mk_pp(e, m) << " : " << w << "\n";);
         m_asm2weight.insert(e, w);
         m_asms.push_back(e);
@@ -171,7 +173,6 @@ public:
             if (m_cancel) {
                 return l_undef;
             }
-            model_ref mdl;
             switch (is_sat) {
             case l_true: 
                 found_optimum();
@@ -179,7 +180,6 @@ public:
             case l_false:
                 is_sat = process_unsat();
                 if (is_sat != l_true) return is_sat;
-                get_mus_model(mdl);
                 break;
             case l_undef:
                 return l_undef;
@@ -187,6 +187,7 @@ public:
                 break;
             }
         }
+        trace_bounds("maxres");
         return l_true;
     }
 
@@ -370,6 +371,7 @@ public:
     }
 
     void found_optimum() {
+        IF_VERBOSE(1, verbose_stream() << "found optimum\n";);
         s().get_model(m_model);
         DEBUG_CODE(
             for (unsigned i = 0; i < m_asms.size(); ++i) {
@@ -404,6 +406,9 @@ public:
         while (is_sat == l_false) {
             core.reset();
             s().get_unsat_core(core);
+            //verify_core(core);
+            model_ref mdl;
+            get_mus_model(mdl);
             is_sat = minimize_core(core);
             if (is_sat != l_true) {
                 break;
@@ -420,18 +425,12 @@ public:
                 break;
             }
             remove_soft(core, asms);
-            TRACE("opt",
-                  display_vec(tout << "core: ", core.size(), core.c_ptr());
-                  display_vec(tout << "assumptions: ", asms.size(), asms.c_ptr()););
             is_sat = check_sat_hill_climb(asms);
         }
         TRACE("opt", 
               tout << "num cores: " << cores.size() << "\n";
               for (unsigned i = 0; i < cores.size(); ++i) {
-                  for (unsigned j = 0; j < cores[i].size(); ++j) {
-                      tout << mk_pp(cores[i][j], m) << " ";
-                  }
-                  tout << "\n";
+                  display_vec(tout, cores[i].size(), cores[i].c_ptr());
               }
               tout << "num satisfying: " << asms.size() << "\n";);
         
@@ -535,6 +534,7 @@ public:
         if (m_c.sat_enabled()) {
             // SAT solver core extracts some model 
             // during unsat core computation.
+            mdl = 0;
             s().get_model(mdl);
         }
         else {
@@ -601,10 +601,7 @@ public:
         // find the minimal weight:
         rational w = get_weight(core[0]);
         for (unsigned i = 1; i < core.size(); ++i) {
-            rational w2 = get_weight(core[i]);
-            if (w2 < w) {
-                w = w2;
-            }
+            w = std::min(w, get_weight(core[i]));
         }
         // add fresh soft clauses for weights that are above w.
         for (unsigned i = 0; i < core.size(); ++i) {
@@ -614,6 +611,7 @@ public:
                 new_assumption(core[i], w3);
             }
         }
+        
         return w;
     }
 
@@ -754,6 +752,7 @@ public:
             case l_false:
                 core.reset();
                 s().get_unsat_core(core);
+                DEBUG_CODE(verify_core(core););
                 is_sat = minimize_core(core);
                 if (is_sat != l_true) {
                     break;
@@ -786,14 +785,9 @@ public:
         rational upper(0);
         expr_ref tmp(m);
         for (unsigned i = 0; i < m_soft.size(); ++i) {
-            expr* n = m_soft[i];
-            VERIFY(mdl->eval(n, tmp));
-            if (!m.is_true(tmp)) {
+            if (!is_true(mdl, m_soft[i])) {
                 upper += m_weights[i];
             }
-            TRACE("opt", tout << mk_pp(n, m) << " |-> " << mk_pp(tmp, m) << "\n";);
-            CTRACE("opt", !m.is_true(tmp) && !m.is_false(tmp), 
-                   tout << mk_pp(n, m) << " |-> " << mk_pp(tmp, m) << "\n";);
         }
         if (upper >= m_upper) {
             return;
@@ -804,7 +798,7 @@ public:
             m_assignment[i] = is_true(m_soft[i]);
         }
         m_upper = upper;
-        // verify_assignment();
+        DEBUG_CODE(verify_assignment(););
         trace_bounds("maxres");
 
