diff --git a/src/sat/smt/q_solver.cpp b/src/sat/smt/q_solver.cpp
index 97adc6ae6..bba21723a 100644
--- a/src/sat/smt/q_solver.cpp
+++ b/src/sat/smt/q_solver.cpp
@@ -33,14 +33,13 @@ namespace q {
         expr* e = bool_var2expr(l.var());
         SASSERT(is_forall(e) || is_exists(e));
         if (l.sign() == is_forall(e)) {
-            // existential force
             add_clause(~l, skolemize(to_quantifier(e)));
         }
-        else {
-            // universal force
-//          add_clause(~l, uskolemize(to_quantifier(e)));
+        else {            
+            add_clause(~l, specialize(to_quantifier(e)));
             ctx.push_vec(m_universal, l);
         }
+        m_stats.m_num_quantifier_asserts++;
     }
 
     sat::check_result solver::check() {
@@ -59,7 +58,7 @@ namespace q {
     }
 
     void solver::collect_statistics(statistics& st) const {
-        st.update("quantifier inst", m_stats.m_num_inst);
+        st.update("quantifier asserts", m_stats.m_num_quantifier_asserts);
     }
 
     euf::th_solver* solver::clone(sat::solver* s, euf::solver& ctx) {
@@ -77,26 +76,28 @@ namespace q {
         return v;
     }
 
-    sat::literal solver::skolemize(quantifier* q) {
+    sat::literal solver::instantiate(quantifier* q, std::function<expr* (quantifier*, unsigned)>& mk_var) {
         sat::literal sk;
-        if (m_skolems.find(q, sk))
-            return sk;        
         expr_ref tmp(m);
         expr_ref_vector vars(m);
-        unsigned sz = q->get_num_decls();
+        quantifier* q_flat = flatten(q);
+        unsigned sz = q_flat->get_num_decls();
         vars.resize(sz, nullptr);
-        for (unsigned i = 0; i < sz; ++i) {
-            vars[i] = m.mk_fresh_const(q->get_decl_name(i), q->get_decl_sort(i));    
-        }
+        for (unsigned i = 0; i < sz; ++i) 
+            vars[i] = mk_var(q_flat, i);        
         var_subst subst(m);
-        expr_ref body = subst(q->get_expr(), vars.size(), vars.c_ptr());
+        expr_ref body = subst(q_flat->get_expr(), vars);
         ctx.get_rewriter()(body);
-        sk = b_internalize(body);
+        return b_internalize(body);
+    }
+
+    sat::literal solver::skolemize(quantifier* q) {
+        std::function<expr* (quantifier*, unsigned)> mk_var = [&](quantifier* q, unsigned i) {
+            return m.mk_fresh_const(q->get_decl_name(i), q->get_decl_sort(i));
+        };
+        sat::literal sk = instantiate(q, mk_var);
         if (is_forall(q))
             sk.neg();
-        m_skolems.insert(q, sk);
-        // TODO find a different way than rely on backtrack stack, e,g., save body/q in ref-counted stack
-        ctx.push(insert_map<euf::solver, skolem_table, quantifier*>(m_skolems, q));
         return sk;
     }
 
@@ -104,9 +105,14 @@ namespace q {
     * Find initial values to instantiate quantifier with so to make it as hard as possible for solver
     * to find values to free variables. 
     */
-    sat::literal solver::uskolemize(quantifier* q) {
-        NOT_IMPLEMENTED_YET();
-        return sat::null_literal;
+    sat::literal solver::specialize(quantifier* q) {
+        std::function<expr* (quantifier*, unsigned)> mk_var = [&](quantifier* q, unsigned i) {
+            return get_unit(q->get_decl_sort(i));
+        };
+        sat::literal sk = instantiate(q, mk_var);
+        if (is_exists(q))
+            sk.neg();
+        return sk;
     }
 
     void solver::init_search() {
@@ -143,4 +149,34 @@ namespace q {
         ctx.push(insert_ref2_map<euf::solver, ast_manager, quantifier, quantifier>(m, m_flat, q, q_flat));
         return q_flat;
     }
+
+    void solver::init_units() {
+        if (!m_unit_table.empty())
+            return;
+        for (euf::enode* n : ctx.get_egraph().nodes()) {
+            if (!n->interpreted())
+                continue;
+            expr* e = n->get_expr();
+            sort* s = m.get_sort(e);
+            if (m_unit_table.contains(s))
+                continue;
+            m_unit_table.insert(s, e);
+            ctx.push(insert_map<euf::solver, obj_map<sort, expr*>, sort*>(m_unit_table, s));
+        }
+    }
+
+    expr* solver::get_unit(sort* s) {
+        expr* u = nullptr;
+        if (m_unit_table.find(s, u))
+            return u;
+        init_units();
+        if (m_unit_table.find(s, u))
+            return u;
+        model mdl(m);
+        expr* val = mdl.get_some_value(s);
+        m.inc_ref(val);
+        m.inc_ref(s);
+        ctx.push(insert_ref2_map<euf::solver, ast_manager, sort, expr>(m, m_unit_table, s, val));
+        return val;
+    }
 }
diff --git a/src/sat/smt/q_solver.h b/src/sat/smt/q_solver.h
index 58574544e..19778b099 100644
--- a/src/sat/smt/q_solver.h
+++ b/src/sat/smt/q_solver.h
@@ -29,12 +29,11 @@ namespace q {
 
     class solver : public euf::th_euf_solver {
 
-        typedef obj_map<quantifier, sat::literal> skolem_table;
         typedef obj_map<quantifier, quantifier*> flat_table;
         friend class mbqi;
 
         struct stats {
-            unsigned m_num_inst;
+            unsigned m_num_quantifier_asserts;
             void reset() { memset(this, 0, sizeof(*this)); }
             stats() { reset(); }
         };
@@ -42,12 +41,15 @@ namespace q {
         stats                  m_stats;
         mbqi                   m_mbqi;
 
-        skolem_table           m_skolems;
         flat_table             m_flat;
         sat::literal_vector    m_universal;
+        obj_map<sort, expr*>   m_unit_table;
 
+        sat::literal instantiate(quantifier* q, std::function<expr* (quantifier*, unsigned)>& mk_var);
         sat::literal skolemize(quantifier* q);
-        sat::literal uskolemize(quantifier* q);
+        sat::literal specialize(quantifier* q);
+        void init_units();
+        expr* get_unit(sort* s);
 
     public: