diff --git a/src/ast/ast.h b/src/ast/ast.h
index 512501226..511c2cee0 100644
--- a/src/ast/ast.h
+++ b/src/ast/ast.h
@@ -731,6 +731,8 @@ public:
     unsigned get_num_args() const { return m_num_args; }
     expr * get_arg(unsigned idx) const { SASSERT(idx < m_num_args); return m_args[idx]; }
     expr * const * get_args() const { return m_args; }
+    std::tuple<expr*,expr*> args2() const { SASSERT(m_num_args == 2); return {get_arg(0), get_arg(1)}; }
+    std::tuple<expr*,expr*,expr*> args3() const { SASSERT(m_num_args == 3); return {get_arg(0), get_arg(1), get_arg(2)}; }
     unsigned get_size() const { return get_obj_size(get_num_args()); }
     expr * const * begin() const { return m_args; }
     expr * const * end() const { return m_args + m_num_args; }
diff --git a/src/cmd_context/extra_cmds/proof_cmds.cpp b/src/cmd_context/extra_cmds/proof_cmds.cpp
index 03cb3f95c..e429358fa 100644
--- a/src/cmd_context/extra_cmds/proof_cmds.cpp
+++ b/src/cmd_context/extra_cmds/proof_cmds.cpp
@@ -181,6 +181,141 @@ public:
 
 };
 
+namespace sat {
+    /**
+     * Replay proof entierly, then walk backwards extracting reduced proof.
+     */
+    class proof_trim {
+        cmd_context& ctx;
+        ast_manager& m;
+        solver s;
+        literal_vector m_clause;
+        struct hash {
+            unsigned operator()(literal_vector const& v) const {
+                return string_hash((char const*)v.begin(), v.size()*sizeof(literal), 3);
+            }
+        };
+        struct eq {
+            bool operator()(literal_vector const& a, literal_vector const& b) const {
+                return a == b;
+            }
+        };
+        map<literal_vector, clause_vector, hash, eq> m_clauses;
+        
+        void mk_clause(expr_ref_vector const& clause) {
+            m_clause.reset();
+            for (expr* arg: clause)
+                add_literal(arg);
+            std::sort(m_clause.begin(), m_clause.end());
+        }
+        
+        bool_var mk_var(expr* arg) {
+            while (arg->get_id() >= s.num_vars())
+                s.mk_var(true, true);
+            return arg->get_id();
+        }
+        
+        void add_literal(expr* arg) {
+            bool sign = m.is_not(arg, arg);
+            m_clause.push_back(literal(mk_var(arg), sign));
+        }
+
+
+        /**
+           Pseudo-code from Gurfinkel, Vizel, FMCAD 2014
+           Input: trail (a0,d0), ..., (an,dn) = ({},bot)
+           Output: reduced trail - result 
+           result = []
+           C = an
+           for i = n to 0 do
+               if s.is_deleted(ai) then s.revive(ai)
+               else 
+                  if s.isontrail(ai) then
+                     s.undotrailcore(ai,C)
+                  s.delete(ai)
+                  if ai in C then 
+                      if ai is not initial then
+                         s.savetrail()
+                         s.enqueue(not ai)
+                         c = s.propagate()
+                         s.conflictanalysiscore(c, C)
+                         s.restoretrail()
+                       result += [ai]
+            reverse(result)
+            
+            is_deleted(ai):
+               clause was detached
+            revive(ai):
+               attach clause ai
+            isontrail(ai):
+                some literal on the current trail in s is justified by ai
+            undotrailcore(ai, C):
+                pop the trail until dependencies on ai are gone
+            savetrail:
+                store current trail so it can be restored
+            enqueue(not ai):
+                assert negations of ai at a new decision level
+            conflictanalysiscore(c, C):
+                ?
+            restoretrail:
+                restore the trail to the position before enqueue
+                
+                                               
+            
+        */        
+        void trim() {
+            
+        }
+        
+    public:
+        proof_trim(cmd_context& ctx):
+            ctx(ctx),
+            m(ctx.m()),
+            s(gparams::get_module("sat"), m.limit()) {
+            
+        }
+        
+        void assume(expr_ref_vector const& _clause) {        
+            mk_clause(_clause);
+            IF_VERBOSE(3, verbose_stream() << "add: " << m_clause << "\n");
+            auto* cl = s.mk_clause(m_clause, status::redundant());
+            s.propagate(false);            
+            if (!cl)
+                return;
+            IF_VERBOSE(3, verbose_stream() << "add: " << *cl << "\n");
+            auto& v = m_clauses.insert_if_not_there(m_clause, clause_vector());            
+            v.push_back(cl);
+        }
+        
+        void del(expr_ref_vector const& _clause) {
+            mk_clause(_clause);
+            IF_VERBOSE(3, verbose_stream() << "del: " << m_clause << "\n");
+            if (m_clause.size() == 2) {
+                s.detach_bin_clause(m_clause[0], m_clause[1], true);
+                return;
+            }
+            auto* e = m_clauses.find_core(m_clause);
+            if (!e)
+                return;
+            auto& v = e->get_data().m_value;            
+            if (!v.empty()) {
+                IF_VERBOSE(3, verbose_stream() << "del: " << *v.back() << "\n");
+                s.detach_clause(*v.back());
+                v.pop_back();
+            }
+        }
+        
+        void infer(expr_ref_vector const& _clause, app*) {
+            assume(_clause);
+        }
+
+        void updt_params(params_ref const& p) {
+            s.updt_params(p);
+        }
+
+    };
+}
+
 
