diff --git a/src/sat/sat_lookahead.h b/src/sat/sat_lookahead.h
index 4872a548a..7be53e2d1 100644
--- a/src/sat/sat_lookahead.h
+++ b/src/sat/sat_lookahead.h
@@ -27,52 +27,211 @@ namespace sat {
             double   m_dl_success;
         };
 
-        config          m_config;
-        double          m_delta_trigger; 
-        literal_vector  m_trail;
-        literal_vector  m_units;
-        unsigned_vector m_units_lim;
-        unsigned_vector m_learned_lim;
-        unsigned_vector m_binary;
+        struct statistics {
+            unsigned m_propagations;
+            statistics() { reset(); }
+            void reset() { memset(this, 0, sizeof(*this)); }
+        };
 
+        config                 m_config;
+        double                 m_delta_trigger; 
+        literal_vector         m_trail;
+        unsigned_vector        m_trail_lim;
+        literal_vector         m_units;
+        unsigned_vector        m_units_lim;
+        vector<literal_vector> m_binary;        // binary clauses
+        unsigned_vector        m_binary_trail;  // trail of added binary clauses
+        unsigned_vector        m_binary_trail_lim; 
+        clause_vector          m_clauses;       // non-binary clauses
+        clause_allocator       m_cls_allocator;        
+        bool                   m_inconsistent;
+        unsigned_vector        m_bstamp;        // timestamp for binary implication, one for each literal
+        unsigned               m_bstamp_id;     // unique id for binary implication.
+        unsigned               m_qhead;
+        unsigned_vector        m_qhead_lim;
+        char_vector            m_assignment;
+        vector<watch_list>     m_watches;
+        indexed_uint_set       m_free_vars;
+        statistics             m_stats;
+
+        void add_binary(literal l1, literal l2) {
+            SASSERT(l1 != l2);
+            SASSERT(~l1 != l2);
+            m_binary[(~l1).index()].push_back(l2);
+            m_binary[(~l2).index()].push_back(l1);
+            m_binary_trail.push_back((~l1).index());
+        }
+
+        void del_binary(unsigned idx) {
+            literal_vector & lits = m_binary[idx];
+            literal l = lits.back();
+            lits.pop_back();
+            m_binary[(~l).index()].pop_back();
+        }
+
+        // -------------------------------------
+        // track consequences of binary clauses
+        // see also 72 - 77 in sat11.w
+
+        void inc_bstamp() {
+            ++m_bstamp_id;
+            if (m_bstamp_id == 0) {
+                ++m_bstamp_id;
+                m_bstamp.fill(0);
+            }
+        }
+        void set_bstamp(literal l) {
+            m_bstamp[l.index()] = m_bstamp_id;
+        }
+        void set_bstamps(literal l) {
+            set_bstamp(l);
+            literal_vector const& conseq = m_binary[l.index()];
+            for (unsigned i = 0; i < conseq.size(); ++i) {
+                set_bstamp(conseq[i]);
+            }
+        }
+        bool is_stamped(literal l) const { return m_bstamp[l.index()] == m_bstamp_id; }
+
+        /**
+           \brief add one-step transitive closure of binary implications
+                  return false if we learn a unit literal.
+           \pre all implicants of ~u are stamped.
+                u \/ v is true
+        **/
+
+        bool add_tc1(literal u, literal v) {
+            unsigned sz = m_binary[v.index()].size();
+            for (unsigned i = 0; i < sz; ++i) {
+                literal w = m_binary[v.index()][i];
+                // ~v \/ w
+                if (!is_fixed(w)) {
+                    if (is_stamped(~w)) {
+                        // u \/ v, ~v \/ w, u \/ ~w => u is unit
+                        assign(u);        
+                        return false;
+                    }
+                    add_binary(u, w);
+                }
+            }
+            return true;
+        }
+
+        /**
+           \brief main routine for adding a new binary clause dynamically.
+         */
+        void try_add_binary(literal u, literal v) {
+            SASSERT(u.var() != v.var());
+            inc_bstamp();
+            set_bstamps(~u);
+            if (is_stamped(~v)) {
+                // u \/ ~v is a binary clause, u \/ v is true => u is a unit literal
+                assign(u);
+            }
+            else if (!is_stamped(v) && add_tc1(u, v)) {
+                // u \/ v is not in index
+                // all implicants of ~u are stamped.                
+                inc_bstamp();
+                set_bstamps(~v);
+                if (is_stamped(~u)) {
+                    // v \/ ~u is a binary clause, u \/ v is true => v is a unit
+                    assign(v);
+                }
+                else if (add_tc1(v, u)) {
+                    add_binary(u, v);
+                }
+            }
+        }
+        
+        void init_var(bool_var v) {
+            m_assignment.push_back(l_undef);
+            m_assignment.push_back(l_undef);
+            m_binary.push_back(literal_vector());
+            m_binary.push_back(literal_vector());
+            m_watches.push_back(watch_list());
+            m_watches.push_back(watch_list());
+            m_bstamp.push_back(0);
+            m_bstamp.push_back(0);
+        }
 
