diff --git a/scripts/mk_project.py b/scripts/mk_project.py
index 745d7bf5493..59faf0f0641 100644
--- a/scripts/mk_project.py
+++ b/scripts/mk_project.py
@@ -39,6 +39,7 @@ def init_project_def():
     add_lib('solver', ['model', 'tactic', 'proofs'])
     add_lib('cmd_context', ['solver', 'rewriter'])    
     add_lib('sat_tactic', ['tactic', 'sat', 'solver'], 'sat/tactic')
+    add_lib('sat_euf', ['sat_tactic', 'sat', 'euf'], 'sat/euf')    
     add_lib('smt2parser', ['cmd_context', 'parser_util'], 'parsers/smt2')
     add_lib('pattern', ['normal_forms', 'smt2parser', 'rewriter'], 'ast/pattern')
     add_lib('core_tactics', ['tactic', 'macros', 'normal_forms', 'rewriter', 'pattern'], 'tactic/core')
@@ -80,7 +81,7 @@ def init_project_def():
             includes2install=['z3.h', 'z3_v1.h', 'z3_macros.h'] + API_files)
     add_lib('extra_cmds', ['cmd_context', 'subpaving_tactic', 'qe', 'arith_tactics'], 'cmd_context/extra_cmds')
     add_exe('shell', ['api', 'sat', 'extra_cmds','opt'], exe_name='z3')
-    add_exe('test', ['api', 'fuzzing', 'simplex', 'euf'], exe_name='test-z3', install=False)
+    add_exe('test', ['api', 'fuzzing', 'simplex', 'sat_euf'], exe_name='test-z3', install=False)
     _libz3Component = add_dll('api_dll', ['api', 'sat', 'extra_cmds'], 'api/dll',
                               reexports=['api'],
                               dll_name='libz3',
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 5e1ea8f5178..e18e38f6939 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -60,6 +60,7 @@ add_subdirectory(math/subpaving/tactic)
 add_subdirectory(tactic/aig)
 add_subdirectory(solver)
 add_subdirectory(sat/tactic)
+add_subdirectory(sat/euf)
 add_subdirectory(tactic/arith)
 add_subdirectory(nlsat/tactic)
 add_subdirectory(ackermannization)
diff --git a/src/ast/euf/euf_egraph.cpp b/src/ast/euf/euf_egraph.cpp
index b05df0cff7d..c68f743a198 100644
--- a/src/ast/euf/euf_egraph.cpp
+++ b/src/ast/euf/euf_egraph.cpp
@@ -35,8 +35,7 @@ namespace euf {
         unmerge_justification(n1);
     }
 
-    enode* egraph::mk_enode(expr* f, enode * const* args) {
-        unsigned num_args = is_app(f) ? to_app(f)->get_num_args() : 0;
+    enode* egraph::mk_enode(expr* f, unsigned num_args, enode * const* args) {
         enode* n = enode::mk(m_region, f, num_args, args);
         m_nodes.push_back(n);
         m_exprs.push_back(f);
@@ -98,15 +97,15 @@ namespace euf {
         n->set_update_children();            
     }
 
-    enode* egraph::mk(expr* f, enode *const* args) {
+    enode* egraph::mk(expr* f, unsigned num_args, enode *const* args) {
         SASSERT(!find(f));
         force_push();
-        enode *n = mk_enode(f, args);
+        enode *n = mk_enode(f, num_args, args);
         SASSERT(n->class_size() == 1);
         m_expr2enode.setx(f->get_id(), n, nullptr);
-        if (n->num_args() == 0 && m.is_unique_value(f))
+        if (num_args == 0 && m.is_unique_value(f))
             n->mark_interpreted();
-        if (n->num_args() == 0) 
+        if (num_args == 0) 
             return n;
         if (is_equality(n)) {
             update_children(n);
@@ -171,6 +170,8 @@ namespace euf {
             std::swap(r1, r2);
             std::swap(n1, n2);
         }
+        if ((m.is_true(r2->get_owner()) || m.is_false(r2->get_owner())) && j.is_congruence())
+            m_new_lits.push_back(n1);
         for (enode* p : enode_parents(n1)) 
             m_table.erase(p);            
         for (enode* p : enode_parents(n2)) 
@@ -187,6 +188,7 @@ namespace euf {
 
     void egraph::propagate() {
         m_new_eqs.reset();
+        m_new_lits.reset();
         SASSERT(m_num_scopes == 0 || m_worklist.empty());
         unsigned head = 0, tail = m_worklist.size();
         while (head < tail && m.limit().inc() && !inconsistent()) {
@@ -239,6 +241,88 @@ namespace euf {
         SASSERT(n1->get_root()->m_target == nullptr);
     }
 