 class proof_saver {
     cmd_context& ctx;
@@ -218,10 +353,11 @@ class proof_cmds_imp : public proof_cmds {
     bool            m_trim   = false;
     scoped_ptr<smt_checker>     m_checker;
     scoped_ptr<proof_saver>     m_saver;
+    scoped_ptr<sat::proof_trim>      m_trimmer;
     
     smt_checker& checker() { if (!m_checker) m_checker = alloc(smt_checker, m); return *m_checker; }
     proof_saver& saver() { if (!m_saver) m_saver = alloc(proof_saver, ctx); return *m_saver; }
-
+    sat::proof_trim& trim() { if (!m_trimmer) m_trimmer = alloc(sat::proof_trim, ctx); return *m_trimmer; }
     
 public:
     proof_cmds_imp(cmd_context& ctx): ctx(ctx), m(ctx.m()), m_lits(m), m_proof_hint(m) {
@@ -240,6 +376,8 @@ public:
             checker().assume(m_lits);
         if (m_save)
             saver().assume(m_lits);
+        if (m_trim)
+            trim().assume(m_lits);
         m_lits.reset();
         m_proof_hint.reset();
     }
@@ -249,6 +387,8 @@ public:
             checker().check(m_lits, m_proof_hint);
         if (m_save)
             saver().infer(m_lits, m_proof_hint);
+        if (m_trim)
+            trim().infer(m_lits, m_proof_hint);
         m_lits.reset();
         m_proof_hint.reset();
     }
@@ -258,6 +398,8 @@ public:
             checker().del(m_lits);
         if (m_save)
             saver().del(m_lits);
+        if (m_trim)
+            trim().del(m_lits);
         m_lits.reset();
         m_proof_hint.reset();
     }
@@ -266,6 +408,9 @@ public:
         solver_params sp(p);
         m_check = sp.proof_check();
         m_save  = sp.proof_save();        
+        m_trim  = sp.proof_trim();
+        if (m_trim)
+            trim().updt_params(p);
     }
 };
 
diff --git a/src/params/solver_params.pyg b/src/params/solver_params.pyg
index 6e33ca6d7..9ff13864d 100644
--- a/src/params/solver_params.pyg
+++ b/src/params/solver_params.pyg
@@ -10,5 +10,6 @@ def_module_params('solver',
                           ('axioms2files', BOOL, False, 'print negated theory axioms to separate files during search'),
                           ('proof.check', BOOL, True, 'check proof logs'),
                           ('proof.save', BOOL, False, 'save proof log into a proof object that can be extracted using (get-proof)'),
+                          ('proof.trim', BOOL, False, 'trim and save proof into a proof object that an be extracted using (get-proof)'),			  
                           ))
                 
