diff --git a/src/qe/qe_mbi.cpp b/src/qe/qe_mbi.cpp
index eea3087e2..c6927f7d2 100644
--- a/src/qe/qe_mbi.cpp
+++ b/src/qe/qe_mbi.cpp
@@ -50,7 +50,7 @@ namespace qe {
                         lits.push_back(m.mk_const(c));
                     }
                     else if (m.is_false(mdl->get_const_interp(c))) {
-                        lits.push_back(m.mk_const(c));
+                        lits.push_back(m.mk_not(m.mk_const(c)));
                     }
                 }
             }
diff --git a/src/qe/qe_term_graph.cpp b/src/qe/qe_term_graph.cpp
index 73412c50b..5ef543868 100644
--- a/src/qe/qe_term_graph.cpp
+++ b/src/qe/qe_term_graph.cpp
@@ -18,6 +18,7 @@ Notes:
 --*/
 
 #include "util/util.h"
+#include "util/uint_set.h"
 #include "ast/ast_pp.h"
 #include "ast/ast_util.h"
 #include "ast/for_each_expr.h"
@@ -344,7 +345,7 @@ void term_graph::add_lit(app *l) {
     internalize_lit(lit);
 }
 
-bool term_graph::is_internalized(app *a) {
+bool term_graph::is_internalized(expr *a) {
     return m_app2term.contains(a->get_id());
 }
 
@@ -365,14 +366,24 @@ term *term_graph::mk_term(expr *a) {
 }
 
 term *term_graph::internalize_term(expr *t) {
-    term *res = get_term(t);
-
-    if (!res) {
+    ptr_buffer<expr> todo;
+    todo.push_back(t);
+    term* res = nullptr;
+    while (!todo.empty()) {
+        term* res = get_term(t);
+        if (res) {
+            todo.pop_back();
+            continue;
+        }
+        unsigned sz = todo.size();
         if (is_app(t)) {
             for (expr * arg : *::to_app(t)) {
-                internalize_term(arg);
+                if (!get_term(arg)) 
+                    todo.push_back(arg);
             }
         }
+        if (sz < todo.size()) continue;
+        todo.pop_back();
         res = mk_term(t);
     }
     return res;
@@ -384,7 +395,7 @@ void term_graph::internalize_eq(expr *a1, expr* a2) {
     merge(get_term(a1)->get_root(), get_term(a2)->get_root());
 }
 
-void term_graph::internalize_lit(app* lit) {
+void term_graph::internalize_lit(expr* lit) {
     expr *e1 = nullptr, *e2 = nullptr;
     if (m.is_eq (lit, e1, e2)) {        
         internalize_eq (e1, e2);
@@ -590,15 +601,51 @@ void term_graph::reset() {
 }
 
 expr_ref_vector term_graph::project(func_decl_ref_vector const& decls, bool exclude) {
-    obj_hashtable<func_decl> _decls;
-    for (func_decl* f : decls) _decls.insert(f);
+    uint_set _decls;
+    for (func_decl* f : decls) _decls.insert(f->get_id());
     // . propagate representatives up over parents.
     //   use work-list + marking to propagate.
     // . produce equalities over represented classes.
     // . produce other literals over represented classes 
     //    (walk disequalities in m_lits and represent lhs/rhs over decls or excluding decls)
-    
+    ptr_vector<term> worklist(m_terms);
+    while (!worklist.empty()) {
+        term* t = worklist.back();
+        worklist.pop_back();
+        if (t->get_root().is_marked()) continue;
+        // if exclude = true,  but t in decls, then skip
+        // if exclude = false, but t not in decls, then skip
+        if (exclude != _decls.contains(t->get_decl_id())) {
+            continue;
+        }
+        //
+        // if all children roots are marked
+        // then mark this as well, reorganize root
+        // and add parents to worklist
+        // 
+        bool all_marked = true;
+        for (term* ch : term::children(t)) {
+            all_marked &= ch->get_root().is_marked();
+        }
+        if (!all_marked) continue;
+
+        // make this the new root.
+        term* r = t;
+        do {
+            r->set_root(*t);
+            for (term* p : term::parents(r)) {
+                worklist.push_back(p);
+            }        
+            r = &r->get_next();
+        }
+        while (t != r);    
+        t->set_mark(true);
+    }
+    // Now, marked roots in m_terms can be used in projection
+
     expr_ref_vector result(m);
+    
+    reset_marks();
     NOT_IMPLEMENTED_YET();
     return result;
 }
diff --git a/src/qe/qe_term_graph.h b/src/qe/qe_term_graph.h
index 0879fb386..5319c410a 100644
--- a/src/qe/qe_term_graph.h
+++ b/src/qe/qe_term_graph.h
@@ -39,11 +39,11 @@ namespace qe {
     };
     
     class term_graph {
-        ast_manager &    m;
-        ptr_vector<term> m_terms;
-        app_ref_vector   m_lits;
-        u_map<term* >    m_app2term;        
-        app_ref_vector   m_pinned;
+        ast_manager &     m;
+        ptr_vector<term>  m_terms;
+        app_ref_vector    m_lits; // NSB: expr_ref_vector?
+        u_map<term* >     m_app2term;        
+        ast_ref_vector    m_pinned;
         u_map<expr*>      m_term2app;
         
         plugin_manager<term_graph_plugin> m_plugins;
@@ -55,9 +55,9 @@ namespace qe {
         
         term *internalize_term(expr *t);
         void internalize_eq(expr *a1, expr *a2);
-        void internalize_lit(app *lit);
+        void internalize_lit(expr *lit);
         
-        bool is_internalized(app *a);
+        bool is_internalized(expr *a);
         
         bool term_le(term const &t1, term const &t2);
         void pick_root (term &t);
@@ -77,16 +77,16 @@ namespace qe {
         
         ast_manager& get_ast_manager() const { return m;}
         
-        void add_lit(app *lit);
+        void add_lit(app *lit); // NSB: replace by expr*
         void add_lits(expr_ref_vector const &lits) {
             for (expr* e : lits) add_lit(::to_app(e));
         }
         void add_eq(expr* a, expr* b);
         
         void reset();
-        void to_lits(app_ref_vector &lits, bool all_equalities = false);
+        void to_lits(app_ref_vector &lits, bool all_equalities = false);  // NSB: swap roles
         void to_lits(expr_ref_vector &lits, bool all_equalities = false);
-        app_ref to_app();
+        app_ref to_app(); 
 
         /**
          * Return literals obtained by projecting added literals