diff --git a/src/math/polysat/clause.h b/src/math/polysat/clause.h
index c440ebeb2..4e652873b 100644
--- a/src/math/polysat/clause.h
+++ b/src/math/polysat/clause.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
@@ -18,6 +18,7 @@ Author:
 namespace polysat {
 
     class signed_constraint;
+    class simplify_clause;
 
     class clause;
     using clause_ref = ref<clause>;
@@ -31,6 +32,7 @@ namespace polysat {
     //
     class clause {
         friend class constraint_manager;
+        friend class simplify_clause;
 
         unsigned m_ref_count = 0;  // TODO: remove refcount once we confirm it's not needed anymore
         bool m_redundant = true;
@@ -58,7 +60,6 @@ namespace polysat {
         static clause_ref from_unit(signed_constraint c);
         static clause_ref from_literals(sat::literal_vector literals);
 
-
         bool empty() const { return m_literals.empty(); }
         unsigned size() const { return m_literals.size(); }
         sat::literal operator[](unsigned idx) const { return m_literals[idx]; }
diff --git a/src/math/polysat/simplify_clause.cpp b/src/math/polysat/simplify_clause.cpp
index b8de97dae..7455bfcc1 100644
--- a/src/math/polysat/simplify_clause.cpp
+++ b/src/math/polysat/simplify_clause.cpp
@@ -23,7 +23,107 @@ namespace polysat {
 
     bool simplify_clause::apply(clause& cl)
     {
-        (void)s;
-        return false;
+        bool changed = false;
+        if (try_unilinear_subsumption(cl)) changed = true;
+        return changed;
     }
+
+    struct subs_entry : fi_record {
+        unsigned lit_idx;
+        pvar var;
+        bool subsumed;
+    };
+
+    /**
+     * Test simple subsumption between univariate and linear literals, i.e.,
+     * the case where both literals can be represented by a single contiguous forbidden interval.
+     *
+     * A literal C subsumes literal D if the forbidden interval of C is a subset of the forbidden interval of D.
+     * C subsumes D  <==  fi(C) subset fi(D)
+     */
+    bool simplify_clause::try_unilinear_subsumption(clause& cl)
+    {
+        LOG_H2("Unilinear subsumption for: " << cl);
+        subs_entry entry;
+        vector<subs_entry> entries;  // TODO: we don't need to store the full fi_record
+        forbidden_intervals fi(s);
+        // Find univariate and linear constraints and their forbidden intervals
+        for (unsigned i = 0; i < cl.size(); ++i) {
+            sat::literal lit = cl[i];
+            signed_constraint c = s.lit2cnstr(lit);
+            if (!c->is_ule())
+                continue;
+            auto const& ule = c->to_ule();
+            pdd const& lhs = ule.lhs();
+            pdd const& rhs = ule.rhs();
+            if (!lhs.is_val() && !lhs.is_unilinear())
+                continue;
+            if (!rhs.is_val() && !rhs.is_unilinear())
+                continue;
+            if (!lhs.is_val() && !rhs.is_val() && lhs.var() != rhs.var())
+                continue;
+            LOG("Literal " << lit_pp(s, lit));
+            SASSERT(!lhs.is_val() || !rhs.is_val());  // purely numeric constraints should have been filtered out by the clause_builder
+            pvar v = rhs.is_val() ? lhs.var() : rhs.var();
+            VERIFY(fi.get_interval(c, v, entry));
+            if (entry.coeff != 1)
+                continue;
+            entry.lit_idx = i;
+            entry.var = v;
+            entry.subsumed = false;
+            entries.push_back(entry);
+        }
+        // Check subsumption between intervals for the same variable
+        bool any_subsumed = false;
+        for (unsigned i = 0; i < entries.size(); ++i) {
+            subs_entry& e = entries[i];
+            if (e.subsumed)
+                continue;
+            for (unsigned j = i + 1; j < entries.size(); ++j) {
+                subs_entry& f = entries[j];
+                SASSERT(e.lit_idx != f.lit_idx);
+                if (e.var != f.var)
+                    continue;
+                if (e.interval.currently_contains(f.interval)) {
+                    // f subset of e  ==>  f.src subsumes e.src
+                    LOG("Literal " << cl[e.lit_idx] << " subsumed by " << cl[f.lit_idx]);
+                    e.subsumed = true;
+                    any_subsumed = true;
+                    break;
+                }
+                if (f.interval.currently_contains(e.interval)) {
+                    // e subset of f  ==>  e.src subsumes f.src
+                    LOG("Literal " << cl[f.lit_idx] << " subsumed by " << cl[e.lit_idx]);
+                    f.subsumed = true;
+                    any_subsumed = true;
+                    continue;
+                }
+            }
+        }
+        // Remove subsumed literals
+        if (!any_subsumed)
+            return false;
+        auto e_it = entries.begin();
+        while (e_it != entries.end() && !e_it->subsumed)
+            ++e_it;
+        SASSERT(e_it != entries.end() && e_it->subsumed);
+        unsigned next_subsumed_i = e_it->lit_idx;
+        unsigned i = next_subsumed_i;
+        unsigned j = next_subsumed_i;
+        while (i < cl.size()) {
+            if (i == next_subsumed_i) {
+                while (e_it != entries.end() && !e_it->subsumed)
+                    ++e_it;
+                if (e_it != entries.end())
+                    next_subsumed_i = e_it->lit_idx;
+                // NOTE: no need to update next_subsumed_i in the else-branch since we already passed that location
+                i++;
+            }
+            else
+                cl[j++] = cl[i++];
+        }
+        cl.m_literals.shrink(j);
+        return true;
+    }
+
 }
diff --git a/src/math/polysat/simplify_clause.h b/src/math/polysat/simplify_clause.h
index 4b60399a2..e93e24ef3 100644
--- a/src/math/polysat/simplify_clause.h
+++ b/src/math/polysat/simplify_clause.h
@@ -20,6 +20,8 @@ namespace polysat {
     class simplify_clause {
         solver& s;
 
+        bool try_unilinear_subsumption(clause& cl);
+
     public:
         simplify_clause(solver& s);