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index 0b01b777c..5c413ce09 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -235,6 +235,7 @@ namespace sat {
         friend class aig_finder;
         friend class lut_finder;
         friend class npn3_finder;
+        friend class proof_trim;
     public:
         solver(params_ref const & p, reslimit& l);
         ~solver() override;
diff --git a/src/sat/smt/arith_axioms.cpp b/src/sat/smt/arith_axioms.cpp
index 2b02015e0..93917042e 100644
--- a/src/sat/smt/arith_axioms.cpp
+++ b/src/sat/smt/arith_axioms.cpp
@@ -424,7 +424,7 @@ namespace arith {
         ++m_stats.m_assert_diseq;  
         add_farkas_clause(~eq, le);
         add_farkas_clause(~eq, ge);
-        add_clause(~le, ~ge, eq, explain_triangle_eq(le, ge, eq));
+        add_clause(~le, ~ge, eq, explain_trichotomy(le, ge, eq));
     }
 
 
diff --git a/src/sat/smt/arith_diagnostics.cpp b/src/sat/smt/arith_diagnostics.cpp
index cba691319..ec9b11e76 100644
--- a/src/sat/smt/arith_diagnostics.cpp
+++ b/src/sat/smt/arith_diagnostics.cpp
@@ -129,14 +129,16 @@ namespace arith {
             return nullptr;
         m_arith_hint.set_type(ctx, hint_type::implied_eq_h);
         explain_assumptions();
+        m_arith_hint.set_num_le(1); // TODO
         m_arith_hint.add_diseq(a, b);
         return m_arith_hint.mk(ctx);
     }
 
-    arith_proof_hint const* solver::explain_triangle_eq(sat::literal le, sat::literal ge, sat::literal eq) {
+    arith_proof_hint const* solver::explain_trichotomy(sat::literal le, sat::literal ge, sat::literal eq) {
         if (!ctx.use_drat())
             return nullptr;
         m_arith_hint.set_type(ctx, hint_type::implied_eq_h);
+        m_arith_hint.set_num_le(1);
         m_arith_hint.add_lit(rational(1), le);
         m_arith_hint.add_lit(rational(1), ge);
         m_arith_hint.add_lit(rational(1), ~eq);
@@ -149,6 +151,9 @@ namespace arith {
         arith_util arith(m);
         solver& a = dynamic_cast<solver&>(*s.fid2solver(fid));
         char const* name;
+        expr_ref_vector args(m);
+        sort_ref_vector sorts(m);
+
         switch (m_ty) {
         case hint_type::farkas_h:
             name = "farkas";
@@ -158,15 +163,14 @@ namespace arith {
             break;
         case hint_type::implied_eq_h:
             name = "implied-eq";
+            args.push_back(arith.mk_int(m_num_le));
             break;
         }
         rational lc(1);
         for (unsigned i = m_lit_head; i < m_lit_tail; ++i) 
             lc = lcm(lc, denominator(a.m_arith_hint.lit(i).first));
-            
-        expr_ref_vector args(m);
-        sort_ref_vector sorts(m);
-        for (unsigned i = m_lit_head; i < m_lit_tail; ++i) {            
+
+        for (unsigned i = m_lit_head; i < m_lit_tail; ++i) {
             auto const& [coeff, lit] = a.m_arith_hint.lit(i);
             args.push_back(arith.mk_int(abs(coeff*lc)));
             args.push_back(s.literal2expr(lit));
diff --git a/src/sat/smt/arith_proof_checker.h b/src/sat/smt/arith_proof_checker.h
index 56e4cf1f8..df1dc00f1 100644
--- a/src/sat/smt/arith_proof_checker.h
+++ b/src/sat/smt/arith_proof_checker.h
@@ -18,7 +18,7 @@ Notes:
 The module assumes a limited repertoire of arithmetic proof rules.
 
