diff --git a/src/qe/qe_mbi.cpp b/src/qe/qe_mbi.cpp
index 0fe2d49c7..d47c2ab2c 100644
--- a/src/qe/qe_mbi.cpp
+++ b/src/qe/qe_mbi.cpp
@@ -19,9 +19,12 @@ Revision History:
 --*/
 
 #include "ast/ast_util.h"
+#include "ast/for_each_expr.h"
 #include "ast/rewriter/bool_rewriter.h"
+#include "model/model_evaluator.h"
 #include "solver/solver.h"
 #include "qe/qe_mbi.h"
+#include "qe/qe_term_graph.h"
 
 
 namespace qe {
@@ -87,7 +90,35 @@ namespace qe {
     // -------------------------------
     // euf_mbi, TBD
 
-    euf_mbi_plugin::euf_mbi_plugin(solver* s): m(s->get_manager()), m_solver(s) {}
+    struct euf_mbi_plugin::is_atom_proc {
+        ast_manager& m;
+        expr_ref_vector& m_atoms;
+        is_atom_proc(expr_ref_vector& atoms): m(atoms.m()), m_atoms(atoms) {}
+        void operator()(app* a) {
+            if (m.is_eq(a)) {
+                m_atoms.push_back(a);
+            }
+            else if (m.is_bool(a) && a->get_family_id() != m.get_basic_family_id()) {
+                m_atoms.push_back(a);
+            }
+        }
+        void operator()(expr*) {}
+    };
+
+    euf_mbi_plugin::euf_mbi_plugin(solver* s, solver* sNot): 
+        m(s->get_manager()), 
+        m_atoms(m),
+        m_solver(s),
+        m_dual_solver(sNot)
+    {
+        expr_ref_vector fmls(m);
+        m_solver->get_assertions(fmls);
+        expr_fast_mark1 marks;
+        is_atom_proc proc(m_atoms);
+        for (expr* e : fmls) {
+            quick_for_each_expr(proc, marks, e);
+        }
+    }
 
     mbi_result euf_mbi_plugin::operator()(func_decl_ref_vector const& vars, expr_ref_vector& lits, model_ref& mdl) {
         lbool r = m_solver->check_sat(lits);
@@ -95,16 +126,39 @@ namespace qe {
         case l_false:
             lits.reset();
             m_solver->get_unsat_core(lits);
+            // optionally minimize core using superposition.
             return mbi_unsat;
         case l_true: {
             expr_ref_vector fmls(m);
             m_solver->get_model(mdl);
+            model_evaluator mev(*mdl.get());
             lits.reset();
-            // 1. extract formulas from solver
-            // 2. extract implicant over formulas
-            // 3. extract equalities or other assignments over the congruence classes
-            m_solver->get_assertions(fmls);
-            NOT_IMPLEMENTED_YET();
+            for (expr* e : m_atoms) {
+                if (mev.is_true(e)) {
+                    lits.push_back(e);
+                }
+                else if (mev.is_false(e)) {
+                    lits.push_back(m.mk_not(e));
+                }
+            }
+            r = m_dual_solver->check_sat(lits);
+            expr_ref_vector core(m);
+            term_graph tg(m);
+            switch (r) {
+            case l_false:
+                // use the dual solver to find a 'small' implicant
+                m_dual_solver->get_unsat_core(core);
+                // project the implicant onto vars 
+                tg.add_lits(core);
+                lits.reset();                
+                lits.append(tg.project(vars, false));
+                return mbi_sat;
+            case l_undef:
+                return mbi_undef;
+            case l_true:
+                UNREACHABLE();
+                return mbi_undef;
+            }
             return mbi_sat;
         }
         default:
diff --git a/src/qe/qe_mbi.h b/src/qe/qe_mbi.h
index d58430602..8ecb6532e 100644
--- a/src/qe/qe_mbi.h
+++ b/src/qe/qe_mbi.h
@@ -76,8 +76,11 @@ namespace qe {
     class euf_mbi_plugin : public mbi_plugin {
         ast_manager& m;
         solver_ref   m_solver;
+        solver_ref   m_dual_solver;
+        expr_ref_vector m_atoms;
+        struct is_atom_proc;
     public:
-        euf_mbi_plugin(solver* s);
+        euf_mbi_plugin(solver* s, solver* sNot);
         ~euf_mbi_plugin() override {}
         mbi_result operator()(func_decl_ref_vector const& vars, expr_ref_vector& lits, model_ref& mdl) override;
         void block(expr_ref_vector const& lits) override;
diff --git a/src/qe/qe_term_graph.cpp b/src/qe/qe_term_graph.cpp
index eaf5a372d..a5e45d389 100644
--- a/src/qe/qe_term_graph.cpp
+++ b/src/qe/qe_term_graph.cpp
@@ -35,7 +35,6 @@ namespace qe {
         term* m_next;
         // -- eq class size
         unsigned m_class_size;
-        
         // -- general purpose mark
         unsigned m_mark:1;
         // -- general purpose second mark
@@ -160,12 +159,10 @@ namespace qe {
     };
     
 
-
     class arith_term_graph_plugin : public term_graph_plugin {
         term_graph &m_g;
         ast_manager &m;
         arith_util m_arith;
-        
     public:
         arith_term_graph_plugin(term_graph &g) :
             term_graph_plugin (g.get_ast_manager().mk_family_id("arith")),
@@ -177,7 +174,6 @@ namespace qe {
             expr *e1, *e2;
             e1 = _e1;
             e2 = _e2;
-            
             if (m_arith.is_zero(e1)) {
                 std::swap(e1, e2);
             }
@@ -245,7 +241,6 @@ namespace qe {
             }
             return false;
         }
-        
         expr * mk_zero () {return m_arith.mk_numeral (rational (0), true);}
         bool is_one (expr const * n) const {
             rational val;
@@ -292,12 +287,10 @@ namespace qe {
             else if (m_arith.is_ge(lit, e1, e2)) {
                 mk_ge_core(e1, e2, res);
             }
-            
             // restore negation
             if (is_neg) {
                 res = mk_not(m, res);
             }
-            
             return res;
         }
     };
@@ -331,7 +324,6 @@ namespace qe {
             return null_family_id;
         }
     }
-    
     void term_graph::add_lit(expr *l) {
         expr_ref lit(m);
         
@@ -509,7 +501,6 @@ namespace qe {
     void term_graph::mk_equalities(term const &t, expr_ref_vector &out) {
         SASSERT(t.is_root());
         expr_ref rep(mk_app(t), m);
-        
         for (term *it = &t.get_next(); it != &t; it = &it->get_next()) {
             expr* mem = mk_app_core(it->get_app());
             out.push_back (m.mk_eq (rep, mem));
@@ -606,7 +597,6 @@ namespace qe {
         }
     }
     
-    
     expr_ref term_graph::to_app() {
         expr_ref_vector lits(m);
         to_lits(lits);