         add_upper_bound_block();
@@ -888,6 +882,38 @@ public:
         }
     }
 
+    void verify_core(exprs const& core) {
+        IF_VERBOSE(3, verbose_stream() << "verify core\n";);        
+        ref<solver> sat_solver = mk_inc_sat_solver(m, m_params);
+
+        for (unsigned i = 0; i < s().get_num_assertions(); ++i) {
+            sat_solver->assert_expr(s().get_assertion(i));
+        }
+        expr_ref n(m);        
+        for (unsigned i = 0; i < core.size(); ++i) {
+            IF_VERBOSE(1, verbose_stream() << mk_pp(core[i],m) << " ";);
+            sat_solver->assert_expr(core[i]);
+        }
+        IF_VERBOSE(1, verbose_stream() << "\n";);
+        lbool is_sat = sat_solver->check_sat(0, 0);
+        if (is_sat != l_false) {
+            IF_VERBOSE(0, verbose_stream() << "!!!not a core\n";);
+        }        
+
+        sat_solver = mk_smt_solver(m, m_params, symbol());
+        for (unsigned i = 0; i < s().get_num_assertions(); ++i) {
+            sat_solver->assert_expr(s().get_assertion(i));
+        }
+        for (unsigned i = 0; i < core.size(); ++i) {
+            sat_solver->assert_expr(core[i]);
+        }
+        is_sat = sat_solver->check_sat(0, 0);
+        if (is_sat == l_true) {
+            IF_VERBOSE(0, verbose_stream() << "not a core\n";);
+        }        
+        
+    }
+
     void verify_assignment() {
         IF_VERBOSE(0, verbose_stream() << "verify assignment\n";);        
         ref<solver> sat_solver = mk_inc_sat_solver(m, m_params);
diff --git a/src/sat/sat_bceq.cpp b/src/sat/sat_bceq.cpp
index 65377caed..7ad0ec837 100644
--- a/src/sat/sat_bceq.cpp
+++ b/src/sat/sat_bceq.cpp
@@ -22,6 +22,7 @@ Revision History:
 #include"trace.h"
 #include"bit_vector.h"
 #include"map.h"
+#include"sat_elim_eqs.h"
 
 namespace sat {
     
@@ -54,7 +55,7 @@ namespace sat {
             }
         }
         bin_clauses bc;
-        m_solver.collect_bin_clauses(bc, false);
+        m_solver.collect_bin_clauses(bc, false); // exclude roots.
         literal lits[2];
         for (unsigned i = 0; i < bc.size(); ++i) {
             lits[0] = bc[i].first;
@@ -215,7 +216,7 @@ namespace sat {
             m_L.append(new_clauses);
             m_L_blits.append(new_blits);
         }
-        std::cout << "Number left after BCE: " << clauses.size() << "\n";
+        if (!clauses.empty()) std::cout << "Number left after BCE: " << clauses.size() << "\n";
         return clauses.empty();
     }
 
@@ -362,7 +363,13 @@ namespace sat {
             while (v != i) {
                 if (!m_solver.was_eliminated(v)) {
                     if (last_v != UINT_MAX) {
-                        check_equality(v, last_v);
+                        if (check_equality(v, last_v)) {
+                            // last_v was eliminated.
+                            
+                        }
+                        else {
+                            // TBD: refine partition.
+                        }
                     }
                     last_v = v;
                 }
@@ -371,7 +378,7 @@ namespace sat {
         }
     }
 