 - farkas - inequalities, equalities and disequalities with coefficients
-- implied-eq - last literal is a disequality. The literals before imply the corresponding equality.
+- implied-eq - last literal is a disequality. The literals before imply the complementary equality.
 - bound - last literal is a bound. It is implied by prior literals.
 
 --*/
@@ -26,8 +26,10 @@ The module assumes a limited repertoire of arithmetic proof rules.
 
 #include "util/obj_pair_set.h"
 #include "ast/ast_trail.h"
+#include "ast/ast_util.h"
 #include "ast/arith_decl_plugin.h"
 #include "sat/smt/euf_proof_checker.h"
+#include <iostream>
 
 
 namespace arith {
@@ -49,8 +51,6 @@ namespace arith {
         row          m_ineq;
         row          m_conseq;
         vector<row>  m_eqs;
-        vector<row>  m_ineqs;
-        vector<row>  m_diseqs;
         symbol       m_farkas;
         symbol       m_implied_eq;
         symbol       m_bound;
@@ -261,26 +261,6 @@ namespace arith {
             return false;
         }
 
-        //
-        // checking disequalities is TBD.
-        // it has to select only a subset of bounds to justify each inequality.
-        // example
-        // c <= x <= c, c <= y <= c => x = y
-        // for the proof of x <= y use the inequalities x <= c <= y
-        // for the proof of y <= x use the inequalities y <= c <= x
-        // example
-        // x <= y, y <= z, z <= u, u <= x => x = z
-        // for the proof of x <= z use the inequalities x <= y, y <= z
-        // for the proof of z <= x use the inequalities z <= u, u <= x
-        // 
-        // so when m_diseqs is non-empty we can't just add inequalities with Farkas coefficients
-        // into m_ineq, since coefficients of the usable subset vanish.
-        // 
-
-        bool check_diseq() {
-            return false;
-        }
-
         std::ostream& display_row(std::ostream& out, row const& r) {
             bool first = true;
             for (auto const& [v, coeff] : r.m_coeffs) {
@@ -329,16 +309,11 @@ namespace arith {
             m_ineq.reset();
             m_conseq.reset();
             m_eqs.reset();
-            m_ineqs.reset();
-            m_diseqs.reset();
             m_strict = false;
         }
         
         bool add_ineq(rational const& coeff, expr* e, bool sign) {
-            if (!m_diseqs.empty())
-                return add_literal(fresh(m_ineqs), abs(coeff), e, sign);
-            else 
-                return add_literal(m_ineq, abs(coeff), e, sign);
+            return add_literal(m_ineq, abs(coeff), e, sign);
         }
         
         bool add_conseq(rational const& coeff, expr* e, bool sign) {
@@ -350,20 +325,12 @@ namespace arith {
             linearize(r, rational(1), a);
             linearize(r, rational(-1), b);
         }
-
-        void add_diseq(expr* a, expr* b) {
-            row& r = fresh(m_diseqs);
-            linearize(r, rational(1), a);
-            linearize(r, rational(-1), b);            
-        }
         
         bool check() {
-            if (!m_diseqs.empty())
-                return check_diseq();
-            else if (!m_conseq.m_coeffs.empty())
-                return check_bound();
-            else
+            if (m_conseq.m_coeffs.empty())
                 return check_farkas();
+            else
+                return check_bound();
         }
 
         std::ostream& display(std::ostream& out) {
@@ -375,14 +342,41 @@ namespace arith {
             return out;
         }
 
