diff --git a/src/ast/rewriter/seq_axioms.cpp b/src/ast/rewriter/seq_axioms.cpp
index bc3b6c66e..ab19a5586 100644
--- a/src/ast/rewriter/seq_axioms.cpp
+++ b/src/ast/rewriter/seq_axioms.cpp
@@ -1061,16 +1061,12 @@ namespace seq {
     // using iterative deepening can be re-used.
     //
     // create recursive relation 'ra' with properties:
-    // ra(s, p, t, r) <- s = "" && r = ""
-    // ra(s, p, t, r) <- s != "" && p = "" && r = t + s
-    // ra(s, p, t, r) <- s != "" && p + s' = s && t + r' = r && ra(s', p, t, r')
-    // ra(s, p, t, r) <- s = [s0] + s' && ~prefix(p, s) && r = [s0] + r' && ra(s', p, t, r')
+    // ra(i, j, s, p, t, r) <- len(s) = i && len(r) = j
+    // ra(i, j, s, p, t, r) <- len(s) > i = 0 && p = "" && r = t + s
+    // ra(i, j, s, p, t, r) <- len(s) > i && p != "" && s = extract(s, 0, i) + p + extract(s, i + len(p), len(s)) && r = extract(r, 0, i) + t + extract(r, i + len(p), len(r)) && ra(i + len(p), j + len(t), s, p, t, r)
+    // ra(i, s, p, t, r) <- ~prefix(p, extract(s, i, len(s)) && at(s,i) = at(r,j) && ra(i + 1, j + 1, s, p, t, r)
     // which amounts to:
     //
-    // s = "" -> r = ""
-    // p = "" -> r = t + s
-    // prefix(p, s) -> p + s' = s && t + r' = r && ra(s', p, t, r')
-    // else ->  s = [s0] + s' && r = [s0] + r' && ra(s', p, t, r')
     //
     // Then assert
     // ra(s, p, t, replace_all(s, p, t))
@@ -1085,16 +1081,23 @@ namespace seq {
         sort* domain[4] = { srt, srt, srt, srt };
         auto d = plugin.ensure_def(symbol("ra"), 4, domain, m.mk_bool_sort(), true);
         func_decl* ra = d.get_def()->get_decl();
+        sort* isrt = a.mk_int();
+        var_ref vi(m.mk_var(5, isrt), m);
+        var_ref vj(m.mk_var(4, isrt), m);
         var_ref vs(m.mk_var(3, srt), m);
         var_ref vp(m.mk_var(2, srt), m);
         var_ref vt(m.mk_var(1, srt), m);
         var_ref vr(m.mk_var(0, srt), m);
-        var* vars[4] = { vs, vp, vt, vr };
-        expr_ref test1(seq.str.mk_is_empty(vs), m);
-        expr_ref branch1(seq.str.mk_is_empty(vr), m);
-        expr_ref test2(seq.str.mk_is_empty(vp), m);
+        var* vars[6] = { vi, vj, vs, vp, vt, vr };
+        expr_ref len_s(seq.str.mk_length(vs), m);
+        expr_ref len_r(seq.str.mk_length(vr), m);
+        expr_ref test1(m.mk_eq(len_s, vi), m);
+        expr_ref branch1(m.mk_eq(len_r, vj), m);
+        expr_ref test2(m.mk_and(a.mk_gt(len_s, vi), m.mk_eq(vi, a.mk_int(0)), seq.str.mk_is_empty(vp)), m);
         expr_ref branch2(m.mk_eq(vr, seq.str.mk_concat(vt, vs)), m);
-        expr_ref test3(seq.str.mk_prefix(vp, vs), m);
+        NOT_IMPLEMENTED_YET();
+#if 0
+        expr_ref test3(, m);
         expr_ref s1(m_sk.mk_prefix_inv(vp, vs), m);
         expr_ref r1(m_sk.mk_prefix_inv(vp, vr), m);
         expr* args1[4] = { s1, vp, vt, r1 };
@@ -1116,6 +1119,7 @@ namespace seq {
         expr* args3[4] = { s, p, t, r };
         expr_ref lit(m.mk_app(ra, 4, args3), m);
         add_clause(lit);
+#endif
     }
 
