diff --git a/scripts/mk_project.py b/scripts/mk_project.py
index 07fa172f6..dd2b190d4 100644
--- a/scripts/mk_project.py
+++ b/scripts/mk_project.py
@@ -39,9 +39,7 @@ def init_project_def():
     add_lib('solver', ['model', 'tactic', 'proofs'])
     add_lib('cmd_context', ['solver', 'rewriter'])
     add_lib('sat_smt', ['sat', 'euf', 'tactic'], 'sat/smt')
-    add_lib('sat_ba',  ['sat', 'sat_smt'], 'sat/ba')    
-    add_lib('sat_euf', ['sat', 'euf', 'sat_ba'], 'sat/euf')    
-    add_lib('sat_tactic', ['tactic', 'sat', 'solver', 'sat_euf'], 'sat/tactic')        
+    add_lib('sat_tactic', ['tactic', 'sat', 'solver', 'sat_smt'], 'sat/tactic')        
     add_lib('smt2parser', ['cmd_context', 'parser_util'], 'parsers/smt2')
     add_lib('pattern', ['normal_forms', 'smt2parser', 'rewriter'], 'ast/pattern')
     add_lib('core_tactics', ['tactic', 'macros', 'normal_forms', 'rewriter', 'pattern'], 'tactic/core')
@@ -83,7 +81,7 @@ def init_project_def():
             includes2install=['z3.h', 'z3_v1.h', 'z3_macros.h'] + API_files)
     add_lib('extra_cmds', ['cmd_context', 'subpaving_tactic', 'qe', 'arith_tactics'], 'cmd_context/extra_cmds')
     add_exe('shell', ['api', 'sat', 'extra_cmds','opt'], exe_name='z3')
-    add_exe('test', ['api', 'fuzzing', 'simplex', 'sat_euf'], exe_name='test-z3', install=False)
+    add_exe('test', ['api', 'fuzzing', 'simplex', 'sat_smt'], exe_name='test-z3', install=False)
     _libz3Component = add_dll('api_dll', ['api', 'sat', 'extra_cmds'], 'api/dll',
                               reexports=['api'],
                               dll_name='libz3',
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index df9d6acaf..0274f28a6 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -60,8 +60,6 @@ add_subdirectory(math/subpaving/tactic)
 add_subdirectory(tactic/aig)
 add_subdirectory(solver)
 add_subdirectory(sat/smt)
-add_subdirectory(sat/ba)
-add_subdirectory(sat/euf)
 add_subdirectory(sat/tactic)
 add_subdirectory(tactic/arith)
 add_subdirectory(nlsat/tactic)
diff --git a/src/ast/euf/euf_egraph.cpp b/src/ast/euf/euf_egraph.cpp
index 5f073a877..1bb193e86 100644
--- a/src/ast/euf/euf_egraph.cpp
+++ b/src/ast/euf/euf_egraph.cpp
@@ -255,7 +255,10 @@ namespace euf {
        explanations up to the least common ancestors.
      */
     void egraph::push_congruence(enode* n1, enode* n2, bool comm) {
+        SASSERT(is_app(n1->get_owner()));
         SASSERT(n1->get_decl() == n2->get_decl());
+        if (m_used_cc) 
+            m_used_cc(to_app(n1->get_owner()), to_app(n2->get_owner()));
         if (comm && 
             n1->get_arg(0)->get_root() == n2->get_arg(1)->get_root() &&
             n1->get_arg(1)->get_root() == n2->get_arg(0)->get_root()) {
@@ -268,30 +271,28 @@ namespace euf {
             push_lca(n1->get_arg(i), n2->get_arg(i));
     }
 
-    void egraph::push_lca(enode* a, enode* b) {
+    enode* egraph::find_lca(enode* a, enode* b) {
         SASSERT(a->get_root() == b->get_root());
-        enode* n = a;
-        while (n) {
-            n->mark2();
-            n = n->m_target;
-        }
-        n = b;
-        while (n) {
-            if (n->is_marked2()) 
-                n->unmark2();   
-            else if (!n->is_marked1()) 
-                m_todo.push_back(n);
-            n = n->m_target;
-        }
-        n = a;
-        while (n->is_marked2()) {            
-            n->unmark2();
-            if (!n->is_marked1())
-                m_todo.push_back(n);
+        a->mark2_targets<true>();
+        while (!b->is_marked2()) 
+            b = b->m_target;
+        a->mark2_targets<false>();
+        return b;
+    }
+    
+    void egraph::push_to_lca(enode* n, enode* lca) {
+        while (n != lca) {
+            m_todo.push_back(n);
             n = n->m_target;
         }
     }
 
+    void egraph::push_lca(enode* a, enode* b) {
+        enode* lca = find_lca(a, b);
+        push_to_lca(a, lca);
+        push_to_lca(b, lca);
+    }
+
     void egraph::push_todo(enode* n) {
         while (n) {
             m_todo.push_back(n);
@@ -313,7 +314,11 @@ namespace euf {
     void egraph::explain_eq(ptr_vector<T>& justifications, enode* a, enode* b, bool comm) {
         SASSERT(m_todo.empty());
         SASSERT(a->get_root() == b->get_root());
-        push_lca(a, b);
+        enode* lca = find_lca(a, b);
+        push_to_lca(a, lca);
+        push_to_lca(b, lca);
+        if (m_used_eq)
+            m_used_eq(a->get_owner(), b->get_owner(), lca->get_owner());
         explain_todo(justifications);
     }
 
diff --git a/src/ast/euf/euf_egraph.h b/src/ast/euf/euf_egraph.h
index 4988ebb32..76f946ee1 100644
--- a/src/ast/euf/euf_egraph.h
+++ b/src/ast/euf/euf_egraph.h
@@ -70,7 +70,8 @@ namespace euf {
         enode_vector           m_new_lits;
         enode_vector           m_todo;
         stats                  m_stats;
-            
+        std::function<void(expr*,expr*,expr*)> m_used_eq;
+        std::function<void(app*,app*)>        m_used_cc;            
 