-        bool check(expr_ref_vector const& clause, app* jst, expr_ref_vector& units) override {
+        expr_ref_vector clause(app* jst) override {
+            expr_ref_vector result(m);
+            for (expr* arg : *jst) 
+                if (m.is_bool(arg))
+                    result.push_back(mk_not(m, arg));
+            return result;
+        }
+
+        /**
+           Add implied equality as an inequality
+         */
+        bool add_implied_ineq(bool sign, app* jst) {
+            unsigned n = jst->get_num_args();
+            if (n < 2)
+                return false;
+            expr* arg1 = jst->get_arg(n - 2);
+            expr* arg2 = jst->get_arg(n - 1);
+            rational coeff;
+            if (!a.is_numeral(arg1, coeff))
+                return false;
+            if (!m.is_not(arg2, arg2))
+                return false;
+            if (!m.is_eq(arg2, arg1, arg2))
+                return false;
+            if (!sign)
+                coeff.neg();
+            auto& r = m_ineq;
+            linearize(r, coeff, arg1);
+            linearize(r, -coeff, arg2);
+            m_strict = true;
+            return true;
+        }
+
+        bool check(app* jst) override {
             reset();
-            expr_mark pos, neg;
-            for (expr* e : clause)
-                if (m.is_not(e, e))
-                    neg.mark(e, true);
-                else
-                    pos.mark(e, true);
             bool is_bound = jst->get_name() == m_bound;
             bool is_implied_eq = jst->get_name() == m_implied_eq;
             bool is_farkas = jst->get_name() == m_farkas;
@@ -393,25 +387,51 @@ namespace arith {
             bool even = true;
             rational coeff;
             expr* x, * y;
-            unsigned j = 0;
+            unsigned j = 0, num_le = 0;
+
+            
             for (expr* arg : *jst) {
                 if (even) {
                     if (!a.is_numeral(arg, coeff)) {
                         IF_VERBOSE(0, verbose_stream() << "not numeral " << mk_pp(jst, m) << "\n");
                         return false;
                     }
+                    if (is_implied_eq) {
+                        is_implied_eq = false;
+                        if (!coeff.is_unsigned()) {
+                            IF_VERBOSE(0, verbose_stream() << "not unsigned " << mk_pp(jst, m) << "\n");
+                            return false;
+                        }
+                        num_le = coeff.get_unsigned();
+                        if (!add_implied_ineq(false, jst))
+                            return false;
+                        ++j;
+                        continue;
+                    }
                 }
                 else {
                     bool sign = m.is_not(arg, arg);
                     if (a.is_le(arg) || a.is_lt(arg) || a.is_ge(arg) || a.is_gt(arg)) {
                         if (is_bound && j + 1 == jst->get_num_args())
                             add_conseq(coeff, arg, sign);
+                        else if (num_le > 0) {
+                            add_ineq(coeff, arg, sign);
+                            --num_le;
+                            if (num_le == 0) {
+                                // we processed all the first inequalities,
+                                // check that they imply one half of the implied equality.
+                                if (!check())
+                                    return false;
+                                reset();
+                                VERIFY(add_implied_ineq(true, jst));
+                            }
+                        }
                         else
                             add_ineq(coeff, arg, sign);
                     }
                     else if (m.is_eq(arg, x, y)) {
-                        if (sign)
-                            add_diseq(x, y);
+                        if (sign) 
+                            return check(); // it should be an implied equality
                         else
                             add_eq(x, y);
                     }
@@ -419,23 +439,11 @@ namespace arith {
                         IF_VERBOSE(0, verbose_stream() << "not a recognized arithmetical relation " << mk_pp(arg, m) << "\n");
                         return false;
                     }
-
-                    if (sign && !pos.is_marked(arg)) {
-                        units.push_back(m.mk_not(arg));
-                        pos.mark(arg, false);
-                    }
-                    else if (!sign && !neg.is_marked(arg)) {
-                        units.push_back(arg);
-                        neg.mark(arg, false);
-                    }
                 }
                 even = !even;
                 ++j;
             }
-            if (check()) 
-                return true;
-            
-            return false;
+            return check();
         }
 
         void register_plugins(euf::proof_checker& pc) override {
diff --git a/src/sat/smt/arith_solver.h b/src/sat/smt/arith_solver.h
index 2142874d5..4fdb57386 100644
--- a/src/sat/smt/arith_solver.h
+++ b/src/sat/smt/arith_solver.h
@@ -51,14 +51,15 @@ namespace arith {
     enum class hint_type {
         farkas_h,
         bound_h,
-        implied_eq_h    
+        implied_eq_h
     };
 