     void axioms::replace_re_all_axiom(expr* e) {
diff --git a/src/sat/sat_solver.cpp b/src/sat/sat_solver.cpp
index 286038dea..0e72de37f 100644
--- a/src/sat/sat_solver.cpp
+++ b/src/sat/sat_solver.cpp
@@ -3009,7 +3009,7 @@ namespace sat {
         svector<double> logits(vars.size(), 0.0);
         double itau = m_config.m_reorder_itau;
         double lse = 0;
-        double mid = m_rand.max_value()/2;
+        double mid = (double)(m_rand.max_value()/2);
         double max = 0;
         for (double& f : logits) {
             f = itau * (m_rand() - mid)/mid;
diff --git a/src/sat/smt/CMakeLists.txt b/src/sat/smt/CMakeLists.txt
index dc7f73c93..3721963c8 100644
--- a/src/sat/smt/CMakeLists.txt
+++ b/src/sat/smt/CMakeLists.txt
@@ -21,7 +21,6 @@ z3_add_component(sat_smt
     euf_invariant.cpp
     euf_model.cpp
     euf_proof.cpp
-    euf_relevancy.cpp
     euf_solver.cpp
     fpa_solver.cpp
     pb_card.cpp
@@ -38,7 +37,6 @@ z3_add_component(sat_smt
     q_queue.cpp
     q_solver.cpp
     recfun_solver.cpp
-    sat_dual_solver.cpp
     sat_th.cpp
     smt_relevant.cpp
     user_solver.cpp
diff --git a/src/sat/smt/euf_internalize.cpp b/src/sat/smt/euf_internalize.cpp
index 68f2295a2..d42a5a353 100644
--- a/src/sat/smt/euf_internalize.cpp
+++ b/src/sat/smt/euf_internalize.cpp
@@ -183,8 +183,6 @@ namespace euf {
         m_egraph.set_bool_var(n, v);
         if (m.is_eq(e) || m.is_or(e) || m.is_and(e) || m.is_not(e))
             m_egraph.set_merge_enabled(n, false);
-        if (!si.is_bool_op(e))
-            track_relevancy(lit.var());
         if (s().value(lit) != l_undef) 
             m_egraph.set_value(n, s().value(lit));
         return lit;
@@ -396,7 +394,7 @@ namespace euf {
         // Remark: The inconsistency is not going to be detected if they are
         // not marked as shared.
 
-        for (auto p : euf::enode_th_vars(n)) 
+        for (auto const& p : euf::enode_th_vars(n)) 
             if (fid2solver(p.get_id())->is_shared(p.get_var()))
                 return true;
 