-    void bceq::check_equality(unsigned v1, unsigned v2) {
+    bool bceq::check_equality(unsigned v1, unsigned v2) {
         TRACE("sat", tout << "check: " << v1 << " = " << v2 << "\n";);
         uint64 val1 = m_rbits[v1];
         uint64 val2 = m_rbits[v2];
@@ -381,9 +388,9 @@ namespace sat {
             SASSERT(val1 == ~val2);
             l2.neg();
         }
-        if (is_equiv(l1, l2)) {
+        if (is_already_equiv(l1, l2)) {
             TRACE("sat", tout << "Already equivalent: " << l1 << " " << l2 << "\n";);
-            return;
+            return false;
         }
 
         literal lits[2];
@@ -397,13 +404,16 @@ namespace sat {
         }
         if (is_sat == l_false) {
             TRACE("sat", tout << "Found equivalent: " << l1 << " " << l2 << "\n";);
+            assert_equality(l1, l2);
         }
         else {
             TRACE("sat", tout << "Not equivalent: " << l1 << " " << l2 << "\n";);
+            // TBD: if is_sat == l_true, then refine partition.
         }
+        return is_sat == l_false;
     }
 
-    bool bceq::is_equiv(literal l1, literal l2) {
+    bool bceq::is_already_equiv(literal l1, literal l2) {
         watch_list const& w1 = m_solver.get_wlist(l1);
         bool found = false;
         for (unsigned i = 0; !found && i < w1.size(); ++i) {
@@ -420,6 +430,24 @@ namespace sat {
         return found;
     }
 
+    void bceq::assert_equality(literal l1, literal l2) {
+        if (l2.sign()) {
+            l1.neg();
+            l2.neg();
+        }
+        literal_vector roots;
+        bool_var_vector vars;
+        for (unsigned i = 0; i < m_solver.num_vars(); ++i) {
+            roots.push_back(literal(i, false));
+        }
+        roots[l2.var()] = l1;
+        vars.push_back(l2.var());
+        elim_eqs elim(m_solver);
+        for (unsigned i = 0; i < vars.size(); ++i) {
+            std::cout << "var: " << vars[i] << " root: " << roots[vars[i]] << "\n";
+        }
+        elim(roots, vars);
+    }
 
     void bceq::cleanup() {
         m_solver.del_clauses(m_bin_clauses.begin(), m_bin_clauses.end());
@@ -430,15 +458,23 @@ namespace sat {
     void bceq::operator()() {
         if (!m_solver.m_config.m_bcd) return;
         flet<bool> _disable_bcd(m_solver.m_config.m_bcd, false);
+        flet<bool> _disable_min(m_solver.m_config.m_minimize_core, false);
+        flet<bool> _disable_opt(m_solver.m_config.m_optimize_model, false);
+        flet<unsigned> _bound_maxc(m_solver.m_config.m_max_conflicts, 1500);
+
         use_list     ul;        
         solver       s(m_solver.m_params, 0);
+        s.m_config.m_bcd            = false;
+        s.m_config.m_minimize_core  = false;
+        s.m_config.m_optimize_model = false;
+        s.m_config.m_max_conflicts  = 1500;
         m_use_list = &ul;
         m_s = &s;
         ul.init(m_solver.num_vars());
         init();
         pure_decompose();
         post_decompose();
-        std::cout << "Decomposed set " << m_L.size() << "\n";
+        std::cout << "Decomposed set " << m_L.size() << " rest: " << m_R.size() << "\n";
 
         TRACE("sat",
               tout << "Decomposed set " << m_L.size() << "\n";
diff --git a/src/sat/sat_bceq.h b/src/sat/sat_bceq.h
index 5552fb255..0b05c45cd 100644
--- a/src/sat/sat_bceq.h
+++ b/src/sat/sat_bceq.h
@@ -65,8 +65,9 @@ namespace sat {
         uint64 eval_clause(clause const& cls) const;
         void verify_sweep();
         void extract_partition();
-        void check_equality(unsigned v1, unsigned v2);
-        bool is_equiv(literal l1, literal l2);
+        bool check_equality(unsigned v1, unsigned v2);
+        bool is_already_equiv(literal l1, literal l2);
+        void assert_equality(literal l1, literal l2);
     public:
         bceq(solver & s);
         void operator()();
diff --git a/src/sat/sat_mus.cpp b/src/sat/sat_mus.cpp
index a504a5fe2..c66f8ef6f 100644
--- a/src/sat/sat_mus.cpp
+++ b/src/sat/sat_mus.cpp
@@ -7,7 +7,7 @@ Module Name:
 