         void init() {
             m_delta_trigger = s.num_vars()/10;
             m_config.m_dl_success = 0.8;
+            m_inconsistent = false;
+            m_qhead = 0;
+            m_bstamp_id = 0;
+
+            for (unsigned i = 0; i < s.num_vars(); ++i) {
+                init_var(i);
+            }
+
+            // copy binary clauses
+            unsigned sz = s.m_watches.size();
+            for (unsigned l_idx = 0; l_idx < sz; ++l_idx) {
+                literal l = ~to_literal(l_idx);
+                watch_list const & wlist = s.m_watches[l_idx];
+                watch_list::const_iterator it  = wlist.begin();
+                watch_list::const_iterator end = wlist.end();
+                for (; it != end; ++it) {
+                    if (!it->is_binary_non_learned_clause())
+                        continue;
+                    literal l2 = it->get_literal();
+                    if (l.index() < l2.index()) 
+                        add_binary(l, l2);
+                }
+            }
+
+            // copy clauses
+            clause_vector::const_iterator it =  s.m_clauses.begin();
+            clause_vector::const_iterator end = s.m_clauses.end();
+            for (; it != end; ++it) {
+                clause& c = *(*it);
+                m_clauses.push_back(m_cls_allocator.mk_clause(c.size(), c.begin(), false));
+                // TBD: add watch
+            }
+
+            // copy units
+            unsigned trail_sz = s.init_trail_size();
+            for (unsigned i = 0; i < trail_sz; ++i) {
+                literal l = s.m_trail[i];
+                m_units.push_back(l);
+                assign(l);
+            }
         }
         
         void push(literal lit) { 
-            m_learned_lim.push_back(s.m_learned.size());
+            m_binary_trail_lim.push_back(m_binary_trail.size());
             m_units_lim.push_back(m_units.size());
+            m_trail_lim.push_back(m_trail.size());
+            m_qhead_lim.push_back(m_qhead);
             m_trail.push_back(lit);
-            m_binary.push_back(0);
-            s.push();
             assign(lit);
+            propagate();
         }
 
         void pop() { 
-            s.pop(1); 
-            unsigned old_sz = m_learned_lim.back();
-            m_learned_lim.pop_back();
-            for (unsigned i = old_sz; i < s.m_learned.size(); ++i) {
-                clause* r = s.m_learned[i];
-                s.dettach_clause(*r);
-                s.m_cls_allocator.del_clause(r);
+            // remove local binary clauses
+            unsigned old_sz = m_binary_trail_lim.back();
+            m_binary_trail_lim.pop_back();
+            for (unsigned i = old_sz; i < m_binary_trail.size(); ++i) {
+                del_binary(m_binary_trail[i]);
             }
-            s.m_learned.shrink(old_sz);
+
+            // add implied binary clauses
             unsigned new_unit_sz = m_units_lim.back();
             for (unsigned i = new_unit_sz; i < m_units.size(); ++i) {
-                literal lits[2] = { ~m_trail.back(), m_units[i] };
-                clause * r = s.m_cls_allocator.mk_clause(2, lits, true);
-                s.m_learned.push_back(r);
+                add_binary(~m_trail.back(), m_units[i]);
             }
             m_units.shrink(new_unit_sz);
             m_units_lim.pop_back();
-            m_trail.pop_back();
-            m_binary.pop_back();
+            m_trail.shrink(m_trail_lim.size()); // reset assignment.
+            m_trail_lim.pop_back();
+            m_qhead_lim.pop_back();
+            m_qhead = m_qhead_lim.back();
+
+            m_inconsistent = false;
         }
         
-        unsigned diff() const { return m_binary.back() + m_units.size() - m_units_lim.back(); }
+        unsigned diff() const { return m_units.size() - m_units_lim.back(); }
 
         unsigned mix_diff(unsigned l, unsigned r) const { return l + r + (1 << 10) * l * r; }
 