     struct arith_proof_hint : public euf::th_proof_hint {
-        hint_type                              m_ty;
-        unsigned m_lit_head, m_lit_tail, m_eq_head, m_eq_tail;
-        arith_proof_hint(hint_type t, unsigned lh, unsigned lt, unsigned eh, unsigned et):
-            m_ty(t), m_lit_head(lh), m_lit_tail(lt), m_eq_head(eh), m_eq_tail(et) {}
+        hint_type m_ty;
+        unsigned  m_num_le;
+        unsigned  m_lit_head, m_lit_tail, m_eq_head, m_eq_tail;
+        arith_proof_hint(hint_type t, unsigned num_le, unsigned lh, unsigned lt, unsigned eh, unsigned et):
+            m_ty(t), m_num_le(num_le), m_lit_head(lh), m_lit_tail(lt), m_eq_head(eh), m_eq_tail(et) {}
         expr* get_hint(euf::solver& s) const override;
     };
 
@@ -66,6 +67,7 @@ namespace arith {
         vector<std::pair<rational, literal>>   m_literals;
         svector<std::tuple<euf::enode*,euf::enode*,bool>> m_eqs;
         hint_type                              m_ty;
+        unsigned                               m_num_le = 0;
         unsigned                               m_lit_head = 0, m_lit_tail = 0, m_eq_head = 0, m_eq_tail = 0;
         void reset() { m_lit_head = m_lit_tail; m_eq_head = m_eq_tail; }
         void add(euf::enode* a, euf::enode* b, bool is_eq) {
@@ -82,6 +84,7 @@ namespace arith {
             m_ty = ty; 
             reset(); 
         }
+        void set_num_le(unsigned n) { m_num_le = n; }
         void add_eq(euf::enode* a, euf::enode* b) { add(a, b, true); }
         void add_diseq(euf::enode* a, euf::enode* b) { add(a, b, false); }
         void add_lit(rational const& coeff, literal lit) { 
@@ -94,7 +97,7 @@ namespace arith {
         std::pair<rational, literal> const& lit(unsigned i) const { return m_literals[i]; }
         std::tuple<enode*, enode*, bool> const& eq(unsigned i) const { return m_eqs[i]; }
         arith_proof_hint* mk(euf::solver& s) { 
-            return new (s.get_region()) arith_proof_hint(m_ty, m_lit_head, m_lit_tail, m_eq_head, m_eq_tail);
+            return new (s.get_region()) arith_proof_hint(m_ty, m_num_le, m_lit_head, m_lit_tail, m_eq_head, m_eq_tail);
         }
     };
 
@@ -474,7 +477,7 @@ namespace arith {
 
         arith_proof_hint const* explain(hint_type ty, sat::literal lit = sat::null_literal);
         arith_proof_hint const* explain_implied_eq(euf::enode* a, euf::enode* b);
-        arith_proof_hint const* explain_triangle_eq(sat::literal le, sat::literal ge, sat::literal eq);
+        arith_proof_hint const* explain_trichotomy(sat::literal le, sat::literal ge, sat::literal eq);
         void explain_assumptions();
 
 
diff --git a/src/sat/smt/euf_proof_checker.cpp b/src/sat/smt/euf_proof_checker.cpp
index d0a4e4ab1..4774e154f 100644
--- a/src/sat/smt/euf_proof_checker.cpp
+++ b/src/sat/smt/euf_proof_checker.cpp
@@ -17,6 +17,7 @@ Author:
 
 #include "util/union_find.h"
 #include "ast/ast_pp.h"
+#include "ast/ast_util.h"
 #include "ast/ast_ll_pp.h"
 #include "sat/smt/euf_proof_checker.h"
 #include "sat/smt/arith_proof_checker.h"
@@ -120,24 +121,23 @@ namespace euf {
 