 Abstract:
    
-    Faster MUS extraction based on Belov et.al. HYB (Algorithm 3, 4)
+    Faster MUS extraction
 
 Author:
 
@@ -33,12 +33,27 @@ namespace sat {
         m_mus.reset();
         m_model.reset();
         m_best_value = 0;
+        m_max_restarts = 10;
+        m_restart = s.m_stats.m_restart;
     }
 
-    void mus::set_core() {        
-        m_core.append(m_mus);                
+    void mus::set_core() {   
+        m_mus.append(m_core);
         s.m_core.reset();
-        s.m_core.append(m_core);
+        s.m_core.append(m_mus);
+    }
+
+    void mus::update_model() {
+        double new_value = s.m_wsls.evaluate_model(s.m_model);
+        if (m_model.empty()) {
+            m_model.append(s.m_model);
+            m_best_value = new_value;
+        }
+        else if (m_best_value > new_value) {
+            m_model.reset();
+            m_model.append(s.m_model);
+            m_best_value = new_value;
+        }
     }
 
     lbool mus::operator()() {
@@ -56,6 +71,9 @@ namespace sat {
         TRACE("sat", tout << "old core: " << s.get_core() << "\n";);
         literal_vector& core = get_core();
         literal_vector& mus = m_mus;
+        if (core.size() > 64) {
+            return mus2();
+        }
         unsigned delta_time  = 0;
         unsigned core_miss = 0;
         while (!core.empty()) {
@@ -75,41 +93,31 @@ namespace sat {
 
             literal lit = core.back();
             core.pop_back();
-            unsigned sz = mus.size();
-            mus.append(core);
-            if (true || core_miss < 2) {
-                mus.push_back(~lit); // TBD: measure
+            lbool is_sat;
+            {
+                scoped_append _sa(mus, core);
+                if (true || core_miss < 2) {
+                    mus.push_back(~lit); // TBD: measure
+                }
+                is_sat = s.check(mus.size(), mus.c_ptr());
+                TRACE("sat", tout << "mus: " << mus << "\n";);
             }
-            lbool is_sat = s.check(mus.size(), mus.c_ptr());
-            TRACE("sat", tout << "mus: " << mus << "\n";);
             switch (is_sat) {
             case l_undef:
-                mus.resize(sz);
                 core.push_back(lit);
                 set_core();
                 return l_undef;
             case l_true: {
                 SASSERT(value_at(lit, s.get_model()) == l_false);
-                mus.resize(sz);
                 mus.push_back(lit);
+                update_model();
                 if (!core.empty()) {
                     // mr(); // TBD: measure
                 }
-                double new_value = s.m_wsls.evaluate_model(s.m_model);
-                if (m_model.empty()) {
-                    m_model.append(s.m_model);
-                    m_best_value = new_value;
-                }
-                else if (m_best_value > new_value) {
-                    m_model.reset();
-                    m_model.append(s.m_model);
-                    m_best_value = new_value;
-                }
                 break;
             }
             case l_false:
                 literal_vector const& new_core = s.get_core();
-                mus.resize(sz);
                 if (new_core.contains(~lit)) {
                     IF_VERBOSE(2, verbose_stream() << "miss core " << lit << "\n";);
                     ++core_miss;
@@ -141,27 +149,93 @@ namespace sat {
         IF_VERBOSE(2, verbose_stream() << "(sat.mus.new " << core << ")\n";);
         return l_true;
     }
+    
 