@@ -82,52 +241,129 @@ namespace sat {
         }
 
         bool is_nary_propagation(clause const& c, literal l) const {
-            bool r = c.size() > 2 && ((c[0] == l && s.value(c[1]) == l_false) || (c[1] == l && s.value(c[0]) == l_false));
-            DEBUG_CODE(if (r) for (unsigned j = 2; j < c.size(); ++j) SASSERT(s.value(c[j]) == l_false););
+            bool r = c.size() > 2 && ((c[0] == l && value(c[1]) == l_false) || (c[1] == l && value(c[0]) == l_false));
+            DEBUG_CODE(if (r) for (unsigned j = 2; j < c.size(); ++j) SASSERT(value(c[j]) == l_false););
             return r;
         }
 
-        void get_resolvent_units(literal lit) {
+        void propagate_clauses(literal l) {
+            SASSERT(value(l) == l_true);
+            SASSERT(value(~l) == l_false);
             if (inconsistent()) return;
-            for (unsigned i = s.m_trail.size(); i > 0; ) {
-                --i;
-                literal l = s.m_trail[i];
-                if (l == lit) break;
-                SASSERT(s.lvl(l) == s.scope_lvl());
-                watch_list& wlist = s.m_watches[(~l).index()];
-                watch_list::iterator it = wlist.begin(), end = wlist.end();
-                for (; it != end; ++it) {
-                    switch (it->get_kind()) {
-                    case watched::TERNARY:
-                        if (s.value(it->get_literal1()) == l_false && 
-                            s.value(it->get_literal2()) == l_false) {
-                            m_units.push_back(l);
-                            goto done_finding_unit;
-                        }
-                        break;
-                    case watched::CLAUSE: {
-                        clause const & c = get_clause(it);
-                        SASSERT(c[0] == l || c[1] == l);
-                        if (is_nary_propagation(c, l)) {
-                            m_units.push_back(l);
-                            goto done_finding_unit;
-                        }
-                        break;
+            watch_list& wlist = m_watches[l.index()];
+            watch_list::iterator it = wlist.begin(), it2 = it, end = wlist.end();
+            for (; it != end && !inconsistent(); ++it) {
+                switch (it->get_kind()) {
+                case watched::BINARY:
+                    UNREACHABLE();
+                    break;
+                case watched::TERNARY: {
+                    literal l1 = it->get_literal1();
+                    literal l2 = it->get_literal2();
+                    lbool val1 = value(l1);
+                    lbool val2 = value(l2);
+                    if (val1 == l_false && val2 == l_undef) {
+                        m_stats.m_propagations++;
+                        assign(l2);
                     }
-                    default:
-                        break;
+                    else if (val1 == l_undef && val2 == l_false) {
+                        m_stats.m_propagations++;
+                        assign(l1);
                     }
+                    else if (val1 == l_false && val2 == l_false) {
+                        set_conflict();
+                    }
+                    else if (val1 == l_undef && val2 == l_undef) {
+                        // TBD: the clause has become binary.
+                    }
+                    *it2 = *it;
+                    it2++;
+                    break;
+                }
+                case watched::CLAUSE: {
+                    clause_offset cls_off = it->get_clause_offset();
+                    clause & c = *(s.m_cls_allocator.get_clause(cls_off));
+                    TRACE("propagate_clause_bug", tout << "processing... " << c << "\nwas_removed: " << c.was_removed() << "\n";);
+                    if (c[0] == ~l)
+                        std::swap(c[0], c[1]);
+                    if (value(c[0]) == l_true) {
+                        it2->set_clause(c[0], cls_off);
+                        it2++;
+                        break;
+                    }
+                    literal * l_it  = c.begin() + 2;
+                    literal * l_end = c.end();
+                    unsigned found = 0;
+                    for (; l_it != l_end && found < 2; ++l_it) {
+                        if (value(*l_it) != l_false) {
+                            ++found;
+                            if (found == 2) {
+                                break;
+                            }
+                            else {
+                                c[1]  = *l_it;
+                                *l_it = ~l;
+                                m_watches[(~c[1]).index()].push_back(watched(c[0], cls_off));
+                            }
+                        }
+                    }
+                    if (found == 1) {
+                        // TBD: clause has become binary
+                        break; 
+                    }
+                    if (found > 1) {
+                        // not a binary clause
+                        break;
+                    }
+                    else if (value(c[0]) == l_false) {
+                        set_conflict();
+                    }
+                    else {
+                        SASSERT(value(c[0]) == l_undef);
+                        *it2 = *it;
+                        it2++;
+                        m_stats.m_propagations++;
+                        assign(c[0]);
+                    }
+                    break;
+                }
+                case watched::EXT_CONSTRAINT:
+                    UNREACHABLE();
+                    break;
+                default:
+                    UNREACHABLE();
+                    break;
                 }
-            done_finding_unit:
-
-                //
-                // TBD: count binary clauses created by propagation.
-                // They used to be in the watch list of l.index(), 
-                // both new literals in watch list should be unassigned.
-                //
-                continue;
-
             }
+            for (; it != end; ++it, ++it2) {
+                *it2 = *it;                         
+            }
+            wlist.set_end(it2);
+        
+            
+            //
+            // TBD: count binary clauses created by propagation.
+            // They used to be in the watch list of l.index(), 
+            // both new literals in watch list should be unassigned.
+            //
+        }
+
+        void propagate_binary(literal l) {
+            literal_vector const& lits = m_binary[l.index()];
+            unsigned sz = lits.size();
+            for (unsigned i = 0; !inconsistent() && i < sz; ++i) {
+                assign(lits[i]);
+            }
+        }
+
+        void propagate() {
+            for (; m_qhead < m_trail.size(); ++m_qhead) {
+                if (inconsistent()) break;
+                literal l = m_trail[m_qhead];
+                propagate_binary(l);
+                propagate_clauses(l);
+            }
+            TRACE("sat", s.display(tout << scope_lvl() << " " << (inconsistent()?"unsat":"sat") << "\n"););
         }
 