+    /**
+       \brief generate an explanation for a congruence.
+       Each pair of children under a congruence have the same roots
+       and therefore have a least common ancestor. We only need
+       explanations up to the least common ancestors.
+     */
+    void egraph::push_congruence(enode* n1, enode* n2, bool comm) {
+        SASSERT(n1->get_decl() == n2->get_decl());
+        if (comm && 
+            n1->get_arg(0)->get_root() == n2->get_arg(1)->get_root() &&
+            n1->get_arg(1)->get_root() == n2->get_arg(0)->get_root()) {
+            push_lca(n1->get_arg(0), n2->get_arg(1));
+            push_lca(n1->get_arg(1), n2->get_arg(0));
+            return;
+        }
+            
+        for (unsigned i = 0; i < n1->num_args(); ++i) 
+            push_lca(n1->get_arg(i), n2->get_arg(i));
+    }
+
+    void egraph::push_lca(enode* a, enode* b) {
+        SASSERT(a->get_root() == b->get_root());
+        enode* n = a;
+        while (n) {
+            n->mark2();
+            n = n->m_target;
+        }
+        n = b;
+        while (n) {
+            if (n->is_marked2()) 
+                n->unmark2();   
+            else if (!n->is_marked1()) 
+                m_todo.push_back(n);
+            n = n->m_target;
+        }
+        n = a;
+        while (n->is_marked2()) {            
+            n->unmark2();
+            if (!n->is_marked1())
+                m_todo.push_back(n);
+            n = n->m_target;
+        }
+    }
+
+    void egraph::push_todo(enode* n) {
+        while (n) {
+            m_todo.push_back(n);
+            n = n->m_target;
+        }
+    }
+
+    template <typename T>
+    void egraph::explain(ptr_vector<T>& justifications) {
+        SASSERT(m_inconsistent);
+        SASSERT(m_todo.empty());
+        push_todo(m_n1);
+        push_todo(m_n2);
+        explain_eq(justifications, m_n1, m_n2, m_justification);
+        explain_todo(justifications);
+    }
+
+    template <typename T>
+    void egraph::explain_eq(ptr_vector<T>& justifications, enode* a, enode* b, bool comm) {
+        SASSERT(m_todo.empty());
+        push_congruence(a, b, comm);
+        explain_todo(justifications);
+    }
+
+    template <typename T>
+    void egraph::explain_todo(ptr_vector<T>& justifications) {
+        for (unsigned i = 0; i < m_todo.size(); ++i) {
+            enode* n = m_todo[i];
+            if (n->m_target && !n->is_marked1()) {
+                n->mark1();
+                explain_eq(justifications, n, n->m_target, n->m_justification);
+            }
+        }
+        for (enode* n : m_todo) 
+            n->unmark1();
+        m_todo.reset();        
+    }
+
     void egraph::invariant() {
         for (enode* n : m_nodes)
             n->invariant();
@@ -267,3 +351,12 @@ namespace euf {
         return out;
     }
 }
+
+template void euf::egraph::explain(ptr_vector<int>& justifications);
+template void euf::egraph::explain_todo(ptr_vector<int>& justifications);
+template void euf::egraph::explain_eq(ptr_vector<int>& justifications, enode* a, enode* b, bool comm);
+
+template void euf::egraph::explain(ptr_vector<unsigned>& justifications);
+template void euf::egraph::explain_todo(ptr_vector<unsigned>& justifications);
+template void euf::egraph::explain_eq(ptr_vector<unsigned>& justifications, enode* a, enode* b, bool comm);
+
diff --git a/src/ast/euf/euf_egraph.h b/src/ast/euf/euf_egraph.h
index 2f4bfed898b..6844a2dc507 100644
--- a/src/ast/euf/euf_egraph.h
+++ b/src/ast/euf/euf_egraph.h
@@ -58,13 +58,14 @@ namespace euf {
         enode                  *m_n2 { nullptr };
         justification          m_justification;
         enode_vector           m_new_eqs;
+        enode_vector           m_new_lits;
         enode_vector           m_todo;
 