diff --git a/src/sat/smt/euf_relevancy.cpp b/src/sat/smt/euf_relevancy.cpp
deleted file mode 100644
index 07960c584..000000000
--- a/src/sat/smt/euf_relevancy.cpp
+++ /dev/null
@@ -1,208 +0,0 @@
-/*++
-Copyright (c) 2020 Microsoft Corporation
-
-Module Name:
-
-    euf_relevancy.cpp
-
-Abstract:
-
-    Features for relevancy tracking.
-    A reduced (minimal) implicant is extracted by running a dual solver.
-    Then the literals in the implicant are used as a basis for marking
-    subterms relevant.
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2020-09-22
-
---*/
-
-#include "sat/smt/euf_solver.h"
-
-namespace euf {
-
-    void solver::mark_relevant(sat::literal lit) {
-        if (m_relevancy.enabled()) {
-            m_relevancy.mark_relevant(lit);
-            return;
-        }
-        if (!relevancy_enabled())
-            return;
-        for (; m_auto_relevant_scopes > 0; --m_auto_relevant_scopes) 
-            m_auto_relevant_lim.push_back(m_auto_relevant.size());
-        expr* e = bool_var2expr(lit.var());
-        m_auto_relevant.push_back(e);
-    }
-    
-    void solver::pop_relevant(unsigned n) {
-        if (m_relevancy.enabled()) {
-            m_relevancy.pop(n);
-            return;
-        }
-        if (m_auto_relevant_scopes >= n) {
-            m_auto_relevant_scopes -= n;
-            return;
-        }
-        n -= m_auto_relevant_scopes;
-        m_auto_relevant_scopes = 0;
-        unsigned top = m_auto_relevant_lim.size() - n;
-        unsigned lim = m_auto_relevant_lim[top];
-        m_auto_relevant_lim.shrink(top);
-        m_auto_relevant.shrink(lim);        
-    }
-    
-    void solver::push_relevant() {
-        if (m_relevancy.enabled()) {
-            m_relevancy.push();
-            return;
-        }
-        ++m_auto_relevant_scopes;
-    }
-
-    bool solver::is_relevant(enode* n) const { 
-        if (m_relevancy.enabled())
-            return m_relevancy.is_relevant(n);
-        return m_relevant_expr_ids.get(n->get_expr_id(), true); 
-    }
-
-    bool solver::is_relevant(bool_var v) const {
-        if (m_relevancy.enabled())
-            return m_relevancy.is_relevant(v);
-        auto* e = bool_var2enode(v);
-        return !e || is_relevant(e);
-    }
-
-    void solver::ensure_dual_solver() {
-        if (m_relevancy.enabled())
-            return;
-        if (m_dual_solver)
-            return;
-        m_dual_solver = alloc(sat::dual_solver, s(), s().rlimit());
-        for (unsigned i = s().num_user_scopes(); i-- > 0; )
-            m_dual_solver->push();        
-    }
-
-    /**
-     * Add a root clause. Root clauses must all be satisfied by the 
-     * final assignment. If a clause is added above search level it
-     * is subject to removal on backtracking. These clauses are therefore
-     * not tracked.
-     */
-    void solver::add_root(unsigned n, sat::literal const* lits) {
-        if (m_relevancy.enabled()) {
-            m_relevancy.add_root(n, lits);
-            return;
-        }
-        if (!relevancy_enabled())
-            return;
-        ensure_dual_solver();
-        m_dual_solver->add_root(n, lits);
-    }
-
-    void solver::add_aux(unsigned n, sat::literal const* lits) {
-        if (m_relevancy.enabled()) {
-            m_relevancy.add_def(n, lits);
-            return;
-        }
-        if (!relevancy_enabled())
-            return;
-        ensure_dual_solver();
-        m_dual_solver->add_aux(n, lits);
-    }
-
-    void solver::track_relevancy(sat::bool_var v) {
-        if (m_relevancy.enabled())
-            return;
-        ensure_dual_solver();
-        m_dual_solver->track_relevancy(v);
-    }
-
-    bool solver::init_relevancy() {
-        if (m_relevancy.enabled())
-            return true;
-        m_relevant_expr_ids.reset();
-        if (!relevancy_enabled())
-            return true;
-        if (!m_dual_solver)
-            return true;
-        if (!(*m_dual_solver)())
-            return false;
-        init_relevant_expr_ids();
-        
-        for (auto lit : m_dual_solver->core()) 
-            push_relevant(lit.var());
-
-        relevant_subterms();
-
-        return true;
-    }
-
-    void solver::push_relevant(sat::bool_var v) {
-        SASSERT(!m_relevancy.enabled());
-        expr* e = m_bool_var2expr.get(v, nullptr);
-        if (e)
-            m_relevant_todo.push_back(e);
-    }
-
-    bool solver::is_propagated(sat::literal lit) {
-        SASSERT(!m_relevancy.enabled());        
-        return s().value(lit) == l_true && !s().get_justification(lit.var()).is_none();
-    }
-
-    void solver::init_relevant_expr_ids() {
-        SASSERT(!m_relevancy.enabled());
-        unsigned max_id = 0;
-        for (enode* n : m_egraph.nodes())
-            max_id = std::max(max_id, n->get_expr_id());
-        m_relevant_expr_ids.resize(max_id + 1, false);
-        m_relevant_todo.reset();
-        m_relevant_todo.append(m_auto_relevant);
-    }
-
-    void solver::relevant_subterms() {
-        SASSERT(!m_relevancy.enabled());
-        ptr_vector<expr>& todo = m_relevant_todo;
-        bool_vector& visited = m_relevant_visited;
-        for (unsigned i = 0; i < todo.size(); ++i) {
-            expr* e = todo[i];
-            if (visited.get(e->get_id(), false))
-                continue;
-            visited.setx(e->get_id(), true, false);
-            if (si.is_bool_op(e))
-                continue;
-            else
-                m_relevant_expr_ids.setx(e->get_id(), true, false);
-            if (!is_app(e))
-                continue;
-            expr* c = nullptr, *th = nullptr, *el = nullptr;
-            if (m.is_ite(e, c, th, el) && get_enode(c)) {
-                sat::literal lit = expr2literal(c);
-                todo.push_back(c);
-                switch (s().value(lit)) {
-                case l_true:
-                    todo.push_back(th);
-                    break;
-                case l_false:
-                    todo.push_back(el);
-                    break;
-                default:
-                    todo.push_back(th);
-                    todo.push_back(el);
-                    break;
-                }
-                continue;
-            }
-            for (expr* arg : *to_app(e))
-                todo.push_back(arg);
-        }
-
-        for (auto * e : todo)
-            visited[e->get_id()] = false;
-
-        TRACE("euf",
-            for (enode* n : m_egraph.nodes())
-                if (is_relevant(n))
-                    tout << "relevant " << n->get_expr_id() << " [r" << n->get_root_id() << "]: " << mk_bounded_pp(n->get_expr(), m) << "\n";);
-    }
-}
diff --git a/src/sat/smt/euf_solver.cpp b/src/sat/smt/euf_solver.cpp
index f6d6e73dd..79b86e9a9 100644
--- a/src/sat/smt/euf_solver.cpp
+++ b/src/sat/smt/euf_solver.cpp
@@ -479,9 +479,6 @@ namespace euf {
 