         literal choose() {
@@ -187,7 +423,7 @@ namespace sat {
             bool unsat;
             for (unsigned i = 0; !inconsistent() && i < P.size(); ++i) {
                 literal lit = P[i];
-                if (s.value(lit) != l_undef) continue;
+                if (value(lit) != l_undef) continue;
 
                 push(lit);
                 unsat = inconsistent();
@@ -205,37 +441,39 @@ namespace sat {
                     TRACE("sat", tout << "unit: " << lit << "\n";);
                     assign(lit);
                 }
-
             }
             update_delta_trigger();
         }
 
+        bool is_fixed(literal l) const { return value(l) != l_undef; }
+        bool is_contrary(literal l) const { return value(l) == l_false; }
+        void set_conflict() { m_inconsistent = true; }
+        lbool value(literal l) const { return static_cast<lbool>(m_assignment[l.index()]); }
+        unsigned scope_lvl() const { return m_trail_lim.size(); }
+
         void assign(literal l) {
-            s.assign(l, justification());
-            s.propagate(false);
-            get_resolvent_units(l);
-            TRACE("sat", s.display(tout << l << " @ " << s.scope_lvl() << " " << (inconsistent()?"unsat":"sat") << "\n"););
+            switch (value(l)) {
+            case l_true: 
+                break;
+            case l_false: 
+                set_conflict(); 
+                break;
+            default:
+                m_assignment[l.index()] = l.sign() ? l_false : l_true;
+                m_assignment[(~l).index()] = l.sign() ? l_false : l_true;
+                m_trail.push_back(l);
+                break;
+            }
         }
 
-        bool inconsistent() { return s.inconsistent(); }
+        void set_inconsistent() { m_inconsistent = true; }
+        bool inconsistent() { return m_inconsistent; }
 
         void pre_select(literal_vector& P) {
             select_variables(P);
             order_by_implication_trees(P);            
         }
 
-        void check_binary(clause const& c, literal lit1, literal& lit2) {
-            if (c.size() == 2) {
-                if (c[0] == lit1) {
-                    lit2 = c[1];
-                }
-                else {
-                    SASSERT(c[1] == lit1);
-                    lit2 = c[0];
-                }
-            }
-        }
-
         void order_by_implication_trees(literal_vector& P) {
             literal_set roots;
             literal_vector nodes, parent;
@@ -253,24 +491,11 @@ namespace sat {
                 // make lit1 a root instead of lit2
                 //
 
-                watch_list& wlist = s.m_watches[(~lit1).index()];
-                watch_list::iterator it = wlist.begin(), end = wlist.end();
-                lit2 = null_literal;
-                for (; it != end; ++it) {
-                    switch (it->get_kind()) {
-                    case watched::BINARY:
-                        lit2 = it->get_literal();
-                        break;
-                    case watched::CLAUSE: {
-                        clause const & c = get_clause(it);
-                        check_binary(c, lit1, lit2);
-                        break;
-                    }
-                    default:
-                        break;
-                    }
-                    
-                    if (lit2 != null_literal && roots.contains(~lit2)) {
+                literal_vector const& lits1 = m_binary[(~lit1).index()];
+                unsigned sz = lits1.size();
+                for (unsigned i = 0; i < sz; ++i) {
+                    literal lit2 = lits1[i];
+                    if (roots.contains(~lit2)) {
                         // ~lit2 => lit1
                         // if lit2 is a root, put it under lit2
                         parent.setx((~lit2).index(), lit1, null_literal);
@@ -285,24 +510,11 @@ namespace sat {
                 // if lit2 is a node, put lit1 above lit2
                 //
 