         void push_eq(enode* r1, enode* n1, unsigned r2_num_parents) {
             m_eqs.push_back(add_eq_record(r1, n1, r2_num_parents));
@@ -87,6 +88,8 @@ namespace euf {
         void reinsert_equality(enode* p);
         void update_children(enode* n);
         void push_lca(enode* a, enode* b);
+        enode* find_lca(enode* a, enode* b);
+        void push_to_lca(enode* a, enode* lca);
         void push_congruence(enode* n1, enode* n2, bool commutative);
         void push_todo(enode* n);
         template <typename T>
@@ -126,6 +129,10 @@ namespace euf {
         bool inconsistent() const { return m_inconsistent; }
         enode_vector const& new_eqs() const { return m_new_eqs; }
         enode_vector const& new_lits() const { return m_new_lits; }
+
+        void set_used_eq(std::function<void(expr*,expr*,expr*)>& used_eq) { m_used_eq = used_eq; }
+        void set_used_cc(std::function<void(app*,app*)>& used_cc) { m_used_cc = used_cc; }
+
         template <typename T>
         void explain(ptr_vector<T>& justifications);
         template <typename T>
diff --git a/src/ast/euf/euf_enode.h b/src/ast/euf/euf_enode.h
index 776747db2..59166df31 100644
--- a/src/ast/euf/euf_enode.h
+++ b/src/ast/euf/euf_enode.h
@@ -104,11 +104,29 @@ namespace euf {
         void mark2() { m_mark2 = true; }
         void unmark2() { m_mark2 = false; }
         bool is_marked2() { return m_mark2; }
+
+        template<bool m> void mark1_targets() {
+            enode* n = this;
+            while (n) {
+                if (m) n->mark1(); else n->unmark1();
+                n = n->m_target;
+            }
+        }
+        template<bool m> void mark2_targets() {
+            enode* n = this;
+            while (n) {
+                if (m) n->mark2(); else n->unmark2();
+                n = n->m_target;
+            }
+        }
+
         void add_parent(enode* p) { m_parents.push_back(p); }
         unsigned class_size() const { return m_class_size; }
+        bool is_root() const { return m_root == this; }
         enode* get_root() const { return m_root; }
         expr*  get_owner() const { return m_owner; }
         unsigned get_owner_id() const { return m_owner->get_id(); }
+        unsigned get_root_id() const { return m_root->m_owner->get_id(); }
         void inc_class_size(unsigned n) { m_class_size += n; }
         void dec_class_size(unsigned n) { m_class_size -= n; }
 
diff --git a/src/sat/ba/CMakeLists.txt b/src/sat/ba/CMakeLists.txt
deleted file mode 100644
index fc94b42f8..000000000
--- a/src/sat/ba/CMakeLists.txt
+++ /dev/null
@@ -1,8 +0,0 @@
-z3_add_component(sat_ba
-  SOURCES
-    ba_solver.cpp
-    ba_internalize.cpp
-  COMPONENT_DEPENDENCIES
-    sat
-)
-
diff --git a/src/sat/euf/CMakeLists.txt b/src/sat/euf/CMakeLists.txt
deleted file mode 100644
index b716ea015..000000000
--- a/src/sat/euf/CMakeLists.txt
+++ /dev/null
@@ -1,9 +0,0 @@
-z3_add_component(sat_euf
-  SOURCES
-    euf_solver.cpp
-    euf_model.cpp
-  COMPONENT_DEPENDENCIES
-    sat
-    sat_smt
-    euf
-)
diff --git a/src/sat/euf/euf_model.cpp b/src/sat/euf/euf_model.cpp
deleted file mode 100644
index 9c789140e..000000000
--- a/src/sat/euf/euf_model.cpp
+++ /dev/null
@@ -1,72 +0,0 @@
-/*++
-Copyright (c) 2020 Microsoft Corporation
-
-Module Name:
-
-    euf_model.cpp
-
-Abstract:
-
-    Model building for EUF solver plugin.
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2020-08-25
-
---*/
-
-#include "ast/ast_pp.h"
-#include "sat/euf/euf_solver.h"
-#include "model/value_factory.h"
-
-namespace euf {
-
-    model_converter* solver::get_model() {
-        sat::th_dependencies deps;
-        collect_dependencies(deps);
-        // deps.sort();
-        expr_ref_vector values(m);
-        dependencies2values(deps, values);
-        return nullptr;
-    }
-
-    void solver::collect_dependencies(sat::th_dependencies& deps) {
-
-    }
-
-
-    void solver::dependencies2values(sat::th_dependencies& deps, expr_ref_vector& values) {
-
-        user_sort_factory user_sort(m);
-        for (enode* n : deps) {
-            unsigned id = n->get_root()->get_owner_id();
-            if (values.get(id) != nullptr)
-                continue;
-            expr* e = n->get_owner();
-            values.reserve(id + 1);
-            if (m.is_bool(e)) {
-                switch (s().value(m_expr2var.to_bool_var(e))) {
-                case l_true:
-                    values.set(id, m.mk_true());
-                    break;
-                default:
-                    values.set(id, m.mk_false());
-                    break;
-                }
-                continue;
-            }
-            auto* mb = get_model_builder(e);
-            if (mb) 
-                mb->add_value(n, values);
-            else if (m.is_uninterp(m.get_sort(e))) {
-                expr* v = user_sort.get_fresh_value(m.get_sort(e));
-                values.set(id, v);
-            }
-            else {
-                IF_VERBOSE(1, verbose_stream() << "no model values created for " << mk_pp(e, m) << "\n");
-            }
-                
-        }
-        NOT_IMPLEMENTED_YET();
-    }
-}
diff --git a/src/sat/sat_extension.h b/src/sat/sat_extension.h
index 1493044ca..9ab1fcd0c 100644
--- a/src/sat/sat_extension.h
+++ b/src/sat/sat_extension.h
@@ -86,7 +86,7 @@ namespace sat {
         virtual unsigned max_var(unsigned w) const = 0;
 
         virtual bool extract_pb(std::function<void(unsigned sz, literal const* c, unsigned k)>& card,
-                                std::function<void(unsigned sz, literal const* c, unsigned const* coeffs, unsigned k)>& pb) {
+                                std::function<void(unsigned sz, literal const* c, unsigned const* coeffs, unsigned k)>& pb) {                                
             return false;
         }
     };
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index c52bf4d7c..06b843b44 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -454,6 +454,8 @@ namespace sat {
         
         void display_lookahead_scores(std::ostream& out);
 