     // bisection search.
     lbool mus::mus2() {
-        literal_vector& core = get_core();
-        literal_vector& mus = m_mus;
-        while (true) {
+        literal_set core(get_core());
+        literal_set support;
+        lbool is_sat = qx(core, support, false);
+        s.m_core.reset();
+        s.m_core.append(core.to_vector());
+        IF_VERBOSE(2, verbose_stream() << "(sat.mus.new " << s.m_core << ")\n";);
+        return is_sat;
+    }
 
-#if 0
-            unsigned start = 0;
-            unsigned len = core.size();
-            SASSERT(start < len);
-            unsigned mid = (len-start+1)/2;
-            mus.append(mid, core.c_ptr() + start);
-            start = start + mid;
-#endif
+    lbool mus::qx(literal_set& assignment, literal_set& support, bool has_support) {
+        lbool is_sat = l_true;
+        if (s.m_stats.m_restart - m_restart > m_max_restarts) {
+            IF_VERBOSE(1, verbose_stream() << "restart budget exceeded\n";);
+            return l_true;
         }
-        return l_undef;
+        if (has_support) {
+            scoped_append _sa(m_mus, support.to_vector());
+            is_sat = s.check(m_mus.size(), m_mus.c_ptr());
+            switch (is_sat) {
+            case l_false: {
+                literal_set core(s.get_core());
+                support &= core;
+                assignment.reset();
+                return l_true;
+            }
+            case l_undef:
+                return l_undef;
+            case l_true:
+                update_model();
+                break;
+            default:
+                break;
+            }
+        }
+        if (assignment.size() == 1) {
+            return l_true;
+        }
+        literal_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 mus::unsplit(literal_set& A, literal_set& B) {
+        literal_set A1, B1;
+        literal_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 mus::split(literal_set& lits1, literal_set& lits2) {
+        unsigned half = lits1.size()/2;
+        literal_set lits3;
+        literal_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;
     }
 
     literal_vector& mus::get_core() {
         m_core.reset();
+        m_mus.reset();
         literal_vector& core = m_core;
         core.append(s.get_core());        
         for (unsigned i = 0; i < core.size(); ++i) {
@@ -175,6 +249,11 @@ namespace sat {
         return core;
     }
 
+    void mus::verify_core(literal_vector const& core) {
+        lbool is_sat = s.check(core.size(), core.c_ptr());
+        IF_VERBOSE(3, verbose_stream() << "core verification: " << is_sat << " " << core << "\n";);
+    }
+
     void mus::mr() {
         sls sls(s);
         literal_vector tabu;
diff --git a/src/sat/sat_mus.h b/src/sat/sat_mus.h
index ed7b8b13e..944cceffb 100644
--- a/src/sat/sat_mus.h
+++ b/src/sat/sat_mus.h
@@ -26,6 +26,8 @@ namespace sat {
         bool           m_is_active;
         model          m_model;       // model obtained during minimal unsat core
         double         m_best_value;
+        unsigned       m_restart;
+        unsigned       m_max_restarts;
 
 
         solver& s;
@@ -38,10 +40,30 @@ namespace sat {
     private:
         lbool mus1();
         lbool mus2();
+        lbool qx(literal_set& assignment, literal_set& support, bool has_support);
         void mr();
         void reset();
         void set_core();
+        void update_model();
         literal_vector & get_core();
+        void verify_core(literal_vector const& lits);
+        void split(literal_set& src, literal_set& dst);
+        void intersect(literal_set& dst, literal_set const& src);
+        void unsplit(literal_set& A, literal_set& B);
+        class scoped_append {
+            unsigned m_size;
+            literal_vector& m_lits;
+        public:
+            scoped_append(literal_vector& lits, literal_vector const& other):
+                m_size(lits.size()),
+                m_lits(lits) {
+                m_lits.append(other);
+            }
+            ~scoped_append() {
+                m_lits.resize(m_size);
+            }
+                
+        };
     };
 