-                it  = s.m_watches[lit1.index()].begin();
-                end = s.m_watches[lit1.index()].end();
-                for (; it != end; ++it) {
-                    lit2 = null_literal;
-                    switch (it->get_kind()) {
-                    case watched::BINARY:
-                        lit2 = it->get_literal();
-                        break;
-                    case watched::CLAUSE: {
-                        clause const & c = get_clause(it);
-                        check_binary(c, ~lit1, lit2);
-                        break;
-                    }
-                    default:
-                        break;
-                    }
-                    
-                    if (lit2 != null_literal && nodes.contains(lit2)) {
+                literal_vector const& lits2 = m_binary[(~lit2).index()];
+                sz = lits2.size();
+                for (unsigned i = 0; i < sz; ++i) {
+                    literal lit2 = lits2[i];
+                    if (nodes.contains(lit2)) {
                         // lit1 => lit2
                         parent.setx(lit1.index(), lit2, null_literal);
                         nodes.insert(lit1);
@@ -329,7 +541,7 @@ namespace sat {
 
         void select_variables(literal_vector& P) {
             for (unsigned i = 0; i < s.num_vars(); ++i) {
-                if (s.value(i) == l_undef) {
+                if (value(literal(i,false)) == l_undef) {
                     P.push_back(literal(i, false));
                 }
             }
@@ -351,15 +563,12 @@ namespace sat {
             }
         }
 
-        lbool backtrack(literal_vector& trail) {
-            if (inconsistent()) {                       
-                if (trail.empty()) return l_false;      
-                pop();                                  
-                assign(~trail.back());                  
-                trail.pop_back();               
-                return l_true;
-            }
-            return l_undef;
+        bool backtrack(literal_vector& trail) {
+            if (trail.empty()) return false;      
+            pop();                                  
+            assign(~trail.back());                  
+            trail.pop_back();               
+            return true;
         }
 
         lbool search() {
@@ -367,17 +576,10 @@ namespace sat {
 
             while (true) {
                 s.checkpoint();
-                switch (backtrack(trail)) {
-                case l_true: continue;
-                case l_false: return l_false;
-                case l_undef: break;
-                }
-
                 literal l = choose();
-                switch (backtrack(trail)) {
-                case l_true: continue;
-                case l_false: return l_false;
-                case l_undef: break;
+                if (inconsistent()) {
+                    if (!backtrack(trail)) return l_false;
+                    continue;
                 }
                 if (l == null_literal) {
                     return l_true;
diff --git a/src/util/uint_set.h b/src/util/uint_set.h
index d0cc8a32a..5633b74b2 100644
--- a/src/util/uint_set.h
+++ b/src/util/uint_set.h
@@ -333,6 +333,45 @@ public:
     }
 };
 
+class indexed_uint_set {
+    unsigned        m_size;
+    unsigned_vector m_elems;
+    unsigned_vector m_index;
+public:
+    indexed_uint_set():
+        m_size(0)
+    {}
+
+    void insert(unsigned x) {
+        SASSERT(!contains(x));
+        m_index.resize(x + 1, UINT_MAX);
+        m_elems.resize(m_size + 1);
+        m_index[x] = m_size;
+        m_elems[m_size] = x;
+        m_size++;
+    }
+    
+    void remove(unsigned x) {
+        SASSERT(contains(x));
+        unsigned y = m_elems[--m_size];
+        if (x != y) {
+            unsigned idx = m_index[x];
+            m_index[y] = idx;
+            m_elems[idx] = y;
+            m_index[x] = m_size;
+            m_elems[m_size] = x; 
+        }
+    }
+
+    bool contains(unsigned x) const { return x < m_index.size() && m_index[x] < m_size && m_elems[m_index[x]] == x; }
+    void reset() { m_size = 0; }
+    bool empty() const { return m_size == 0; }    
+    unsigned size() const { return m_size; }
+    typedef  unsigned_vector::const_iterator iterator;
+    iterator begin() const { return m_elems.begin(); }
+    iterator end() const { return m_elems.begin() + m_size; }
+
+};
 
 #endif /* UINT_SET_H_ */