+        stats const& stats() const { return m_stats; }
+
     protected:
 
         unsigned m_conflicts_since_init;
diff --git a/src/sat/sat_solver/inc_sat_solver.cpp b/src/sat/sat_solver/inc_sat_solver.cpp
index 4bb9563e9..ef020d3de 100644
--- a/src/sat/sat_solver/inc_sat_solver.cpp
+++ b/src/sat/sat_solver/inc_sat_solver.cpp
@@ -615,7 +615,7 @@ public:
 
 private:
 
-    lbool internalize_goal(goal_ref& g, dep2asm_t& dep2asm, bool is_lemma) {
+    lbool internalize_goal(goal_ref& g, dep2asm_t& dep2asm) {
         m_solver.pop_to_base_level();
         if (m_solver.inconsistent()) 
             return l_false;
@@ -662,7 +662,7 @@ private:
 
         // ensure that if goal is already internalized, then import mc from m_solver.
 
-        m_goal2sat(*g, m_params, m_solver, m_map, dep2asm, is_incremental(), is_lemma);
+        m_goal2sat(*g, m_params, m_solver, m_map, dep2asm, is_incremental());
         m_goal2sat.get_interpreted_atoms(atoms);
         if (!m_sat_mc) m_sat_mc = alloc(sat2goal::mc, m);
         m_sat_mc->flush_smc(m_solver, m_map);
@@ -690,7 +690,7 @@ private:
         for (unsigned i = 0; i < get_num_assumptions(); ++i) {
             g->assert_expr(get_assumption(i), m.mk_leaf(get_assumption(i)));
         }
-        lbool res = internalize_goal(g, dep2asm, false);
+        lbool res = internalize_goal(g, dep2asm);
         if (res == l_true) {
             extract_assumptions(sz, asms, dep2asm);
         }
@@ -831,7 +831,7 @@ private:
             expr* fml = m_fmls.get(i);
             g->assert_expr(fml);
         }
-        lbool res = internalize_goal(g, dep2asm, false);
+        lbool res = internalize_goal(g, dep2asm);
         if (res != l_undef) {
             m_fmls_head = m_fmls.size();
         }
diff --git a/src/sat/smt/CMakeLists.txt b/src/sat/smt/CMakeLists.txt
index a4c9e363a..e90730620 100644
--- a/src/sat/smt/CMakeLists.txt
+++ b/src/sat/smt/CMakeLists.txt
@@ -1,7 +1,12 @@
 z3_add_component(sat_smt
   SOURCES
     atom2bool_var.cpp
-    sat_th.cpp
+    ba_solver.cpp
+    xor_solver.cpp
+    ba_internalize.cpp
+    euf_ackerman.cpp
+    euf_solver.cpp
+    euf_model.cpp
   COMPONENT_DEPENDENCIES
     sat
     ast
diff --git a/src/sat/ba/ba_internalize.cpp b/src/sat/smt/ba_internalize.cpp
similarity index 76%
rename from src/sat/ba/ba_internalize.cpp
rename to src/sat/smt/ba_internalize.cpp
index 27606ff55..00ebd0d19 100644
--- a/src/sat/ba/ba_internalize.cpp
+++ b/src/sat/smt/ba_internalize.cpp
@@ -7,7 +7,7 @@ Module Name:
 
 Abstract:
 
-    INternalize methods for Boolean algebra operators.
+    Internalize methods for Boolean algebra operators.
 
 Author:
 
@@ -16,12 +16,11 @@ Author:
 --*/
 
 
-#include "sat/ba/ba_internalize.h"
+#include "sat/smt/ba_internalize.h"
 
 namespace sat {
 
-    literal ba_internalize::internalize(sat_internalizer& si, expr* e, bool sign, bool root) {
-        m_si = &si;
+    literal ba_internalize::internalize(expr* e, bool sign, bool root) {
         if (pb.is_pb(e)) 
             return internalize_pb(e, sign, root);
         if (m.is_xor(e))
@@ -35,7 +34,7 @@ namespace sat {
         sat::bool_var v = m_solver.add_var(true);
         lits.push_back(literal(v, true));
         auto add_expr = [&](expr* a) {
-            literal lit = m_si->internalize(a);
+            literal lit = si.internalize(a);
             m_solver.set_external(lit.var());
             lits.push_back(lit);
         };
@@ -100,7 +99,7 @@ namespace sat {
 