 };
diff --git a/src/sat/sat_simplifier.cpp b/src/sat/sat_simplifier.cpp
index 937c7735f..0fa88d629 100644
--- a/src/sat/sat_simplifier.cpp
+++ b/src/sat/sat_simplifier.cpp
@@ -21,7 +21,6 @@ Revision History:
 #include"sat_simplifier.h"
 #include"sat_simplifier_params.hpp"
 #include"sat_solver.h"
-#include"sat_bceq.h"
 #include"stopwatch.h"
 #include"trace.h"
 
@@ -138,8 +137,10 @@ namespace sat {
             return;
         if (!m_subsumption && !m_elim_blocked_clauses && !m_resolution)
             return;
+
         CASSERT("sat_solver", s.check_invariant());
         TRACE("before_simplifier", s.display(tout););
+
         s.m_cleaner(true);
         m_last_sub_trail_sz = s.m_trail.size();
         TRACE("after_cleanup", s.display(tout););
@@ -157,13 +158,6 @@ namespace sat {
         if (!learned && (m_elim_blocked_clauses || m_elim_blocked_clauses_at == m_num_calls))
             elim_blocked_clauses();
 
-#if 1
-        // experiment is disabled.
-        if (!learned) { // && m_equality_inference
-            bceq bc(s);
-            bc();
-        }
-#endif
 
         if (!learned)
             m_num_calls++;
@@ -188,23 +182,21 @@ namespace sat {
 
         bool vars_eliminated = m_num_elim_vars > old_num_elim_vars;
 
-        if (!m_need_cleanup) {
+        if (m_need_cleanup) {
+            TRACE("after_simplifier", tout << "cleanning watches...\n";);
+            cleanup_watches();
+            cleanup_clauses(s.m_learned, true, vars_eliminated,  learned_in_use_lists);
+            cleanup_clauses(s.m_clauses, false, vars_eliminated, true);
+        }
+        else {
             TRACE("after_simplifier", tout << "skipping cleanup...\n";);
             if (vars_eliminated) {
                 // must remove learned clauses with eliminated variables
                 cleanup_clauses(s.m_learned, true, true, learned_in_use_lists);
             }
-            CASSERT("sat_solver", s.check_invariant());
-            TRACE("after_simplifier", s.display(tout); tout << "model_converter:\n"; s.m_mc.display(tout););
-            free_memory();
-            return;
         }
-        TRACE("after_simplifier", tout << "cleanning watches...\n";);
-        cleanup_watches();
-        cleanup_clauses(s.m_learned, true, vars_eliminated,  learned_in_use_lists);
-        cleanup_clauses(s.m_clauses, false, vars_eliminated, true);
-        TRACE("after_simplifier", s.display(tout); tout << "model_converter:\n"; s.m_mc.display(tout););
         CASSERT("sat_solver", s.check_invariant());
+        TRACE("after_simplifier", s.display(tout); tout << "model_converter:\n"; s.m_mc.display(tout););
         free_memory();
     }
 
@@ -926,10 +918,9 @@ namespace sat {
 
         void process(literal l) {
             TRACE("blocked_clause", tout << "processing: " << l << "\n";);
-            if (s.is_external(l.var()) || s.was_eliminated(l.var())) {
-                return;
-            }
             model_converter::entry * new_entry = 0;
+            if (s.is_external(l.var()) || s.was_eliminated(l.var())) 
+                return;
             {
                 m_to_remove.reset();
                 {
@@ -1186,7 +1177,6 @@ namespace sat {
                 continue;
             m_visited[l2.index()] = false;
         }
-
         return res;
     }
 
diff --git a/src/sat/sat_solver.cpp b/src/sat/sat_solver.cpp
index d97ebed46..86c81f071 100644
--- a/src/sat/sat_solver.cpp
+++ b/src/sat/sat_solver.cpp
@@ -483,7 +483,6 @@ namespace sat {
     void solver::set_conflict(justification c, literal not_l) {
         if (m_inconsistent)
             return;
-        TRACE("sat", tout << "conflict: " << not_l << "\n";);
         m_inconsistent = true;
         m_conflict = c;
         m_not_l    = not_l;
@@ -960,7 +959,11 @@ namespace sat {
         m_stopwatch.start();
         m_core.reset();
         TRACE("sat", display(tout););
-
+        
+        if (m_config.m_bcd) {
+            bceq bc(*this);
+            bc();
+        }
     }
 
