diff --git a/src/math/polysat/constraint_manager.cpp b/src/math/polysat/constraint_manager.cpp
index c7a3d3921..317ee9378 100644
--- a/src/math/polysat/constraint_manager.cpp
+++ b/src/math/polysat/constraint_manager.cpp
@@ -401,8 +401,8 @@ namespace polysat {
         if (it != m_dedup.m_quot_rem_expr.end())
             return { m.mk_var(it->m_value.first), m.mk_var(it->m_value.second) };
 
-        pdd q = m.mk_var(s.add_var(sz));  // quotient
-        pdd r = m.mk_var(s.add_var(sz));  // remainder
+        pdd q = m.mk_var(s.add_var(sz, pvar_kind::internal));  // quotient
+        pdd r = m.mk_var(s.add_var(sz, pvar_kind::internal));  // remainder
         m_dedup.m_quot_rem_expr.insert(args, { q.var(), r.var() });
         m_dedup.m_div_rem_list.push_back({ a, b, q.var(), r.var() });
 
@@ -467,7 +467,7 @@ namespace polysat {
         if (it != m_dedup.op_constraint_expr.end())
             return m.mk_var(it->m_value);
 
-        pdd r = m.mk_var(s.add_var(sz));
+        pdd r = m.mk_var(s.add_var(sz, pvar_kind::op));
         m_dedup.op_constraint_expr.insert(args, r.var());
 
         signed_constraint c = mk_op_constraint(op, p, q, r);
@@ -644,7 +644,7 @@ namespace polysat {
         auto const it = m_dedup.m_bv_ext_expr.find_iterator(args);
         if (it != m_dedup.m_bv_ext_expr.end())
             return s.var(it->m_value);
-        pvar const v = s.add_var(v_sz);
+        pvar const v = s.add_var(v_sz, pvar_kind::internal);
         pdd const V = s.var(v);
         m_dedup.m_bv_ext_expr.insert(args, v);
         // (1)  v[|p|-1:0] = p
@@ -665,7 +665,7 @@ namespace polysat {
         auto const it = m_dedup.m_bv_ext_expr.find_iterator(args);
         if (it != m_dedup.m_bv_ext_expr.end())
             return s.var(it->m_value);
-        pdd const v = s.var(s.add_var(v_sz));
+        pdd const v = s.var(s.add_var(v_sz, pvar_kind::internal));
         m_dedup.m_bv_ext_expr.insert(args, v.var());
         // (1)  v[|p|-1:0] = p
         s.add_eq(q, extract(v, p_sz - 1, 0));
diff --git a/src/math/polysat/naming.cpp b/src/math/polysat/naming.cpp
index 64583fa16..9996b2b95 100644
--- a/src/math/polysat/naming.cpp
+++ b/src/math/polysat/naming.cpp
@@ -40,6 +40,7 @@ namespace polysat {
         SASSERT(!m_names.contains(key));
         m_names.insert(key, v);
         m_terms[v] = t;
+        LOG("set_name v" << v << " := " << t);
     }
 
     pvar name_manager::get_name(pdd const& t) const {
@@ -57,7 +58,7 @@ namespace polysat {
         pvar v = get_name(t);
         if (v != null_var)
             return v;
-        v = s.add_var(t.power_of_2());
+        v = s.add_var(t.power_of_2(), pvar_kind::name);
         s.add_eq(s.var(v), t);
         set_name(v, t);
         return v;
diff --git a/src/math/polysat/slicing.cpp b/src/math/polysat/slicing.cpp
index c23024b4d..11c9ca368 100644
--- a/src/math/polysat/slicing.cpp
+++ b/src/math/polysat/slicing.cpp
@@ -943,7 +943,7 @@ namespace polysat {
         }
         // allocate new variable if we cannot reuse it
         if (v == null_var) {
-            v = m_solver.add_var(hi - lo + 1);
+            v = m_solver.add_var(hi - lo + 1, pvar_kind::internal);
 #if 1
             // slice didn't have a variable yet; so we can re-use it for the new variable
             // (we end up with a "phantom" enode that was first created for the variable)
@@ -984,6 +984,7 @@ namespace polysat {
         m_extract_dedup.insert(args, v);
         m_extract_trail.push_back(args);
         m_trail.push_back(trail_item::mk_extract);
+        LOG("mk_extract: v" << src << "[" << hi << ":" << lo << "] = v" << v);
         return v;
     }
 