         ~eq_proof_checker() override {}
 
-        bool check(expr_ref_vector const& clause, app* jst, expr_ref_vector& units) override {
-            IF_VERBOSE(10, verbose_stream() << clause << "\n" << mk_pp(jst, m) << "\n");
+        expr_ref_vector clause(app* jst) override {
+            expr_ref_vector result(m);
+            for (expr* arg : *jst) 
+                if (m.is_bool(arg)) 
+                    result.push_back(mk_not(m, arg));
+            return result;
+        }
+
+        bool check(app* jst) override {
+            IF_VERBOSE(10, verbose_stream() << mk_pp(jst, m) << "\n");
             reset();
-            expr_mark pos, neg;
-            expr* x, *y;
-            for (expr* e : clause)
-                if (m.is_not(e, e))
-                    neg.mark(e, true);
-                else
-                    pos.mark(e, true);
 
             for (expr* arg : *jst) {
-                if (m.is_bool(arg)) { 
-                    bool sign = m.is_not(arg, arg);
-                    if (sign && !pos.is_marked(arg))
-                        units.push_back(m.mk_not(arg));
-                    else if (!sign & !neg.is_marked(arg))
-                        units.push_back(arg);
+                expr* x, *y;
+                bool sign = m.is_not(arg, arg);
+
+                if (m.is_bool(arg)) {
                     if (m.is_eq(arg, x, y)) {
                         if (sign)
                             m_diseqs.push_back({x, y});
@@ -198,38 +198,144 @@ namespace euf {
         void register_plugins(proof_checker& pc) override {
             pc.register_plugin(symbol("euf"), this);
         }
+    };
 
+    /**
+       A resolution proof term is of the form
+       (res pivot proof1 proof2)
+       The pivot occurs with opposite signs in proof1 and proof2
+     */
+
+    class res_proof_checker : public proof_checker_plugin {
+        ast_manager&   m;
+        proof_checker& pc;
+
+    public:
+        res_proof_checker(ast_manager& m, proof_checker& pc): m(m), pc(pc) {}
+        
+        ~res_proof_checker() override {}
+
+        bool check(app* jst) override {
+            if (jst->get_num_args() != 3)
+                return false;
+            auto [pivot, proof1, proof2] = jst->args3();
+            if (!m.is_bool(pivot) || !m.is_proof(proof1) || !m.is_proof(proof2))
+                return false;
+            expr* narg;
+            bool found1 = false, found2 = false, found3 = false, found4 = false;
+            for (expr* arg : pc.clause(proof1)) {
+                found1 |= arg == pivot;
+                found2 |= m.is_not(arg, narg) && narg == pivot;
+            }
+            if (found1 == found2)
+                return false;
+            
+            for (expr* arg : pc.clause(proof2)) {
+                found3 |= arg == pivot;
+                found4 |= m.is_not(arg, narg) && narg == pivot;
+            }
+            if (found3 == found4)
+                return false;
+            if (found3 == found1)
+                return false;
+            return pc.check(proof1) && pc.check(proof2);            
+        }
+
+        expr_ref_vector clause(app* jst) override {
+            expr_ref_vector result(m);
+            auto [pivot, proof1, proof2] = jst->args3();
+            expr* narg;
+            auto is_pivot = [&](expr* arg) {
+                if (arg == pivot)
+                    return true;
+                return m.is_not(arg, narg) && narg == pivot;                
+            };
+            for (expr* arg : pc.clause(proof1))
+                if (!is_pivot(arg))
+                    result.push_back(arg);
+            for (expr* arg : pc.clause(proof2))
+                if (!is_pivot(arg))
+                    result.push_back(arg);            
+            return result;
+        }
+
+        void register_plugins(proof_checker& pc) override {
+            pc.register_plugin(symbol("res"), this);
+        }
     };
 
     proof_checker::proof_checker(ast_manager& m):
         m(m) {
-        arith::proof_checker* apc = alloc(arith::proof_checker, m);
-        eq_proof_checker* epc = alloc(eq_proof_checker, m);
-        m_plugins.push_back(apc);
-        m_plugins.push_back(epc);
-        apc->register_plugins(*this);
-        epc->register_plugins(*this);
+        add_plugin(alloc(arith::proof_checker, m));
+        add_plugin(alloc(eq_proof_checker, m));
+        add_plugin(alloc(res_proof_checker, m, *this));
     }
 