     void ba_internalize::convert_pb_args(app* t, literal_vector& lits) {
         for (expr* arg : *t) {
-            lits.push_back(m_si->internalize(arg));
+            lits.push_back(si.internalize(arg));
             m_solver.set_external(lits.back().var());
         }
     }
@@ -192,10 +191,10 @@ namespace sat {
             literal l1(v1, false), l2(v2, false);
             bool_var v = m_solver.add_var(false);
             literal l(v, false);
-            m_si->mk_clause(~l, l1);
-            m_si->mk_clause(~l, l2);
-            m_si->mk_clause(~l1, ~l2, l);
-            m_si->cache(t, l);
+            si.mk_clause(~l, l1);
+            si.mk_clause(~l, l2);
+            si.mk_clause(~l1, ~l2, l);
+            si.cache(t, l);
             if (sign) l.neg();
             return l;
         }
@@ -218,7 +217,7 @@ namespace sat {
             bool_var v = m_solver.add_var(true);
             literal lit(v, false);
             ba.add_at_least(v, lits, k.get_unsigned());
-            m_si->cache(t, lit);
+            si.cache(t, lit);
             if (sign) lit.neg();
             TRACE("ba", tout << "root: " << root << " lit: " << lit << "\n";);
             return lit;
@@ -245,7 +244,7 @@ namespace sat {
             bool_var v = m_solver.add_var(true);
             literal lit(v, false);
             ba.add_at_least(v, lits, k2);
-            m_si->cache(t, lit);
+            si.cache(t, lit);
             if (sign) lit.neg();
             return lit;
         }
@@ -267,10 +266,10 @@ namespace sat {
             literal l1(v1, false), l2(v2, false);
             bool_var v = m_solver.add_var(false);
             literal l(v, false);
-            m_si->mk_clause(~l, l1);
-            m_si->mk_clause(~l, l2);
-            m_si->mk_clause(~l1, ~l2, l);
-            m_si->cache(t, l);
+            si.mk_clause(~l, l1);
+            si.mk_clause(~l, l2);
+            si.mk_clause(~l1, ~l2, l);
+            si.cache(t, l);
             if (sign) l.neg();
             return l;
         }
@@ -278,4 +277,63 @@ namespace sat {
             return null_literal;
         }
     }
+
+    expr_ref ba_decompile::get_card(std::function<expr_ref(sat::literal)>& lit2expr, ba_solver::card const& c) {
+        ptr_buffer<expr> lits;
+        for (sat::literal l : c) {
+            lits.push_back(lit2expr(l));
+        }
+        expr_ref fml(pb.mk_at_least_k(c.size(), lits.c_ptr(), c.k()), m);
+
+        if (c.lit() != sat::null_literal) {
+            fml = m.mk_eq(lit2expr(c.lit()), fml);
+        }
+        return fml;
+    }
+
+    expr_ref ba_decompile::get_pb(std::function<expr_ref(sat::literal)>& lit2expr, ba_solver::pb const& p)  {
+        ptr_buffer<expr> lits;
+        vector<rational> coeffs;
+        for (auto const& wl : p) {
+            lits.push_back(lit2expr(wl.second));
+            coeffs.push_back(rational(wl.first));
+        }
+        rational k(p.k());
+        expr_ref fml(pb.mk_ge(p.size(), coeffs.c_ptr(), lits.c_ptr(), k), m);
+
+        if (p.lit() != sat::null_literal) {
+            fml = m.mk_eq(lit2expr(p.lit()), fml);
+        }
+        return fml;
+    }
+
+    expr_ref ba_decompile::get_xor(std::function<expr_ref(sat::literal)>& lit2expr, ba_solver::xr const& x) {
+        ptr_buffer<expr> lits;
+        for (sat::literal l : x) {
+            lits.push_back(lit2expr(l));
+        }
+        expr_ref fml(m.mk_xor(x.size(), lits.c_ptr()), m);
+
+        if (x.lit() != sat::null_literal) {
+            fml = m.mk_eq(lit2expr(x.lit()), fml);
+        }
+        return fml;
+    }
+
+    bool ba_decompile::to_formulas(std::function<expr_ref(sat::literal)>& l2e, expr_ref_vector& fmls) {
+        for (auto* c : ba.constraints()) {
+            switch (c->tag()) {
+            case ba_solver::card_t:
+                fmls.push_back(get_card(l2e, c->to_card()));
+                break;
+            case sat::ba_solver::pb_t:
+                fmls.push_back(get_pb(l2e, c->to_pb()));
+                break;
+            case sat::ba_solver::xr_t:
+                fmls.push_back(get_xor(l2e, c->to_xr()));
+                break;
+            }
+        }
+        return true;
+    }
 }
diff --git a/src/sat/ba/ba_internalize.h b/src/sat/smt/ba_internalize.h
similarity index 58%
rename from src/sat/ba/ba_internalize.h
rename to src/sat/smt/ba_internalize.h
index 71ab20614..39864acae 100644
--- a/src/sat/ba/ba_internalize.h
+++ b/src/sat/smt/ba_internalize.h
@@ -19,7 +19,7 @@ Author:
 #pragma once
 
 #include "sat/smt/sat_th.h"
-#include "sat/ba/ba_solver.h"
+#include "sat/smt/ba_solver.h"
 #include "ast/pb_decl_plugin.h"
 
 
@@ -31,7 +31,7 @@ namespace sat {
         pb_util pb;
         ba_solver& ba;
         solver_core& m_solver;
-        sat_internalizer* m_si;
+        sat_internalizer& si;
         literal convert_eq_k(app* t, rational const& k, bool root, bool sign);
         literal convert_at_most_k(app* t, rational const& k, bool root, bool sign);
         literal convert_at_least_k(app* t, rational const& k, bool root, bool sign);
@@ -44,10 +44,30 @@ namespace sat {
         void convert_pb_args(app* t, literal_vector& lits);
         literal internalize_pb(expr* e, bool sign, bool root);
         literal internalize_xor(expr* e, bool sign, bool root);
+
     public:
-        ba_internalize(ba_solver& ba, solver_core& s, ast_manager& m) : m(m), pb(m), ba(ba), m_solver(s) {}
+        ba_internalize(ba_solver& ba, solver_core& s, sat_internalizer& si, ast_manager& m) : 
+            m(m), pb(m), ba(ba), m_solver(s), si(si) {}
         ~ba_internalize() override {}
-        literal internalize(sat_internalizer& si, expr* e, bool sign, bool root) override;
-        
+        literal internalize(expr* e, bool sign, bool root) override;
+       
+    };
+
+    class ba_decompile : public sat::th_decompile {
+        ast_manager& m;
+        ba_solver& ba;
+        solver_core& m_solver;
+        pb_util pb;
+
+        expr_ref get_card(std::function<expr_ref(sat::literal)>& l2e, ba_solver::card const& c);
+        expr_ref get_pb(std::function<expr_ref(sat::literal)>& l2e, ba_solver::pb const& p);
+        expr_ref get_xor(std::function<expr_ref(sat::literal)>& l2e, ba_solver::xr const& x);
+    public:
+        ba_decompile(ba_solver& ba, solver_core& s, ast_manager& m) :
+            m(m),  ba(ba), m_solver(s), pb(m) {}
+
+        ~ba_decompile() override {}
+
+        bool to_formulas(std::function<expr_ref(sat::literal)>& l2e, expr_ref_vector& fmls) override;
     };
 }
diff --git a/src/sat/ba/ba_solver.cpp b/src/sat/smt/ba_solver.cpp
similarity index 89%
rename from src/sat/ba/ba_solver.cpp
rename to src/sat/smt/ba_solver.cpp
index 646cb6534..96e18b8bb 100644
--- a/src/sat/ba/ba_solver.cpp
+++ b/src/sat/smt/ba_solver.cpp
@@ -7,7 +7,7 @@ Module Name:
 
