diff --git a/src/math/polysat/constraint.cpp b/src/math/polysat/constraint.cpp
index 2574dd517..94e159f4f 100644
--- a/src/math/polysat/constraint.cpp
+++ b/src/math/polysat/constraint.cpp
@@ -28,15 +28,6 @@ namespace polysat {
         return eval(s.get_assignment());
     }
 
-    bool signed_constraint::is_eq() const {
-        return is_positive() && m_constraint->is_eq();
-    }
-
-    pdd const& signed_constraint::eq() const {
-        SASSERT(is_eq());
-        return m_constraint->to_ule().lhs();
-    }
-
     inequality inequality::from_ule(signed_constraint src)
     {
         ule_constraint& c = src->to_ule();
@@ -91,6 +82,11 @@ namespace polysat {
         return { std::move(lhs), std::move(rhs), m_src };
     }
 
+    pdd const& constraint::to_eq() const {
+        SASSERT(is_eq());
+        return to_ule().lhs();
+    }
+
     ule_constraint& constraint::to_ule() {
         return *dynamic_cast<ule_constraint*>(this);
     }
diff --git a/src/math/polysat/constraint.h b/src/math/polysat/constraint.h
index 9be3b0e81..2c63f9231 100644
--- a/src/math/polysat/constraint.h
+++ b/src/math/polysat/constraint.h
@@ -90,6 +90,7 @@ namespace polysat {
          */
         virtual clause_ref produce_lemma(solver& s, assignment const& a, bool is_positive) { return {}; }
 
+        pdd const& to_eq() const;
         ule_constraint& to_ule();
         ule_constraint const& to_ule() const;
         umul_ovfl_constraint& to_umul_ovfl();
@@ -180,10 +181,8 @@ namespace polysat {
         constraint& operator*() { return *m_constraint; }
         constraint const& operator*() const { return *m_constraint; }
 
-        bool is_eq() const;
-        bool is_diseq() const { return negated().is_eq(); }
-        pdd const& eq() const;
-        pdd const& diseq() const { return negated().eq(); }
+        bool is_pos_eq() const { return is_positive() && m_constraint->is_eq(); }
+        bool is_neg_eq() const { return is_negative() && m_constraint->is_eq(); }
 
         signed_constraint& operator=(std::nullptr_t) { m_constraint = nullptr; return *this; }
 
diff --git a/src/math/polysat/eq_explain.cpp b/src/math/polysat/eq_explain.cpp
index 8dc20c8e7..9abb8a01a 100644
--- a/src/math/polysat/eq_explain.cpp
+++ b/src/math/polysat/eq_explain.cpp
@@ -45,7 +45,7 @@ namespace polysat {
     }
 
     bool eq_explain::try_explain1(pvar v, signed_constraint c, conflict& core) {
-        if (!c.is_eq())
+        if (!c.is_pos_eq())
             return false;
         if (!c.is_currently_false(s))
             return false;
diff --git a/src/math/polysat/simplify_clause.cpp b/src/math/polysat/simplify_clause.cpp
index 159e8a2ae..1d45c6fd8 100644
--- a/src/math/polysat/simplify_clause.cpp
+++ b/src/math/polysat/simplify_clause.cpp
@@ -106,7 +106,7 @@ namespace polysat {
      */
     bool simplify_clause::try_remove_equations(clause& cl) {
         LOG_H2("Remove superfluous equations from: " << cl);
-        bool const has_eqn = any_of(cl, [&](sat::literal lit) { return s.lit2cnstr(lit).is_eq(); });
+        bool const has_eqn = any_of(cl, [&](sat::literal lit) { return !lit.sign() && s.lit2cnstr(lit)->is_eq(); });
         if (!has_eqn)
             return false;
         bool any_removed = false;
@@ -189,8 +189,8 @@ namespace polysat {
                     return false;
             }
             SASSERT(v != null_var);  // constraints without unassigned variables would be evaluated at this point
-            if (c.is_diseq() && c.diseq().is_unilinear()) {
-                pdd const& p = c.diseq();
+            if (c.is_negative() && c->is_eq() && c->to_eq().is_unilinear()) {
+                pdd const& p = c->to_eq();
                 if (p.hi().is_one()) {
                     eq = lit;
                     k = (-p.lo()).val();
@@ -589,7 +589,7 @@ namespace polysat {
             trailing_bits mask;
             single_bit bit;
             pdd p = c->to_ule().lhs();
-            if ((c.is_eq() || c.is_diseq()) && get_lsb(c->to_ule().lhs(), c->to_ule().rhs(), p, mask, c.is_positive())) {
+            if (c->is_eq() && get_lsb(c->to_ule().lhs(), c->to_ule().rhs(), p, mask, c.is_positive())) {
                 if (mask.bits.bitsize() > mask.length) {
                     removed[i] = true; // skip this constraint. e.g., 2^(k-3)*x = 9*2^(k-3) is false as 9 >= 2^3
                     continue;
diff --git a/src/math/polysat/superposition.cpp b/src/math/polysat/superposition.cpp
index 59a24de80..f4049add9 100644
--- a/src/math/polysat/superposition.cpp
+++ b/src/math/polysat/superposition.cpp
@@ -37,8 +37,8 @@ namespace polysat {
         LOG_H3("Resolving upon v" << v);
         LOG("c1: " << lit_pp(s, c1));
         LOG("c2: " << lit_pp(s, c2));
-        pdd a = c1.eq();
-        pdd b = c2.eq();
+        pdd a = c1->to_eq();
+        pdd b = c2->to_eq();
         unsigned degree_a = a.degree();
         unsigned degree_b = b.degree();
         pdd r = a;
@@ -67,7 +67,7 @@ namespace polysat {
         for (auto c1 : s.m_viable.get_constraints(v)) {
             if (!c1->contains_var(v))  // side conditions do not contain v; skip them here
                 continue;
-            if (!c1.is_eq())
+            if (!c1.is_pos_eq())
                 continue;
             SASSERT(c1.is_currently_true(s));
             SASSERT(c2.is_currently_false(s));
@@ -102,7 +102,7 @@ namespace polysat {
     // true = done, false = abort, undef = continue
     lbool ex_polynomial_superposition::try_explain1(pvar v, conflict& core) {
         for (auto c2 : core) {
-            if (!c2.is_eq())
+            if (!c2.is_pos_eq())
                 continue;
             if (!c2->contains_var(v))
                 continue;
@@ -128,7 +128,7 @@ namespace polysat {
             for (auto c : core) {
                 if (!c->contains_var(v))
                     continue;
-                if (!c.is_eq())
+                if (!c.is_pos_eq())
                     continue;
 #if 0
                 if (!c.is_currently_true(s))
@@ -151,7 +151,7 @@ namespace polysat {
                 continue;
             if (!c->contains_var(v))
                 continue;
-            if (c.is_eq())
+            if (c.is_pos_eq())
                 continue;
             LOG("try-reduce: " << c << " " << c.is_currently_false(s));
             if (!c->is_ule())
diff --git a/src/math/polysat/ule_constraint.cpp b/src/math/polysat/ule_constraint.cpp
index 0258365dd..20e4c260f 100644
--- a/src/math/polysat/ule_constraint.cpp
+++ b/src/math/polysat/ule_constraint.cpp
@@ -8,7 +8,7 @@ Module Name:
 Author:
 