@@ -1020,7 +1021,7 @@ namespace polysat {
             v = replay_var;
         }
         else
-            v = m_solver.add_var(total_width);
+            v = m_solver.add_var(total_width, pvar_kind::internal);
         enode* sv = var2slice(v);
         VERIFY(merge(slices, sv, dep_t()));
         // NOTE: add_concat_node must be done after merge to preserve the invariant: "a base slice is never equivalent to a congruence node".
diff --git a/src/math/polysat/solver.cpp b/src/math/polysat/solver.cpp
index 80e86747c..5249e0d4a 100644
--- a/src/math/polysat/solver.cpp
+++ b/src/math/polysat/solver.cpp
@@ -168,12 +168,16 @@ namespace polysat {
         return sz2pdd(size(v));
     }
 
-    unsigned solver::add_var(unsigned sz) {
+    unsigned solver::add_var(unsigned sz, pvar_kind k) {
+#ifndef NDEBUG
+        if (m_is_solving) {
+            SASSERT(k != pvar_kind::external);  // NOTE: if this assertion fails, most likely pvar_kind wasn't set for some internal variable.
+        }
+#endif
         pvar const v = m_value.size();
+        m_kind.push_back(k);
         m_value.push_back(rational::zero());
         m_justification.push_back(justification::unassigned());
-        m_viable.push_var(sz);
-        m_viable_fallback.push_var(sz);
         m_pwatch.push_back({});
         m_activity.push_back(0);
         m_vars.push_back(sz2pdd(sz).mk_var(v));
@@ -182,6 +186,8 @@ namespace polysat {
         m_free_pvars.mk_var_eh(v);
         m_names.push_var(var(v));  // needs m_vars
         m_slicing.add_var(sz);
+        m_viable.push_var(sz);
+        m_viable_fallback.push_var(sz);
         return v;
     }
 
@@ -195,6 +201,8 @@ namespace polysat {
         pvar v = m_value.size() - 1;
         m_viable.pop_var();
         m_viable_fallback.pop_var();
+        m_names.pop_var();
+        m_kind.pop_back();
         m_value.pop_back();
         m_justification.pop_back();
         m_pwatch.pop_back();
@@ -202,7 +210,6 @@ namespace polysat {
         m_vars.pop_back();
         m_size.pop_back();
         m_free_pvars.del_var_eh(v);
-        m_names.pop_var();
     }
 
     void solver::assign_eh(signed_constraint c, dependency dep) {
diff --git a/src/math/polysat/solver.h b/src/math/polysat/solver.h
index d1a8daa6e..530168cae 100644
--- a/src/math/polysat/solver.h
+++ b/src/math/polysat/solver.h
@@ -173,6 +173,7 @@ namespace polysat {
         slicing                  m_slicing;
 
         // Per variable information
+        svector<pvar_kind>       m_kind;
         vector<rational>         m_value;         // assigned value
         vector<justification>    m_justification; // justification for variable assignment
         vector<constraints>      m_pwatch;        // watch list datastructure into constraints.
@@ -240,6 +241,7 @@ namespace polysat {
          * Each struct is a subclass of trail and implements undo().
          */
 
+        pvar add_var(unsigned sz, pvar_kind k);
         void del_var();
 
         dd::pdd_manager& sz2pdd(unsigned sz) const;
@@ -409,7 +411,7 @@ namespace polysat {
         /**
          * Add variable with bit-size.
          */
-        pvar add_var(unsigned sz);
+        pvar add_var(unsigned sz) { return add_var(sz, pvar_kind::external); }
 