     /**
@@ -1737,11 +1740,10 @@ namespace sat {
             // TBD: 
             // apply optional clause minimization by detecting subsumed literals.
             // initial experiment suggests it has no effect.
-
             m_mus(); // ignore return value on cancelation.
             m_model.reset();
             m_model.append(m_mus.get_model());            
-            m_model_is_current = true;
+            m_model_is_current = !m_model.empty();
         }
     }
 
diff --git a/src/sat/sat_types.h b/src/sat/sat_types.h
index db8de94a9..075c88fa1 100644
--- a/src/sat/sat_types.h
+++ b/src/sat/sat_types.h
@@ -160,6 +160,12 @@ namespace sat {
             m_in_set[v] = true; 
             m_set.push_back(v); 
         }
+
+        uint_set& operator=(uint_set const& other) {
+            m_in_set = other.m_in_set;
+            m_set = other.m_set;
+            return *this;
+        }
         
         bool contains(unsigned v) const { 
             return v < m_in_set.size() && m_in_set[v] != 0; 
@@ -177,10 +183,31 @@ namespace sat {
             m_in_set[v] = false; 
             return v; 
         }
+        unsigned size() const { return m_set.size(); }
         iterator begin() const { return m_set.begin(); }
         iterator end() const { return m_set.end(); }
         void reset() { m_set.reset(); m_in_set.reset(); }
         void cleanup() { m_set.finalize(); m_in_set.finalize(); }
+        uint_set& operator&=(uint_set const& other) {
+            unsigned j = 0;
+            for (unsigned i = 0; i < m_set.size(); ++i) {
+                if (other.contains(m_set[i])) {
+                    m_set[j] = m_set[i];
+                    ++j;
+                }
+                else {
+                    m_in_set[m_set[i]] = false;
+                }
+            }
+            m_set.resize(j);
+            return *this;
+        }
+        uint_set& operator|=(uint_set const& other) {
+            for (unsigned i = 0; i < other.m_set.size(); ++i) {
+                insert(other.m_set[i]);
+            }
+            return *this;
+        }
     };
 
     typedef uint_set bool_var_set;
@@ -188,11 +215,44 @@ namespace sat {
     class literal_set {
         uint_set m_set;
     public:
+        literal_set(literal_vector const& v) {
+            for (unsigned i = 0; i < v.size(); ++i) insert(v[i]);
+        }
+        literal_set() {}
+        literal_vector to_vector() const {
+            literal_vector result;
+            iterator it = begin(), e = end();
+            for (; it != e; ++it) {
+                result.push_back(*it);
+            }
+            return result;
+        }
         void insert(literal l) { m_set.insert(l.index()); }
         bool contains(literal l) const { return m_set.contains(l.index()); }
         bool empty() const { return m_set.empty(); }
+        unsigned size() const { return m_set.size(); }
         void reset() { m_set.reset(); }
         void cleanup() { m_set.cleanup(); }
+        class iterator {
+            uint_set::iterator m_it;
+        public:
+            iterator(uint_set::iterator it):m_it(it) {}
+            literal operator*() const { return to_literal(*m_it); }
+            iterator& operator++() { ++m_it; return *this; }
+            iterator operator++(int) { iterator tmp = *this; ++m_it; return tmp; }
+            bool operator==(iterator const& it) const { return m_it == it.m_it; }
+            bool operator!=(iterator const& it) const { return m_it != it.m_it; }
+        };
+        iterator begin() const { return iterator(m_set.begin()); }
+        iterator end() const { return iterator(m_set.end()); }
+        literal_set& operator&=(literal_set const& other) {
+            m_set &= other.m_set;
+            return *this;
+        }
+        literal_set& operator|=(literal_set const& other) {
+            m_set |= other.m_set;
+            return *this;
+        }
     };
     
     struct mem_stat {