 Abstract:
 
-    Extension for cardinality and xr reasoning.
+    Extension for cardinality and xor reasoning.
 
 Author:
 
@@ -18,9 +18,9 @@ Revision History:
 --*/
 
 #include <cmath>
-#include "sat/ba/ba_solver.h"
-#include "sat/sat_types.h"
 #include "util/mpz.h"
+#include "sat/sat_types.h"
+#include "sat/smt/ba_solver.h"
 #include "sat/sat_simplifier_params.hpp"
 #include "sat/sat_xor_finder.h"
 
@@ -55,15 +55,6 @@ namespace sat {
         return static_cast<pb_base const&>(*this);
     }
 
-    ba_solver::xr& ba_solver::constraint::to_xr() {
-        SASSERT(is_xr());
-        return static_cast<xr&>(*this);
-    }
-
-    ba_solver::xr const& ba_solver::constraint::to_xr() const{
-        SASSERT(is_xr());
-        return static_cast<xr const&>(*this);
-    }
 
     unsigned ba_solver::constraint::fold_max_var(unsigned w) const {
         if (lit() != null_literal) w = std::max(w, lit().var());
@@ -205,32 +196,7 @@ namespace sat {
     }
 
 
-    // -----------------------------------
-    // xr
     
-    ba_solver::xr::xr(extension* e, unsigned id, literal_vector const& lits):
-    constraint(e, xr_t, id, null_literal, lits.size(), get_obj_size(lits.size())) {
-        for (unsigned i = 0; i < size(); ++i) {
-            m_lits[i] = lits[i];
-        }
-    }
-
-    bool ba_solver::xr::is_watching(literal l) const {
-        return 
-            l == (*this)[0] || l == (*this)[1] ||
-            ~l == (*this)[0] || ~l == (*this)[1];            
-    }
-
-    bool ba_solver::xr::well_formed() const {
-        uint_set vars;        
-        if (lit() != null_literal) vars.insert(lit().var());
-        for (literal l : *this) {
-            bool_var v = l.var();
-            if (vars.contains(v)) return false;
-            vars.insert(v);            
-        }
-        return true;
-    }
 
     // ----------------------------            
     // card
@@ -908,107 +874,6 @@ namespace sat {
         out << ">= " << p.k()  << "\n";
     }
 
-    // --------------------
-    // xr:
-
-    void ba_solver::clear_watch(xr& x) {
-        x.clear_watch();
-        unwatch_literal(x[0], x);
-        unwatch_literal(x[1], x);         
-        unwatch_literal(~x[0], x);
-        unwatch_literal(~x[1], x);         
-    }
-
-    bool ba_solver::parity(xr const& x, unsigned offset) const {
-        bool odd = false;
-        unsigned sz = x.size();
-        for (unsigned i = offset; i < sz; ++i) {
-            SASSERT(value(x[i]) != l_undef);
-            if (value(x[i]) == l_true) {
-                odd = !odd;
-            }
-        }
-        return odd;
-    }
-
-    bool ba_solver::init_watch(xr& x) {
-        clear_watch(x);
-        VERIFY(x.lit() == null_literal);
-        TRACE("ba", display(tout, x, true););
-        unsigned sz = x.size();
-        unsigned j = 0;
-        for (unsigned i = 0; i < sz && j < 2; ++i) {
-            if (value(x[i]) == l_undef) {
-                x.swap(i, j);
-                ++j;
-            }
-        }
-        switch (j) {
-        case 0: 
-            if (!parity(x, 0)) {
-                unsigned l = lvl(x[0]);
-                j = 1;
-                for (unsigned i = 1; i < sz; ++i) {
-                    if (lvl(x[i]) > l) {
-                        j = i;
-                        l = lvl(x[i]);
-                    } 
-                }
-                set_conflict(x, x[j]);
-            }
-            return false;
-        case 1: 
-            SASSERT(x.lit() == null_literal || value(x.lit()) == l_true);
-            assign(x, parity(x, 1) ? ~x[0] : x[0]);
-            return false;
-        default: 
-            SASSERT(j == 2);
-            watch_literal(x[0], x);
-            watch_literal(x[1], x);
-            watch_literal(~x[0], x);
-            watch_literal(~x[1], x);
-            return true;
-        }
-    }
-
-
-    lbool ba_solver::add_assign(xr& x, literal alit) {
-        // literal is assigned     
-        unsigned sz = x.size();
-        TRACE("ba", tout << "assign: "  << ~alit << "@" << lvl(~alit) << " " << x << "\n"; display(tout, x, true); );
-
-        VERIFY(x.lit() == null_literal);
-        SASSERT(value(alit) != l_undef);
-        unsigned index = (x[1].var() == alit.var()) ? 1 : 0;
-        VERIFY(x[index].var() == alit.var());
-        
-        // find a literal to swap with:
-        for (unsigned i = 2; i < sz; ++i) {
-            literal lit = x[i];
-            if (value(lit) == l_undef) {
-                x.swap(index, i);
-                unwatch_literal(~alit, x);
-                // alit gets unwatched by propagate_core because we return l_undef
-                watch_literal(lit, x);
-                watch_literal(~lit, x);
-                TRACE("ba", tout << "swap in: " << lit << " " << x << "\n";);
-                return l_undef;
-            }
-        }
-        if (index == 0) {
-            x.swap(0, 1);
-        }
-        // alit resides at index 1.
-        VERIFY(x[1].var() == alit.var());        
-        if (value(x[0]) == l_undef) {
-            bool p = parity(x, 1);
-            assign(x, p ? ~x[0] : x[0]);            
-        }
-        else if (!parity(x, 0)) {
-            set_conflict(x, ~x[1]);
-        }      
-        return inconsistent() ? l_false : l_true;  
-    }
 