         if (unit_propagate())
             return sat::check_result::CR_CONTINUE;
-
-        if (!init_relevancy())
-            give_up = true;    
         
         unsigned num_nodes = m_egraph.num_nodes();
         auto apply_solver = [&](th_solver* e) {
@@ -546,9 +543,7 @@ namespace euf {
         for (auto* e : m_solvers)
             e->push();
         m_egraph.push();
-        if (m_dual_solver)
-            m_dual_solver->push();
-        push_relevant();
+        m_relevancy.push();
     }
 
     void solver::pop(unsigned n) {
@@ -558,7 +553,7 @@ namespace euf {
             e->pop(n);
         si.pop(n);
         m_egraph.pop(n);
-        pop_relevant(n);
+        m_relevancy.pop(n);
         scope const & sc = m_scopes[m_scopes.size() - n];
         for (unsigned i = m_var_trail.size(); i-- > sc.m_var_lim; ) {
             bool_var v = m_var_trail[i];
@@ -567,8 +562,6 @@ namespace euf {
         }
         m_var_trail.shrink(sc.m_var_lim);        
         m_scopes.shrink(m_scopes.size() - n);
-        if (m_dual_solver)
-            m_dual_solver->pop(n);
         SASSERT(m_egraph.num_scopes() == m_scopes.size());
         TRACE("euf_verbose", display(tout << "pop to: " << m_scopes.size() << "\n"););
     }
@@ -741,6 +734,13 @@ namespace euf {
         }
     }
 
+    bool solver::is_relevant(bool_var v) const {
+        if (m_relevancy.enabled())
+            return m_relevancy.is_relevant(v);
+        auto* e = bool_var2enode(v);
+        return !e || is_relevant(e);
+    }
+
     void solver::relevant_eh(euf::enode* n) {
         if (m_qsolver)
             m_qsolver->relevant_eh(n);
diff --git a/src/sat/smt/euf_solver.h b/src/sat/smt/euf_solver.h
index 12afc492f..77fce4a20 100644
--- a/src/sat/smt/euf_solver.h
+++ b/src/sat/smt/euf_solver.h
@@ -25,7 +25,6 @@ Author:
 #include "sat/sat_extension.h"
 #include "sat/smt/atom2bool_var.h"
 #include "sat/smt/sat_th.h"
-#include "sat/smt/sat_dual_solver.h"
 #include "sat/smt/euf_ackerman.h"
 #include "sat/smt/user_solver.h"
 #include "sat/smt/smt_relevant.h"
@@ -184,14 +183,11 @@ namespace euf {
         void init_drat();
 