-    proof_checker::~proof_checker() {}
+    proof_checker::~proof_checker() {
+        for (auto& [k, v] : m_checked_clauses)
+            dealloc(v);
+    }
+
+    void proof_checker::add_plugin(proof_checker_plugin* p) {
+        m_plugins.push_back(p);
+        p->register_plugins(*this);
+    }
 
     void proof_checker::register_plugin(symbol const& rule, proof_checker_plugin* p) {
         m_map.insert(rule, p);
     }
 
-    bool proof_checker::check(expr_ref_vector const& clause, expr* e, expr_ref_vector& units) {
+    bool proof_checker::check(expr* e) {
+        if (m_checked_clauses.contains(e))
+            return true;
+        
         if (!e || !is_app(e))
             return false;
-        units.reset();
         app* a = to_app(e);
         proof_checker_plugin* p = nullptr;
         if (!m_map.find(a->get_decl()->get_name(), p))
             return false;
-        if (p->check(clause, a, units))
-            return true;
-        
-        std::cout << "(missed-hint " << mk_pp(e, m) << ")\n";
-        return false;
+        if (!p->check(a)) {
+            std::cout << "(missed-hint " << mk_pp(e, m) << ")\n";
+            return false;
+        }
+        return true;
+    }
+
+    expr_ref_vector proof_checker::clause(expr* e) {
+        expr_ref_vector* rr;
+        if (m_checked_clauses.find(e, rr))
+            return *rr;
+        SASSERT(is_app(e) && m_map.contains(to_app(e)->get_decl()->get_name()));
+        auto& r = m_map[to_app(e)->get_decl()->get_name()]->clause(to_app(e));
+        m_checked_clauses.insert(e, alloc(expr_ref_vector, r));
+        return r;
+    }
+
+    bool proof_checker::check(expr_ref_vector const& clause1, expr* e, expr_ref_vector & units) {
+        if (!check(e))
+            return false;
+        units.reset();
+        expr_mark literals;
+        auto clause2 = clause(e);
+
+        // check that all literals in clause1 are in clause2
+        for (expr* arg : clause2)
+            literals.mark(arg, true);
+        for (expr* arg : clause1)
+            if (!literals.is_marked(arg))
+                return false;
+
+        // extract negated units for literals in clause2 but not in clause1
+        // the literals should be rup
+        literals.reset();
+        for (expr* arg : clause1)
+            literals.mark(arg, true);
+        for (expr* arg : clause2)
+            if (!literals.is_marked(arg))
+                units.push_back(mk_not(m, arg));
+
+        return true;
     }
 
 }
diff --git a/src/sat/smt/euf_proof_checker.h b/src/sat/smt/euf_proof_checker.h
index 464d90559..023bfae48 100644
--- a/src/sat/smt/euf_proof_checker.h
+++ b/src/sat/smt/euf_proof_checker.h
@@ -27,18 +27,23 @@ namespace euf {
     class proof_checker_plugin {
     public:
         virtual ~proof_checker_plugin() {}
-        virtual bool check(expr_ref_vector const& clause, app* jst, expr_ref_vector& units) = 0;        
+        virtual bool check(app* jst) = 0;
+        virtual expr_ref_vector clause(app* jst) = 0;
         virtual void register_plugins(proof_checker& pc) = 0;
     };
 
     class proof_checker {
         ast_manager& m;
-        scoped_ptr_vector<proof_checker_plugin> m_plugins;
-        map<symbol, proof_checker_plugin*, symbol_hash_proc, symbol_eq_proc> m_map;
+        scoped_ptr_vector<proof_checker_plugin> m_plugins;                          // plugins of proof checkers
+        map<symbol, proof_checker_plugin*, symbol_hash_proc, symbol_eq_proc> m_map; // symbol table of proof checkers
+        obj_map<expr, expr_ref_vector*> m_checked_clauses;                          // cache of previously checked proofs and their clauses.
+        void add_plugin(proof_checker_plugin* p);
     public:
         proof_checker(ast_manager& m);
         ~proof_checker();
         void register_plugin(symbol const& rule, proof_checker_plugin*);
+        bool check(expr* jst);
+        expr_ref_vector clause(expr* jst);
         bool check(expr_ref_vector const& clause, expr* e, expr_ref_vector& units);
     };