     Nikolaj Bjorner (nbjorner) 2021-03-19
-    Jakob Rath 2021-04-6
+    Jakob Rath 2021-04-06
 
 Notes:
 
diff --git a/src/math/polysat/ule_constraint.h b/src/math/polysat/ule_constraint.h
index 06ecd2172..ed0ba2c8c 100644
--- a/src/math/polysat/ule_constraint.h
+++ b/src/math/polysat/ule_constraint.h
@@ -8,7 +8,7 @@ Module Name:
 Author:
 
     Nikolaj Bjorner (nbjorner) 2021-03-19
-    Jakob Rath 2021-04-6
+    Jakob Rath 2021-04-06
 
 --*/
 #pragma once
diff --git a/src/math/polysat/variable_elimination.cpp b/src/math/polysat/variable_elimination.cpp
index 9d2b816f5..052ea9b16 100644
--- a/src/math/polysat/variable_elimination.cpp
+++ b/src/math/polysat/variable_elimination.cpp
@@ -279,9 +279,9 @@ namespace polysat {
         // find constraint that allows computing v from other variables
         // (currently, consider only equations that contain v with degree 1)
         for (signed_constraint c : core) {
-            if (!c.is_eq())
+            if (!c.is_pos_eq())
                 continue;
-            if (c.eq().degree(v) != 1)
+            if (c->to_eq().degree(v) != 1)
                 continue;
             find_lemma(v, c, core);
         }
@@ -289,7 +289,7 @@ namespace polysat {
     
     void free_variable_elimination::find_lemma(pvar v, signed_constraint c, conflict& core) {
         LOG_H3("Free Variable Elimination for v" << v << " using equation " << c);
-        pdd const& p = c.eq();
+        pdd const& p = c->to_eq();
         SASSERT_EQ(p.degree(v), 1);
         auto& m = p.manager();
         pdd fac = m.zero();
diff --git a/src/math/polysat/viable.cpp b/src/math/polysat/viable.cpp
index 9052014a2..3820eac37 100644
--- a/src/math/polysat/viable.cpp
+++ b/src/math/polysat/viable.cpp
@@ -985,8 +985,8 @@ namespace {
 					justifications[bit.position].clear();
 					justifications[bit.position].push_back(e1);
 				}
-				else if ((src->is_eq() || src.is_diseq()) &&
-					simplify_clause::get_lsb(s.subst(src->to_ule().lhs()), s.subst(src->to_ule().rhs()), p, lsb, src.is_positive()) && p.is_var()) {
+				else if (src->is_eq() &&
+                         simplify_clause::get_lsb(s.subst(src->to_ule().lhs()), s.subst(src->to_ule().rhs()), p, lsb, src.is_positive()) && p.is_var()) {
 					if (src.is_positive()) {
 						for (unsigned i = 0; i < lsb.length; i++) {
 							lbool prev = fixed[i];
@@ -1179,7 +1179,7 @@ namespace {
                 justifications[bit.position].clear();
                 justifications[bit.position].push_back(src);
             }
-            else if ((src->is_eq() || src.is_diseq()) &&
+            else if (src->is_eq() &&
                 simplify_clause::get_lsb(src->to_ule().lhs(), src->to_ule().rhs(), p, mask, src.is_positive()) && p.is_var()) {
                 if (src.is_positive()) {
                     for (unsigned i = 0; i < mask.length; i++) {