     // ---------------------------
     // conflict resolution
@@ -1977,116 +1842,7 @@ namespace sat {
         add_pb_ge(lit, wlits, k, false);
     }
 
-    void ba_solver::add_xr(literal_vector const& lits) {
-        add_xr(lits, false);
-    }
 
-    bool ba_solver::all_distinct(literal_vector const& lits) {
-        return s().all_distinct(lits);
-    }
-
-    bool ba_solver::all_distinct(clause const& c) {
-        return s().all_distinct(c);
-    }
-
-    bool ba_solver::all_distinct(xr const& x) {
-        init_visited();
-        for (literal l : x) {
-            if (is_visited(l.var())) {
-                return false;
-            }
-            mark_visited(l.var());
-        }
-        return true;
-    }
-
-    literal ba_solver::add_xor_def(literal_vector& lits, bool learned) {
-        unsigned sz = lits.size();
-        SASSERT (sz > 1);
-        VERIFY(all_distinct(lits));
-        init_visited();
-        bool parity1 = true;
-        for (literal l : lits) {            
-            mark_visited(l.var());
-            parity1 ^= l.sign();
-        }
-        for (auto const & w : get_wlist(lits[0])) {
-            if (w.get_kind() != watched::EXT_CONSTRAINT) continue;
-            constraint& c = index2constraint(w.get_ext_constraint_idx());
-            if (!c.is_xr()) continue;
-            xr& x = c.to_xr();
-            if (sz + 1 != x.size()) continue;
-            bool is_match = true;
-            literal l0 = null_literal;
-            bool parity2 = true;
-            for (literal l : x) {
-                if (!is_visited(l.var())) {
-                    if (l0 == null_literal) {
-                        l0 = l;
-                    }
-                    else {
-                        is_match = false;
-                        break;
-                    }
-                }
-                else {
-                    parity2 ^= l.sign();
-                }
-            }
-            if (is_match) {
-                SASSERT(all_distinct(x));
-                if (parity1 == parity2) l0.neg();
-                if (!learned && x.learned()) {
-                    set_non_learned(x);
-                }
-                return l0;
-            }
-        }
-        bool_var v = s().mk_var(true, true);
-        literal lit(v, false);
-        lits.push_back(~lit);
-        add_xr(lits, learned);
-        return lit;
-    }
-
-
-    ba_solver::constraint* ba_solver::add_xr(literal_vector const& _lits, bool learned) {
-        literal_vector lits;
-        u_map<bool> var2sign;
-        bool sign = false, odd = false;
-        for (literal lit : _lits) {
-            if (var2sign.find(lit.var(), sign)) {
-                var2sign.erase(lit.var());
-                odd ^= (sign ^ lit.sign());
-            }
-            else {
-                var2sign.insert(lit.var(), lit.sign());
-            }
-        }       
-        
-        for (auto const& kv : var2sign) {
-            lits.push_back(literal(kv.m_key, kv.m_value));
-        }
-        if (odd && !lits.empty()) {
-            lits[0].neg();
-        }
-        switch (lits.size()) {
-        case 0:
-            if (!odd)
-                s().set_conflict(justification(0));
-            return nullptr;
-        case 1:            
-            s().assign_scoped(lits[0]);
-            return nullptr;
-        default:
-            break;
-        }
-        void * mem = m_allocator.allocate(xr::get_obj_size(lits.size()));
-        xr* x = new (mem) xr(this, next_id(), lits);
-        x->set_learned(learned);
-        add_constraint(x);
-        return x;
-    }
 
     /*
       \brief return true to keep watching literal.
@@ -2178,89 +1934,6 @@ namespace sat {
         m_parity_marks[v] = 0;
     }
     
-    /**
-       \brief perform parity resolution on xr premises.
-       The idea is to collect premises based on xr resolvents. 
-       Variables that are repeated an even number of times cancel out.
-     */
-
-    void ba_solver::get_xr_antecedents(literal l, unsigned index, justification js, literal_vector& r) {
-        unsigned level = lvl(l);
-        bool_var v = l.var();
-        SASSERT(js.get_kind() == justification::EXT_JUSTIFICATION);
-        TRACE("ba", tout << l << ": " << js << "\n"; 
-              for (unsigned i = 0; i <= index; ++i) tout << s().m_trail[i] << " "; tout << "\n";
-              s().display_units(tout);
-              );
-
-
-        unsigned num_marks = 0;
-        while (true) {
-            TRACE("ba", tout << "process: " << l << " " << js << "\n";);
-            if (js.get_kind() == justification::EXT_JUSTIFICATION) {
-                constraint& c = index2constraint(js.get_ext_justification_idx());
-                TRACE("ba", tout << c << "\n";);
-                if (!c.is_xr()) {
-                    r.push_back(l);
-                }
-                else {
-                    xr& x = c.to_xr();                    
-                    if (x[1].var() == l.var()) {
-                        x.swap(0, 1);
-                    }
-                    VERIFY(x[0].var() == l.var());
-                    for (unsigned i = 1; i < x.size(); ++i) {
-                        literal lit(value(x[i]) == l_true ? x[i] : ~x[i]);
-                        inc_parity(lit.var());
-                        if (lvl(lit) == level) {
-                            TRACE("ba", tout << "mark: " << lit << "\n";);
-                            ++num_marks;
-                        }
-                        else {
-                            m_parity_trail.push_back(lit);
-                        }
-                    }
-                }
-            }
-            else {
-                r.push_back(l);
-            }
-            bool found = false;
-            while (num_marks > 0) {
-                l = s().m_trail[index];
-                v = l.var();
-                unsigned n = get_parity(v);
-                if (n > 0 && lvl(l) == level) {
-                    reset_parity(v);
-                    num_marks -= n;
-                    if (n % 2 == 1) {
-                        found = true;
-                        break;
-                    }
-                }
-                --index;
-            }
-            if (!found) {
-                break;
-            }
-            --index;
-            js = s().m_justification[v];
-        }
-
-        // now walk the defined literals 
-
-        for (literal lit : m_parity_trail) {
-            if (get_parity(lit.var()) % 2 == 1) {
-                r.push_back(lit);
-            }
-            else {
-                // IF_VERBOSE(2, verbose_stream() << "skip even parity: " << lit << "\n";);
-            }
-            reset_parity(lit.var());
-        }
-        m_parity_trail.reset();
-        TRACE("ba", tout << r << "\n";);
-    }
 