         void push_eq(enode* r1, enode* n1, unsigned r2_num_parents) {
             m_eqs.push_back(add_eq_record(r1, n1, r2_num_parents));
         }
         void undo_eq(enode* r1, enode* n1, unsigned r2_num_parents);
-        enode* mk_enode(expr* f, enode * const* args);
+        enode* mk_enode(expr* f, unsigned num_args, enode * const* args);
         void reinsert(enode* n);
         void force_push();
         void set_conflict(enode* n1, enode* n2, justification j);
@@ -72,15 +73,30 @@ namespace euf {
         void merge_justification(enode* n1, enode* n2, justification j);
         void unmerge_justification(enode* n1);
         void dedup_equalities();
-        bool is_equality(enode* n) const;
         void reinsert_equality(enode* p);
         void update_children(enode* n);
+        void push_lca(enode* a, enode* b);
+        void push_congruence(enode* n1, enode* n2, bool commutative);
+        void push_todo(enode* n);
+        template <typename T>
+        void explain_eq(ptr_vector<T>& justifications, enode* a, enode* b, justification const& j) {
+            if (j.is_external())
+                justifications.push_back(j.ext<T>());
+            else if (j.is_congruence()) 
+                push_congruence(a, b, j.is_commutative());
+        }
+        template <typename T>
+        void explain_todo(ptr_vector<T>& justifications);
+        
     public:
         egraph(ast_manager& m): m(m), m_table(m), m_exprs(m) {}
         enode* find(expr* f) { return m_expr2enode.get(f->get_id(), nullptr); }
-        enode* mk(expr* f, enode *const* args);
+        enode* mk(expr* f, unsigned n, enode *const* args);
         void push() { ++m_num_scopes; }
         void pop(unsigned num_scopes);
+
+        bool is_equality(enode* n) const;
+
         /**
            \brief merge nodes, all effects are deferred to the propagation step.
          */
@@ -98,45 +114,11 @@ namespace euf {
         void propagate();
         bool inconsistent() const { return m_inconsistent; }
         enode_vector const& new_eqs() const { return m_new_eqs; }
+        enode_vector const& new_lits() const { return m_new_lits; }
         template <typename T>
-        void explain(ptr_vector<T>& justifications) {
-            SASSERT(m_inconsistent);
-            SASSERT(m_todo.empty());
-            auto push_congruence = [&](enode* p, enode* q) {
-                SASSERT(p->get_decl() == q->get_decl());
-                for (enode* arg : enode_args(p))
-                    m_todo.push_back(arg);
-                for (enode* arg : enode_args(q))
-                    m_todo.push_back(arg);
-            };
-            auto explain_node = [&](enode* n) {
-                if (!n->m_target)
-                    return;
-                if (n->is_marked1())
-                    return;
-                n->mark1();
-                if (n->m_justification.is_external())
-                    justifications.push_back(n->m_justification.ext<T>());
-                else if (n->m_justification.is_congruence()) 
-                    push_congruence(n, n->m_target);
-                n = n->m_target;
-                if (!n->is_marked1())
-                    m_todo.push_back(n);
-            };
-            m_todo.push_back(m_n1);
-            m_todo.push_back(m_n2);
-            if (m_justification.is_external())
-                justifications.push_back(m_justification.ext<T>());
-            else if (m_justification.is_congruence())
-                push_congruence(m_n1, m_n2);
-            for (unsigned i = 0; i < m_todo.size(); ++i) 
-                explain_node(m_todo[i]);
-            for (enode* n : m_todo) 
-                n->unmark1();
-            m_todo.reset();
-        }
-        
-        
+        void explain(ptr_vector<T>& justifications);
+        template <typename T>
+        void explain_eq(ptr_vector<T>& justifications, enode* a, enode* b, bool comm);
         void invariant();
         std::ostream& display(std::ostream& out) const;        
     };
diff --git a/src/ast/euf/euf_enode.h b/src/ast/euf/euf_enode.h
index 39034bd0edd..776747db270 100644
--- a/src/ast/euf/euf_enode.h
+++ b/src/ast/euf/euf_enode.h
@@ -43,6 +43,7 @@ namespace euf {
         enode*        m_root;
         enode*        m_target { nullptr };
         justification m_justification;
+        unsigned      m_num_args;
         enode*        m_args[0];        
 