         // relevancy
-        bool_vector m_relevant_expr_ids;
-        bool_vector m_relevant_visited;
-        ptr_vector<expr> m_relevant_todo;
-        void ensure_dual_solver();
-        bool init_relevancy();
-        void relevant_subterms();
-        void init_relevant_expr_ids();
-        void push_relevant(sat::bool_var v);
+        //bool_vector m_relevant_expr_ids;
+        //bool_vector m_relevant_visited;
+        //ptr_vector<expr> m_relevant_todo;
+        //void init_relevant_expr_ids();
+        //void push_relevant(sat::bool_var v);
         bool is_propagated(sat::literal lit);
         // invariant
         void check_eqc_bool_assignment() const;
@@ -376,29 +372,26 @@ namespace euf {
 
         // relevancy
         bool m_relevancy_enabled = true;
-        scoped_ptr<sat::dual_solver>  m_dual_solver;
         ptr_vector<expr>              m_auto_relevant;
         unsigned_vector               m_auto_relevant_lim;
         unsigned                      m_auto_relevant_scopes = 0;
 
         bool relevancy_enabled() const { return m_relevancy_enabled && get_config().m_relevancy_lvl > 0; }
         void disable_relevancy(expr* e) { IF_VERBOSE(0, verbose_stream() << "disabling relevancy " << mk_pp(e, m) << "\n"); m_relevancy_enabled = false;  }
-        void add_root(unsigned n, sat::literal const* lits);
+        void add_root(unsigned n, sat::literal const* lits) { m_relevancy.add_root(n, lits); }
         void add_root(sat::literal_vector const& lits) { add_root(lits.size(), lits.data()); }
         void add_root(sat::literal lit) { add_root(1, &lit); }
         void add_aux(sat::literal_vector const& lits) { add_aux(lits.size(), lits.data()); }
-        void add_aux(unsigned n, sat::literal const* lits);
+        void add_aux(unsigned n, sat::literal const* lits) { m_relevancy.add_def(n, lits); }
         void add_aux(sat::literal a) { sat::literal lits[1] = { a }; add_aux(1, lits); }
         void add_aux(sat::literal a, sat::literal b) { sat::literal lits[2] = {a, b}; add_aux(2, lits); } 
         void add_aux(sat::literal a, sat::literal b, sat::literal c) { sat::literal lits[3] = { a, b, c }; add_aux(3, lits); }
-        void track_relevancy(sat::bool_var v);
-        bool is_relevant(enode* n) const;
+        void mark_relevant(sat::literal lit) { m_relevancy.mark_relevant(lit); }
+        bool is_relevant(enode* n) const { return m_relevancy.is_relevant(n); }
         bool is_relevant(bool_var v) const;
         bool is_relevant(sat::literal lit) const { return is_relevant(lit.var()); }
-        void mark_relevant(sat::literal lit);
-        void pop_relevant(unsigned n);
-        void push_relevant();
         void relevant_eh(euf::enode* n);
+
         smt::relevancy& relevancy() { return m_relevancy; }
 
