diff --git a/src/math/polysat/constraint.h b/src/math/polysat/constraint.h
index d6a38304c..ac42f8cdd 100644
--- a/src/math/polysat/constraint.h
+++ b/src/math/polysat/constraint.h
@@ -255,6 +255,9 @@ namespace polysat {
 
         void add_to_univariate_solver(solver& s, univariate_solver& us, unsigned dep) const { get()->add_to_univariate_solver(s, us, dep, is_positive()); }
 
+        unsigned var(unsigned idx) const { return m_constraint->var(idx); }
+        bool contains_var(pvar v) const { return m_constraint->contains_var(v); }
+
         sat::bool_var bvar() const { return m_constraint->bvar(); }
         sat::literal blit() const { return sat::literal(bvar(), is_negative()); }
         constraint* get() const { return m_constraint; }
diff --git a/src/math/polysat/interval.h b/src/math/polysat/interval.h
index 952d53a1b..9bea56d41 100644
--- a/src/math/polysat/interval.h
+++ b/src/math/polysat/interval.h
@@ -115,6 +115,27 @@ namespace polysat {
                 return true;
             return false;
         }
+
+        eval_interval intersect(eval_interval const& other) const {
+            if (is_full()) return other;
+            if (other.is_full()) return *this;
+
+            pdd i_lo = lo();
+            rational i_lo_val = lo_val();
+            if (lo_val() < other.lo_val()) {
+                i_lo = other.lo();
+                i_lo_val = other.lo_val();
+            }
+
+            pdd i_hi = hi();
+            rational i_hi_val = hi_val();
+            if (hi_val() > other.hi_val()) {
+                i_hi = other.hi();
+                i_hi_val = other.hi_val();
+            }
+
+            return eval_interval::proper(i_lo, i_lo_val, i_hi, i_hi_val);
+        }
     };
 
     inline std::ostream& operator<<(std::ostream& os, eval_interval const& i) {
diff --git a/src/math/polysat/solver.cpp b/src/math/polysat/solver.cpp
index 256f2c1f3..96deda234 100644
--- a/src/math/polysat/solver.cpp
+++ b/src/math/polysat/solver.cpp
@@ -1193,6 +1193,69 @@ namespace polysat {
         if (all_ok) LOG("All good!");
         return all_ok;
     }
+
+
+
+    // All variables of clause 'cl' except 'z' are assigned.
+    // Goal: a possibly weaker clause that implies a restriction on z around z_val
+    clause_ref solver::make_asserting(clause& cl, pvar z, rational z_val) {
+        signed_constraints cz;  // constraints of 'cl' that contain 'z'
+        sat::literal_vector lits;  // literals of the new clause
+        for (sat::literal lit : cl) {
+            signed_constraint c = lit2cnstr(lit);
+            if (c.contains_var(z))
+                cz.push_back(c);
+            else
+                lits.push_back(lit);
+        }
+        SASSERT(!cz.empty());
+        if (cz.size() == 1) {
+            // TODO: even in this case, if the constraint is non-linear in z, we might want to extract a maximal forbidden interval around z_val.
+            return nullptr;
+        }
+        else {
+            // multiple constraints that contain z
+            find_implied_constraint(cz, z, z_val, lits);
+            return clause::from_literals(std::move(lits));
+        }
+    }
+
+    // Each constraint in 'cz' is univariate in 'z' under the current assignment.
+    // Goal: a literal that is implied by the disjunction of cz and ensures z != z_val in viable.
+    //       (plus side conditions that do not depend on z)
+    void solver::find_implied_constraint(signed_constraints const& cz, pvar z, rational z_val, sat::literal_vector& out_lits)
+    {
+        unsigned const out_lits_original_size = out_lits.size();
+
+        forbidden_intervals fi(*this);
+        fi_record entry({ eval_interval::full(), {}, {}, rational::one()});
+
+        auto intersection = eval_interval::full();
+        bool all_unit = true;
+
+        for (signed_constraint const& c : cz) {
+            if (fi.get_interval(c, z, entry) && entry.coeff == 1) {
+                intersection = intersection.intersect(entry.interval);
+                for (auto const& sc : entry.side_cond)
+                    out_lits.push_back(sc.blit());
+            } else {
+                all_unit = false;
+                break;
+            }
+        }
+
+        if (all_unit) {
+            // Unit intervals from all constraints
+            // => build constraint from intersection of forbidden intervals
+            //    z \not\in [l;u[  <=>  z - l >= u - l
+            auto c_new = ule(intersection.hi() - intersection.lo(), z - intersection.lo());
+            out_lits.push_back(c_new.blit());
+            return;
+        } else {
+            out_lits.shrink(out_lits_original_size);
+            // TODO: SAT-based approach
+        }
+    }
 }
 
 
diff --git a/src/math/polysat/solver.h b/src/math/polysat/solver.h
index 5cec5a360..05f939067 100644
--- a/src/math/polysat/solver.h
+++ b/src/math/polysat/solver.h
@@ -234,6 +234,9 @@ namespace polysat {
         bool can_propagate();
         void propagate();
 
+        clause_ref make_asserting(clause& cl, pvar z, rational z_val);
+        void find_implied_constraint(signed_constraints const& cz, pvar z, rational z_val, sat::literal_vector& out_lits);
+
     public:
 
         /**