         friend class enode_args;
@@ -56,12 +57,14 @@ namespace euf {
         }
 
         static enode* mk(region& r, expr* f, unsigned num_args, enode* const* args) {
+            SASSERT(num_args <= (is_app(f) ? to_app(f)->get_num_args() : 0));
             void* mem = r.allocate(get_enode_size(num_args));
             enode* n = new (mem) enode();
             n->m_owner = f;
             n->m_next = n;
             n->m_root = n;
             n->m_commutative = num_args == 2 && is_app(f) && to_app(f)->get_decl()->is_commutative();
+            n->m_num_args = num_args;
             for (unsigned i = 0; i < num_args; ++i) {
                 SASSERT(to_app(f)->get_arg(i) == args[i]->get_owner());
                 n->m_args[i] = args[i];
@@ -83,9 +86,10 @@ namespace euf {
         }
 
         enode* const* args() const { return m_args; }
-        unsigned num_args() const { return is_app(m_owner) ? to_app(m_owner)->get_num_args() : 0; }                
+        unsigned num_args() const { return m_num_args; }
         unsigned num_parents() const { return m_parents.size(); }
         bool interpreted() const { return m_interpreted; }
+        bool commutative() const { return m_commutative; }
         void mark_interpreted() { SASSERT(num_args() == 0); m_interpreted = true; }
 