         // model construction
diff --git a/src/sat/smt/sat_dual_solver.cpp b/src/sat/smt/sat_dual_solver.cpp
deleted file mode 100644
index d4b93b90c..000000000
--- a/src/sat/smt/sat_dual_solver.cpp
+++ /dev/null
@@ -1,189 +0,0 @@
-/*++
-Copyright (c) 2020 Microsoft Corporation
-
-Module Name:
-
-    sat_dual_solver.cpp
-
-Abstract:
-
-    Solver for obtaining implicant.
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2020-08-25
-
---*/
-#include "sat/smt/sat_dual_solver.h"
-
-namespace sat {
-
-    dual_solver::dual_solver(solver& s, reslimit& l):
-        s(s),
-        m_solver(m_params, l)
-    {
-        SASSERT(!m_solver.get_config().m_drat);
-        m_solver.set_incremental(true);
-    }
-
-    void dual_solver::flush() {
-        while (m_num_scopes > 0) {
-            m_solver.user_push();
-            m_roots.push_scope();
-            m_tracked_vars.push_scope();
-            m_units.push_scope();
-            m_vars.push_scope();
-            --m_num_scopes;
-        }
-    }
-
-    void dual_solver::push() {
-        ++m_num_scopes;
-    }
-
-    void dual_solver::pop(unsigned num_scopes) {        
-        if (m_num_scopes >= num_scopes) {
-            m_num_scopes -= num_scopes;
-            return;
-        }
-        num_scopes -= m_num_scopes;
-        m_num_scopes = 0;
-        m_solver.user_pop(num_scopes);
-        unsigned old_sz = m_tracked_vars.old_size(num_scopes);
-        for (unsigned i = m_tracked_vars.size(); i-- > old_sz; )
-            m_is_tracked[m_tracked_vars[i]] = false; 
-        old_sz = m_vars.old_size(num_scopes);
-        for (unsigned i = m_vars.size(); i-- > old_sz; ) {
-            unsigned v = m_vars[i];
-            unsigned w = m_ext2var[v];
-            m_ext2var[v] = null_bool_var;
-            m_var2ext[w] = null_bool_var;
-        }
-        m_vars.pop_scope(num_scopes);
-        m_units.pop_scope(num_scopes);
-        m_roots.pop_scope(num_scopes);
-        m_tracked_vars.pop_scope(num_scopes);
-    }
-
-    bool_var dual_solver::ext2var(bool_var v) {
-        bool_var w = m_ext2var.get(v, null_bool_var);
-        if (null_bool_var == w) {
-            w = m_solver.mk_var();
-            m_solver.set_external(w);
-            s.set_external(v);
-            m_ext2var.setx(v, w, null_bool_var);
-            m_var2ext.setx(w, v, null_bool_var);
-            m_vars.push_back(v);
-        }
-        return w;
-    }
-
-    void dual_solver::track_relevancy(bool_var w) {
-        flush();
-        bool_var v = ext2var(w);
-        if (!m_is_tracked.get(v, false)) {
-            m_is_tracked.setx(v, true, false);
-            m_tracked_vars.push_back(v);
-        }
-    }
-
-    literal dual_solver::ext2lit(literal lit) {
-        return literal(ext2var(lit.var()), lit.sign());
-    }
-
-    literal dual_solver::lit2ext(literal lit) {
-        return literal(m_var2ext[lit.var()], lit.sign());
-    }
-
-    void dual_solver::add_root(unsigned sz, literal const* clause) {      
-        flush();
-        if (false && sz == 1) {
-            TRACE("dual", tout << "unit: " << clause[0] << "\n";);
-            m_units.push_back(clause[0]);
-            return;
-        }
-        literal root;
-        if (sz == 1) 
-            root = ext2lit(clause[0]);
-        else {
-            root = literal(m_solver.mk_var(), false);
-            for (unsigned i = 0; i < sz; ++i)
-                m_solver.mk_clause(root, ~ext2lit(clause[i]), status::input());
-        }        
-        m_solver.set_external(root.var());
-        m_roots.push_back(~root);
-        TRACE("dual", tout << "root: " << ~root << " => " << literal_vector(sz, clause) << "\n";);
-    }
-
-    void dual_solver::add_aux(unsigned sz, literal const* clause) {
-        flush();        
-        m_lits.reset();
-        for (unsigned i = 0; i < sz; ++i) 
-            m_lits.push_back(ext2lit(clause[i]));
-        TRACE("dual", tout << "aux: " << literal_vector(sz, clause) << " -> " << m_lits << "\n";);
-        m_solver.mk_clause(sz, m_lits.data(), status::input());
-    }
-
-    void dual_solver::add_assumptions() {
-        flush();
-        m_lits.reset();
-        for (bool_var v : m_tracked_vars)
-            m_lits.push_back(literal(v, l_false == s.value(m_var2ext[v])));
-        for (auto lit : m_units) {
-            bool_var w = m_ext2var.get(lit.var(), null_bool_var);
-            if (w != null_bool_var)
-                m_lits.push_back(ext2lit(lit));            
-        }
-    }
-
-    bool dual_solver::operator()() {        
-        m_core.reset();
-        m_core.append(m_units);
-        if (m_roots.empty())
-            return true;
-        m_solver.user_push();
-        m_solver.add_clause(m_roots.size(), m_roots.data(), status::input());
-        add_assumptions();
-        lbool is_sat = m_solver.check(m_lits.size(), m_lits.data());
-        if (is_sat == l_false) 
-            for (literal lit : m_solver.get_core())
-                m_core.push_back(lit2ext(lit));        
-        if (is_sat == l_true) {
-            TRACE("dual", display(tout); s.display(tout););
-            IF_VERBOSE(0, verbose_stream() << "unexpected SAT\n");
-            IF_VERBOSE(0, verbose_stream() << "assumptions: " << m_lits << "\n");
-            IF_VERBOSE(0, display(verbose_stream()); s.display(verbose_stream()););
-            UNREACHABLE();
-            return false;
-        }
-        TRACE("dual", m_solver.display(tout << "is-sat: " << is_sat << " core: " << m_core << "\n"););
-        m_solver.user_pop(1);
-        return is_sat == l_false;
-    }
-
-    std::ostream& dual_solver::display(std::ostream& out) const {        
-        for (unsigned v = 0; v < m_solver.num_vars(); ++v) {
-            bool_var w = m_var2ext.get(v, null_bool_var);
-            if (w == null_bool_var)
-                continue;
-            lbool v1 = m_solver.value(v);
-            lbool v2 = s.value(w);
-            if (v1 == v2 || v2 == l_undef)
-                continue;
-            out << "ext: " << w << " " << v2 << "\n";
-            out << "int: " << v << " " << v1 << "\n";
-        }
-        literal_vector lits;
-        for (bool_var v : m_tracked_vars) 
-            lits.push_back(literal(m_var2ext[v], l_false == s.value(m_var2ext[v])));
-        out << "tracked: " << lits << "\n";  
-        lits.reset();
-        for (literal r : m_roots) 
-            if (m_solver.value(r) == l_true)
-                lits.push_back(r);
-        out << "roots: " << lits << "\n";
-        m_solver.display(out);
-
-        return out;
-    }
-}
diff --git a/src/sat/smt/sat_dual_solver.h b/src/sat/smt/sat_dual_solver.h
deleted file mode 100644
index d9b43f7af..000000000
--- a/src/sat/smt/sat_dual_solver.h
+++ /dev/null
@@ -1,84 +0,0 @@
-/*++
-Copyright (c) 2020 Microsoft Corporation
-
-Module Name:
-
-    sat_dual_solver.h
-
-Abstract:
-
-    Solver for obtaining implicant.
-    Based on an idea by Armin Biere to use dual propagation 
-    for representation of negated goal.
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2020-08-25
-
---*/
-#pragma once
-#include "util/lim_vector.h"
-#include "sat/sat_solver.h"
-
-namespace sat {
-
-    class dual_solver {
-        class dual_params : public no_drat_params {
-        public:
-            dual_params() {
-                set_bool("core.minimize", false);
-            }
-        };
-        solver&         s;
-        dual_params     m_params;
-        solver          m_solver;
-        lim_svector<literal> m_units, m_roots;
-        lim_svector<bool_var> m_tracked_vars;
-        literal_vector  m_lits, m_core;
-        bool_var_vector m_is_tracked;
-        unsigned_vector m_ext2var;
-        unsigned_vector m_var2ext;
-        lim_svector<unsigned> m_vars;
-        unsigned        m_num_scopes = 0;
-        void add_literal(literal lit);
-
-        bool_var ext2var(bool_var v);
-        bool_var var2ext(bool_var v);
-        literal  ext2lit(literal lit);
-        literal  lit2ext(literal lit);
-
-        void add_assumptions();
-
-        std::ostream& display(std::ostream& out) const;
-
-        void flush();
-
-    public:
-        dual_solver(solver& s, reslimit& l);
-        void push();
-        void pop(unsigned num_scopes);
-
-        /*
-        * track model relevancy for variable 
-        */
-        void track_relevancy(bool_var v);
-
-        /*
-        * Add a root clause from the input problem.
-        * At least one literal has to be satisfied in every root.
-        */
-        void add_root(unsigned sz, literal const* clause);
-
-        /*
-        * Add auxiliary clauses that originate from compiling definitions.
-        */
-        void add_aux(unsigned sz, literal const* clause);
-
-        /*
-        * Extract a minimized subset of relevant literals from a model for s.
-        */
-        bool operator()();
-
-        literal_vector const& core() const { return m_core; }
-    };
-}
diff --git a/src/sat/smt/smt_relevant.cpp b/src/sat/smt/smt_relevant.cpp
index a037090a2..87a85f61b 100644
--- a/src/sat/smt/smt_relevant.cpp
+++ b/src/sat/smt/smt_relevant.cpp
@@ -44,6 +44,8 @@ namespace smt {
     }
     