         /**
          * Create polynomial terms
diff --git a/src/math/polysat/types.h b/src/math/polysat/types.h
index bcc8d76fa..756565070 100644
--- a/src/math/polysat/types.h
+++ b/src/math/polysat/types.h
@@ -44,8 +44,7 @@ namespace polysat {
         external,           // regular variables (from the input formula)
         name,               // name for a polynomial term
         op,                 // result of an op_constraint
-        extract,            // result of an extract operation
-        concat,             // result of a concat operation
+        internal,           // other internal variable
     };
 
     class dependency {
diff --git a/src/math/polysat/variable_elimination.cpp b/src/math/polysat/variable_elimination.cpp
index 052ea9b16..84aab8cc0 100644
--- a/src/math/polysat/variable_elimination.cpp
+++ b/src/math/polysat/variable_elimination.cpp
@@ -98,7 +98,7 @@ namespace polysat {
         
         pdd power = get_dyadic_valuation(p).second;
         
-        pvar rest = s.add_var(p.power_of_2());
+        pvar rest = s.add_var(p.power_of_2(), pvar_kind::internal);
         pdd rest_pdd = m.mk_var(rest);
         m_rest_constants.setx(v, rest, -1);
         s.add_clause(s.eq(power * rest_pdd, p), false);
@@ -119,7 +119,7 @@ namespace polysat {
         if (m_inverse_constants.size() > v && m_inverse_constants[v] != -1)
             return optional<pdd>(s.var(m_inverse_constants[v]));
         
-        pvar inv = s.add_var(p.power_of_2());
+        pvar inv = s.add_var(p.power_of_2(), pvar_kind::internal);
         pdd inv_pdd = m.mk_var(inv);
         m_inverse_constants.setx(v, inv, -1);
         s.add_clause(s.eq(inv_pdd * p, m.one()), false);
@@ -138,8 +138,8 @@ namespace polysat {
         pvar pv2;
         bool new_var = false;
         if (m_pv_constants.size() <= v || m_pv_constants[v] == -1) {
-            pv = s.add_var(m.power_of_2()); // TODO: What's a good value? Unfortunately we cannot use an integer
-            pv2 = s.add_var(m.power_of_2());
+            pv = s.add_var(m.power_of_2(), pvar_kind::internal); // TODO: What's a good value? Unfortunately we cannot use an integer
+            pv2 = s.add_var(m.power_of_2(), pvar_kind::internal);
             m_pv_constants.setx(v, pv, -1);
             m_pv_power_constants.setx(v, pv2, -1);
             // [nsb cr]: why these calls to m.mk_var()?
@@ -586,7 +586,7 @@ namespace polysat {
         pvar p_inv = m_pseudo_inverse[v][parity];
         
         if (p_inv == -1) {
-            p_inv = s.add_var(p.power_of_2());
+            p_inv = s.add_var(p.power_of_2(), pvar_kind::internal);
             m_pseudo_inverse[v][parity] = p_inv;
             // NB: Strictly speaking this condition does not say that "p_inv" is the pseudo-inverse.
             // However, the variable elimination lemma stays valid even if "p_inv" is not really the pseudo-inverse anymore (e.g., because of parity was reduced)
@@ -608,7 +608,7 @@ namespace polysat {
         if (m_inverse.size() > v && m_inverse[v] != -1)
             return s.var(m_inverse[v]);
         
-        pvar inv = s.add_var(p.power_of_2());
+        pvar inv = s.add_var(p.power_of_2(), pvar_kind::internal);
         pdd inv_pdd = s.var(inv);
         m_inverse.setx(v, inv, -1);
         s.add_clause(s.eq(inv_pdd * p, p.manager().one()), false);
@@ -634,7 +634,7 @@ namespace polysat {
             needs_propagate = !tuple.second[parity];
         }
         else {
-            odd_v = s.add_var(p.power_of_2());
+            odd_v = s.add_var(p.power_of_2(), pvar_kind::internal);
             verbose_stream() << "Odd part v" << odd_v << " of " << p << " introduced\n";
             m_odd.setx(v, optional<std::pair<pvar, bool_vector>>({ odd_v, bool_vector(p.power_of_2(), false) }), optional<std::pair<pvar, bool_vector>>::undef());
         }