         enode* get_arg(unsigned i) const { SASSERT(i < num_args()); return m_args[i]; }        
@@ -97,6 +101,9 @@ namespace euf {
         void mark1() { m_mark1 = true; }
         void unmark1() { m_mark1 = false; }
         bool is_marked1() { return m_mark1; }
+        void mark2() { m_mark2 = true; }
+        void unmark2() { m_mark2 = false; }
+        bool is_marked2() { return m_mark2; }
         void add_parent(enode* p) { m_parents.push_back(p); }
         unsigned class_size() const { return m_class_size; }
         enode* get_root() const { return m_root; }
diff --git a/src/sat/euf/CMakeLists.txt b/src/sat/euf/CMakeLists.txt
new file mode 100644
index 00000000000..0be16aa8b75
--- /dev/null
+++ b/src/sat/euf/CMakeLists.txt
@@ -0,0 +1,8 @@
+z3_add_component(sat_euf
+  SOURCES
+    euf_solver.cpp
+  COMPONENT_DEPENDENCIES
+    sat
+    sat_tactic
+    euf
+)
diff --git a/src/sat/euf/euf_solver.cpp b/src/sat/euf/euf_solver.cpp
new file mode 100644
index 00000000000..0b5a257dc27
--- /dev/null
+++ b/src/sat/euf/euf_solver.cpp
@@ -0,0 +1,186 @@
+/*++
+Copyright (c) 2020 Microsoft Corporation
+
+Module Name:
+
+    euf_solver.cpp
+
+Abstract:
+
+    Solver plugin for EUF
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2020-08-25
+
+--*/
+#include "sat/euf/euf_solver.h"
+#include "sat/sat_solver.h"
+#include "tactic/tactic_exception.h"
+
+namespace euf_sat {
+
+    bool solver::propagate(literal l, ext_constraint_idx idx) { 
+        UNREACHABLE();
+        return true;
+    }
+
+    void solver::get_antecedents(literal l, ext_justification_idx idx, literal_vector & r) {
+        m_explain.reset();
+        euf::enode* n = nullptr;
+        bool sign = false;
+        if (idx != 0) {
+            auto p = m_var2node[l.var()];
+            n = p.first;  
+            sign = l.sign() != p.second;
+        }
+
+        switch (idx) {
+        case 0:
+            SASSERT(m_egraph.inconsistent());
+            m_egraph.explain<unsigned>(m_explain);
+            break;
+        case 1:
+            SASSERT(m_egraph.is_equality(n));
+            m_egraph.explain_eq<unsigned>(m_explain, n->get_arg(0), n->get_arg(1), n->commutative());
+            break;
+        case 2:
+            SASSERT(m.is_bool(n->get_owner()));
+            m_egraph.explain_eq<unsigned>(m_explain, n, (sign ? m_false : m_true), false);
+            break;
+        default:
+            UNREACHABLE();
+        }
+        for (unsigned* idx : m_explain) 
+            r.push_back(sat::to_literal((unsigned)(idx - base_ptr())));
+    }
+
+    void solver::asserted(literal l) {
+        auto p = m_var2node[l.var()];
+        bool sign = p.second != l.sign();
+        euf::enode* n = p.first;
+        expr* e = n->get_owner();        
+        if (m.is_eq(e) && !sign) {            
+            euf::enode* na = n->get_arg(0); 
+            euf::enode* nb = n->get_arg(1);
+            m_egraph.merge(na, nb, base_ptr() + l.index());
+        }
+        else {
+            euf::enode* nb = sign ? m_false : m_true;
+            m_egraph.merge(n, nb, base_ptr() + l.index());
+        }
+
+        // TBD: delay propagation?
+        m_egraph.propagate();
+        if (m_egraph.inconsistent()) {       
+            s().set_conflict(sat::justification::mk_ext_justification(s().scope_lvl(), 0));
+            return;
+        }
+        for (euf::enode* eq : m_egraph.new_eqs()) {
+            bool_var v = m_expr2var.to_bool_var(eq->get_owner());
+            s().assign(literal(v, false), sat::justification::mk_ext_justification(s().scope_lvl(), 1));
+        }
+        for (euf::enode* p : m_egraph.new_lits()) {
+            expr* e = p->get_owner();
+            bool sign = m.is_false(p->get_root()->get_owner());
+            SASSERT(m.is_bool(e));
+            SASSERT(m.is_true(p->get_root()->get_owner()) || sign);
+            bool_var v = m_expr2var.to_bool_var(e);
+            s().assign(literal(v, sign), sat::justification::mk_ext_justification(s().scope_lvl(), 2));
+        }
+    }
+
+    sat::check_result solver::check() { 
+        return sat::CR_DONE; 
+    }
+    void solver::push() {
+        m_egraph.push();
+    }
+    void solver::pop(unsigned n) {
+        m_egraph.pop(n);
+    }
+    void solver::pre_simplify() {}
+    void solver::simplify() {}
+    // have a way to replace l by r in all constraints
+    void solver::clauses_modifed() {}
+    lbool solver::get_phase(bool_var v) { return l_undef; }
+    std::ostream& solver::display(std::ostream& out) const {
+        m_egraph.display(out);
+        return out; 
+    }
+    std::ostream& solver::display_justification(std::ostream& out, ext_justification_idx idx) const { return out; }
+    std::ostream& solver::display_constraint(std::ostream& out, ext_constraint_idx idx) const { return out; }
+    void solver::collect_statistics(statistics& st) const {}
+    sat::extension* solver::copy(sat::solver* s) { return nullptr; }       
+    sat::extension* solver::copy(sat::lookahead* s, bool learned) { return nullptr; }       
+    void solver::find_mutexes(literal_vector& lits, vector<literal_vector> & mutexes) {}
+    void solver::gc() {}
+    void solver::pop_reinit() {}
+    bool solver::validate() { return true; }
+    void solver::init_use_list(sat::ext_use_list& ul) {}
+    bool solver::is_blocked(literal l, ext_constraint_idx) { return false; }
+    bool solver::check_model(sat::model const& m) const { return true;}
+    unsigned solver::max_var(unsigned w) const { return w; }
+   
+    void solver::internalize(sat_internalizer& si, expr* e) {
+        SASSERT(!si.is_bool_op(e));
+        unsigned sz = m_stack.size();
+        euf::enode* n = visit(si, e);
+        while (m_stack.size() > sz) {
+        loop:
+            if (!m.inc())
+                throw tactic_exception(m.limit().get_cancel_msg());