     void relevancy::pop(unsigned n) {
+        if (!m_enabled)
+            return;
         if (n <= m_num_scopes) {
             m_num_scopes -= n;
             return;
@@ -55,7 +57,7 @@ namespace smt {
         SASSERT(n > 0);
         unsigned sz = m_lim[m_lim.size() - n];
         for (unsigned i = m_trail.size(); i-- > sz; ) {
-            auto [u, idx] = m_trail[i];
+            auto const& [u, idx] = m_trail[i];
             switch (u) {
             case update::relevant_var:
                 m_relevant_var_ids[idx] = false;
@@ -168,7 +170,7 @@ namespace smt {
             return;
         m_trail.push_back(std::make_pair(update::set_qhead, m_qhead));
         while (m_qhead < m_queue.size() && !ctx.s().inconsistent() && ctx.get_manager().inc()) {
-            auto [lit, n] = m_queue[m_qhead++];
+            auto const& [lit, n] = m_queue[m_qhead++];
             SASSERT(n || lit != sat::null_literal);
             SASSERT(!n || lit == sat::null_literal);
             if (n)
diff --git a/src/sat/smt/smt_relevant.h b/src/sat/smt/smt_relevant.h
index 723cf613a..e27694ae2 100644
--- a/src/sat/smt/smt_relevant.h
+++ b/src/sat/smt/smt_relevant.h
@@ -137,7 +137,7 @@ namespace smt {
     public:
         relevancy(euf::solver& ctx);
 