     /**
        \brief retrieve a sufficient set of literals from p that imply l.
@@ -2400,12 +2073,6 @@ namespace sat {
         }
     }
 
-    void ba_solver::simplify(xr& x) {
-        if (x.learned()) {
-            x.set_removed();
-            m_constraint_removed = true;            
-        }
-    }
 
     void ba_solver::get_antecedents(literal l, card const& c, literal_vector& r) {
         if (l == ~c.lit()) {
@@ -2431,24 +2098,6 @@ namespace sat {
         }
     }
 
-    void ba_solver::get_antecedents(literal l, xr const& x, literal_vector& r) {
-        if (x.lit() != null_literal) r.push_back(x.lit());
-        // TRACE("ba", display(tout << l << " ", x, true););
-        SASSERT(x.lit() == null_literal || value(x.lit()) == l_true);
-        SASSERT(x[0].var() == l.var() || x[1].var() == l.var());
-        if (x[0].var() == l.var()) {
-            SASSERT(value(x[1]) != l_undef);
-            r.push_back(value(x[1]) == l_true ? x[1] : ~x[1]);                
-        }
-        else {
-            SASSERT(value(x[0]) != l_undef);
-            r.push_back(value(x[0]) == l_true ? x[0] : ~x[0]);                
-        }
-        for (unsigned i = 2; i < x.size(); ++i) {
-            SASSERT(value(x[i]) != l_undef);
-            r.push_back(value(x[i]) == l_true ? x[i] : ~x[i]);                
-        }
-    }
 
     // ----------------------------
     // constraint generic methods
@@ -2617,31 +2266,6 @@ namespace sat {
         return l_undef;        
     }
 
-    lbool ba_solver::eval(xr const& x) const {
-        bool odd = false;
-        
-        for (auto l : x) {
-            switch (value(l)) {
-            case l_true: odd = !odd; break;
-            case l_false: break;
-            default: return l_undef;
-            }
-        }
-        return odd ? l_true : l_false;
-    }
-
-    lbool ba_solver::eval(model const& m, xr const& x) const {
-        bool odd = false;
-        
-        for (auto l : x) {
-            switch (value(m, l)) {
-            case l_true: odd = !odd; break;
-            case l_false: break;
-            default: return l_undef;
-            }
-        }
-        return odd ? l_true : l_false;
-    }
 
     bool ba_solver::validate() {
         if (!validate_watch_literals()) {
@@ -2940,52 +2564,9 @@ namespace sat {
         }                
     }
 
-    void ba_solver::pre_simplify() {
-        VERIFY(s().at_base_lvl());
-        if (s().inconsistent())
-            return;
-        m_constraint_removed = false;
-        xor_finder xf(s());
-        for (unsigned sz = m_constraints.size(), i = 0; i < sz; ++i) pre_simplify(xf, *m_constraints[i]);
-        for (unsigned sz = m_learned.size(), i = 0; i < sz; ++i) pre_simplify(xf, *m_learned[i]);   
-        bool change = m_constraint_removed;
-        cleanup_constraints();
-        if (change) {
-            // remove non-used variables.
-            init_use_lists();
-            remove_unused_defs();
-            set_non_external();
-        }
-    }
-
-    void ba_solver::pre_simplify(xor_finder& xf, constraint& c) {
-        if (c.is_xr() && c.size() <= xf.max_xor_size()) {
-            unsigned sz = c.size();
-            literal_vector lits;
-            bool parity = false;
-            xr const& x = c.to_xr();
-            for (literal lit : x) {
-                parity ^= lit.sign();
-            }
-
-            // IF_VERBOSE(0, verbose_stream() << "blast: " << c << "\n");
-            for (unsigned i = 0; i < (1ul << sz); ++i) {
-                if (xf.parity(sz, i) == parity) {
-                    lits.reset();
-                    for (unsigned j = 0; j < sz; ++j) {
-                        lits.push_back(literal(x[j].var(), (0 != (i & (1 << j)))));
-                    }
-                    // IF_VERBOSE(0, verbose_stream() << lits << "\n");
-                    s().mk_clause(lits);
-                }
-            }
-            c.set_removed();
-            m_constraint_removed = true;
-        }
-    }
-
     void ba_solver::simplify() {        
-        if (!s().at_base_lvl()) s().pop_to_base_level();
+        if (!s().at_base_lvl()) 
+            s().pop_to_base_level();
         if (s().inconsistent())
             return;
         unsigned trail_sz, count = 0;
@@ -3381,9 +2962,6 @@ namespace sat {
         return false;
     }
 
-    bool ba_solver::clausify(xr& x) {
-        return false;
-    }
 
     bool ba_solver::clausify(card& c) {
         return false;
@@ -3771,82 +3349,6 @@ namespace sat {
         }
     }
 