+            frame & fr = m_stack.back();
+            expr* e = fr.m_e;
+            if (m_egraph.find(e)) {
+                m_stack.pop_back();
+                continue;
+            }
+            unsigned num = is_app(e) ? to_app(e)->get_num_args() : 0;
+            m_args.reset();
+            while (fr.m_idx < num) {
+                expr* arg = to_app(e)->get_arg(fr.m_idx);
+                fr.m_idx++;
+                n = visit(si, arg);
+                if (!n)
+                    goto loop;
+                m_args.push_back(n);
+            }
+            n = m_egraph.mk(e, num, m_args.c_ptr());
+            attach_bool_var(si, n);
+        }        
+        SASSERT(m_egraph.find(e));
+    }
+
+    euf::enode* solver::visit(sat_internalizer& si, expr* e) {
+        euf::enode* n = m_egraph.find(e);
+        if (n)
+            return n;
+        if (si.is_bool_op(e)) {
+            sat::literal lit = si.internalize(e);
+            n = m_egraph.mk(e, 0, nullptr);
+            attach_bool_var(lit.var(), lit.sign(), n);
+            s().set_external(lit.var());
+            return n;
+        }
+        if (is_app(e) && to_app(e)->get_num_args() > 0)
+            return nullptr;
+        n = m_egraph.mk(e, 0, nullptr);
+        attach_bool_var(si, n);
+        return n;
+    }
+
+    void solver::attach_bool_var(sat_internalizer& si, euf::enode* n) {
+        expr* e = n->get_owner();
+        if (m.is_bool(e)) {
+            sat::bool_var v = si.add_bool_var(e);
+            attach_bool_var(v, false, n);
+        }
+    }
+
+    void solver::attach_bool_var(sat::bool_var v, bool sign, euf::enode* n) {
+        m_var2node.reserve(v + 1);
+        m_var2node[v] = euf::enode_bool_pair(n, sign);
+    }
+ 
+}
diff --git a/src/sat/euf/euf_solver.h b/src/sat/euf/euf_solver.h
new file mode 100644
index 00000000000..6a98ea93e85
--- /dev/null
+++ b/src/sat/euf/euf_solver.h
@@ -0,0 +1,98 @@
+/*++
+Copyright (c) 2020 Microsoft Corporation
+
+Module Name:
+
+    euf_solver.h
+
+Abstract:
+
+    Solver plugin for EUF
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2020-08-25
+
+--*/
+#pragma once
+
+#include "sat/sat_extension.h"
+#include "ast/euf/euf_egraph.h"
+#include "sat/tactic/atom2bool_var.h"
+#include "sat/tactic/goal2sat.h"
+
+namespace euf_sat {
+    typedef sat::literal literal;
+    typedef sat::ext_constraint_idx ext_constraint_idx;
+    typedef sat::ext_justification_idx ext_justification_idx;
+    typedef sat::literal_vector literal_vector;
+    typedef sat::bool_var bool_var;
+
+    struct frame {
+        expr* m_e;
+        unsigned m_idx;
+        frame(expr* e) : m_e(e), m_idx(0) {}
+    };
+
+    class solver : public sat::extension {
+        ast_manager& m;
+        atom2bool_var&        m_expr2var;
+        euf::egraph           m_egraph;
+        sat::solver*          m_solver;
+
+        euf::enode*           m_true;
+        euf::enode*           m_false;
+        svector<euf::enode_bool_pair> m_var2node;
+        ptr_vector<unsigned>  m_explain;
+        euf::enode_vector     m_args;
+        svector<frame>        m_stack;
+
+        sat::solver& s() { return *m_solver; }
+        unsigned * base_ptr() { return reinterpret_cast<unsigned*>(this); }
+        euf::enode* visit(sat_internalizer& si, expr* e);
+        void attach_bool_var(sat_internalizer& si, euf::enode* n);
+        void attach_bool_var(sat::bool_var v, bool sign, euf::enode* n);
+
+    public:
+        solver(ast_manager& m, atom2bool_var& expr2var):
+            m(m),
+            m_expr2var(expr2var),
+            m_egraph(m),
+            m_solver(nullptr)
+        {}
+
+        void set_solver(sat::solver* s) override { m_solver = s; }
+        void set_lookahead(sat::lookahead* s) override { }
+        double get_reward(literal l, ext_constraint_idx idx, sat::literal_occs_fun& occs) const override { return 0; }
+        bool is_extended_binary(ext_justification_idx idx, literal_vector & r) override { return false; }
+
+        bool propagate(literal l, ext_constraint_idx idx) override;
+        void get_antecedents(literal l, ext_justification_idx idx, literal_vector & r) override;
+        void asserted(literal l) override;
+        sat::check_result check() override;
+        void push() override;
+        void pop(unsigned n) override;
+        void pre_simplify() override;
+        void simplify() override;
+        // have a way to replace l by r in all constraints
+        void clauses_modifed() override;
+        lbool get_phase(bool_var v) override;
+        std::ostream& display(std::ostream& out) const override;
+        std::ostream& display_justification(std::ostream& out, ext_justification_idx idx) const override;
+        std::ostream& display_constraint(std::ostream& out, ext_constraint_idx idx) const override;
+        void collect_statistics(statistics& st) const override;
+        extension* copy(sat::solver* s) override;       
+        extension* copy(sat::lookahead* s, bool learned) override;       
+        void find_mutexes(literal_vector& lits, vector<literal_vector> & mutexes) override;
+        void gc() override;
+        void pop_reinit() override;
+        bool validate() override;
+        void init_use_list(sat::ext_use_list& ul) override;
+        bool is_blocked(literal l, ext_constraint_idx) override;
+        bool check_model(sat::model const& m) const override;
+        unsigned max_var(unsigned w) const override;
+
+        void internalize(sat_internalizer& si, expr* e);
+
+    };
+};
diff --git a/src/sat/tactic/goal2sat.cpp b/src/sat/tactic/goal2sat.cpp
index 664563cc210..e0ede3523a6 100644
--- a/src/sat/tactic/goal2sat.cpp
+++ b/src/sat/tactic/goal2sat.cpp
@@ -42,7 +42,7 @@ Module Name:
 #include "tactic/generic_model_converter.h"
 #include<sstream>
 