-        void push() { ++m_num_scopes; }
+        void push() { if (m_enabled) ++m_num_scopes; }
         void pop(unsigned n);
 
         void add_root(unsigned n, sat::literal const* lits);
diff --git a/src/sat/tactic/goal2sat.cpp b/src/sat/tactic/goal2sat.cpp
index e3386b4e2..a6d5625ee 100644
--- a/src/sat/tactic/goal2sat.cpp
+++ b/src/sat/tactic/goal2sat.cpp
@@ -186,8 +186,6 @@ struct goal2sat::imp : public sat::sat_internalizer {
             return v;
         v = m_solver.add_var(is_ext);
         log_def(v, n);
-        if (top_level_relevant() && !is_bool_op(n))
-            ensure_euf()->track_relevancy(v);
         return v;
     }
 
@@ -216,10 +214,6 @@ struct goal2sat::imp : public sat::sat_internalizer {
         if (!m_expr2var_replay || !m_expr2var_replay->find(t, v))  
             v = add_var(true, t);
         m_map.insert(t, v);
-        if (relevancy_enabled() && (m.is_true(t) || m.is_false(t))) {
-            add_dual_root(sat::literal(v, m.is_false(t)));
-            ensure_euf()->track_relevancy(v);
-        }
         return v;
     }
 
@@ -678,8 +672,6 @@ struct goal2sat::imp : public sat::sat_internalizer {
         }
         if (lit == sat::null_literal) 
             return;
-        if (top_level_relevant())
-            euf->track_relevancy(lit.var());
         if (root)
             mk_root_clause(lit);
         else
diff --git a/src/sat/tactic/sat_tactic.cpp b/src/sat/tactic/sat_tactic.cpp
index 892a88f89..ef9c1f4f2 100644
--- a/src/sat/tactic/sat_tactic.cpp
+++ b/src/sat/tactic/sat_tactic.cpp
@@ -135,6 +135,7 @@ class sat_tactic : public tactic {
                 ref<sat2goal::mc> mc;
                 m_sat2goal(*m_solver, map, m_params, *(g.get()), mc);
                 g->add(mc.get());
+                g->display(std::cout);
                 if (produce_core || m_goal2sat.has_interpreted_funs()) {
                     // sat2goal does not preseve assumptions or assignments to interpreted atoms
                     g->updt_prec(goal::OVER);