-struct goal2sat::imp {
+struct goal2sat::imp : public sat_internalizer {
     struct frame {
         app *    m_t;
         unsigned m_root:1;
@@ -131,6 +131,18 @@ struct goal2sat::imp {
         return m_true;
     }
 
+    sat::bool_var add_bool_var(expr* t) override {
+        sat::bool_var v = m_map.to_bool_var(t);
+        if (v == sat::null_bool_var) {
+            v = m_solver.add_var(true);
+            m_map.insert(t, v);
+        }
+        else {
+            m_solver.set_external(v);
+        }
+        return v;
+    }
+
    void convert_atom(expr * t, bool root, bool sign) {
         SASSERT(m.is_bool(t));
         sat::literal  l;
@@ -149,7 +161,7 @@ struct goal2sat::imp {
             }
             else {
                 bool ext = m_default_external || !is_uninterp_const(t) || m_interface_vars.contains(t);
-                sat::bool_var v = m_solver.add_var(ext);
+                v = m_solver.add_var(ext);
                 m_map.insert(t, v);
                 l = sat::literal(v, sign);
                 TRACE("sat", tout << "new_var: " << v << ": " << mk_bounded_pp(t, m, 2) << " " << is_uninterp_const(t) << "\n";);
@@ -812,7 +824,7 @@ struct goal2sat::imp {
         }
     }
 
-    sat::literal internalize(expr* n) {
+    sat::literal internalize(expr* n) override {
         SASSERT(m_result_stack.empty());
         process(n, false);
         SASSERT(m_result_stack.size() == 1);
@@ -820,6 +832,30 @@ struct goal2sat::imp {
         m_result_stack.reset();
         return result;
     }
+
+    bool is_bool_op(expr* t) const override {
+        if (!is_app(t))
+            return false;
+        if (to_app(t)->get_family_id() == m.get_basic_family_id()) {
+            switch (to_app(t)->get_decl_kind()) {
+            case OP_OR:
+            case OP_AND:             
+            case OP_TRUE:
+            case OP_FALSE:
+            case OP_NOT:
+                return true;
+            case OP_ITE:
+            case OP_EQ:
+                return m.is_bool(to_app(t)->get_arg(1));
+            default:
+                return false;
+            }
+        }
+        else if (to_app(t)->get_family_id() == pb.get_family_id()) 
+            return true;        
+        else 
+            return false;       
+    }
     
     void process(expr * n) {
         m_result_stack.reset();
diff --git a/src/sat/tactic/goal2sat.h b/src/sat/tactic/goal2sat.h
index a1ea6a78e34..47a12e93fcc 100644
--- a/src/sat/tactic/goal2sat.h
+++ b/src/sat/tactic/goal2sat.h
@@ -34,6 +34,14 @@ Module Name:
 #include "tactic/generic_model_converter.h"
 #include "sat/tactic/atom2bool_var.h"
 
+
+class sat_internalizer {
+public:
+    virtual bool is_bool_op(expr* e) const = 0;
+    virtual sat::literal internalize(expr* e) = 0;
+    virtual sat::bool_var add_bool_var(expr* e)  = 0;
+};
+
 class goal2sat {
     struct imp;
     imp *  m_imp;
diff --git a/src/test/egraph.cpp b/src/test/egraph.cpp
index f311b503836..692829ff3e6 100644
--- a/src/test/egraph.cpp
+++ b/src/test/egraph.cpp
@@ -83,6 +83,8 @@ static void test2() {
     }    
 }
 
+
+
 static void test3() {
     ast_manager m;
     reg_decl_plugins(m);