-    // merge xors that contain cut variable
-    void ba_solver::merge_xor() {
-        unsigned sz = s().num_vars();
-        for (unsigned i = 0; i < sz; ++i) {
-            literal lit(i, false);
-            unsigned index = lit.index();
-            if (m_cnstr_use_list[index].size() == 2) {
-                constraint& c1 = *m_cnstr_use_list[index][0];
-                constraint& c2 = *m_cnstr_use_list[index][1];
-                if (c1.is_xr() && c2.is_xr() && 
-                    m_clause_use_list.get(lit).empty() && 
-                    m_clause_use_list.get(~lit).empty()) {
-                    bool unique = true;
-                    for (watched w : get_wlist(lit)) {
-                        if (w.is_binary_clause()) unique = false;                        
-                    }
-                    for (watched w : get_wlist(~lit)) {
-                        if (w.is_binary_clause()) unique = false;                        
-                    }
-                    if (!unique) continue;
-                    xr const& x1 = c1.to_xr();
-                    xr const& x2 = c2.to_xr();
-                    literal_vector lits, dups;
-                    bool parity = false;
-                    init_visited();
-                    for (literal l : x1) {
-                        mark_visited(l.var());
-                        lits.push_back(l);
-                    }
-                    for (literal l : x2) {
-                        if (is_visited(l.var())) {
-                            dups.push_back(l);
-                        }
-                        else {
-                            lits.push_back(l);
-                        }
-                    }
-                    init_visited();
-                    for (literal l : dups) mark_visited(l);
-                    unsigned j = 0;
-                    for (unsigned i = 0; i < lits.size(); ++i) {
-                        literal l = lits[i];
-                        if (is_visited(l)) {
-                            // skip
-                        }
-                        else if (is_visited(~l)) {
-                            parity ^= true;
-                        }
-                        else {
-                            lits[j++] = l;
-                        }
-                    }
-                    lits.shrink(j);
-                    if (!parity) lits[0].neg();
-                    IF_VERBOSE(1, verbose_stream() << "binary " << lits << " : " << c1 << " " << c2 << "\n");
-                    c1.set_removed();
-                    c2.set_removed();
-                    add_xr(lits, !c1.learned() && !c2.learned());
-                    m_constraint_removed = true;
-                }
-            }
-        }
-    }
-
-    void ba_solver::extract_xor() {
-        xor_finder xf(s());
-        std::function<void (literal_vector const&)> f = [this](literal_vector const& l) { add_xr(l, false); };
-        xf.set(f);
-        clause_vector clauses(s().clauses());
-        xf(clauses);
-        for (clause* cp : xf.removed_clauses()) {
-            cp->set_removed(true);
-            m_clause_removed = true;
-        }
-    }
-
     void ba_solver::init_visited() { s().init_visited(); }
     void ba_solver::mark_visited(literal l) { s().mark_visited(l); }
     void ba_solver::mark_visited(bool_var v) { s().mark_visited(v); }
@@ -3915,6 +3417,7 @@ namespace sat {
         cs.set_end(it2);
     }
 
+
     /*
       \brief subsumption between two cardinality constraints
       - A >= k       subsumes A + B >= k' for k' <= k
@@ -4380,23 +3883,6 @@ namespace sat {
         out << ">= " << ineq.m_k << "\n";
     }
 
-    void ba_solver::display(std::ostream& out, xr const& x, bool values) const {
-        out << "xr: ";
-        for (literal l : x) {
-            out << l;
-            if (values) {
-                out << "@(" << value(l);
-                if (value(l) != l_undef) {
-                    out << ":" << lvl(l);
-                }
-                out << ") ";
-            }
-            else {
-                out << " ";
-            }
-        }        
-        out << "\n";
-    }
 
     void ba_solver::display_lit(std::ostream& out, literal lit, unsigned sz, bool values) const {
         if (lit != null_literal) {
@@ -4555,13 +4041,6 @@ namespace sat {
         return false;
     }
 
-    bool ba_solver::validate_unit_propagation(xr const& x, literal alit) const {
-        if (value(x.lit()) != l_true) return false;
-        for (unsigned i = 1; i < x.size(); ++i) {
-            if (value(x[i]) == l_undef) return false;
-        }
-        return true;
-    }
 
     bool ba_solver::validate_lemma() { 
         int64_t bound64 = m_bound;
diff --git a/src/sat/ba/ba_solver.h b/src/sat/smt/ba_solver.h
similarity index 100%
rename from src/sat/ba/ba_solver.h
rename to src/sat/smt/ba_solver.h
diff --git a/src/sat/smt/euf_ackerman.cpp b/src/sat/smt/euf_ackerman.cpp
new file mode 100644
index 000000000..bc6f36e6d
--- /dev/null
+++ b/src/sat/smt/euf_ackerman.cpp
@@ -0,0 +1,211 @@
+/*++
+Copyright (c) 2020 Microsoft Corporation
+
+Module Name:
+
+    euf_ackerman.cpp
+
+Abstract:
+
+    Ackerman reduction plugin for EUF
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2020-08-28
+
+--*/
+#pragma once
+
+#include "sat/smt/euf_solver.h"
+#include "sat/smt/euf_ackerman.h"
+
+namespace euf {
+
+    ackerman::ackerman(solver& s, ast_manager& m): s(s), m(m) {
+        new_tmp();
+    }
+
+    ackerman::~ackerman() {
+        reset();
+        dealloc(m_tmp_inference);
+    }
+
+    void ackerman::reset() {
+        for (inference* inf : m_table) {
+            m.dec_ref(inf->a);
+            m.dec_ref(inf->b);
+            m.dec_ref(inf->c);
+        }
+        m_table.reset();
+        m_queue = nullptr;        
+    }
+
+    void ackerman::insert(expr* a, expr* b, expr* lca) {
+        if (a->get_id() > b->get_id())
+            std::swap(a, b);
+        inference& inf = *m_tmp_inference;
+        inf.a = a;
+        inf.b = b;
+        inf.c = lca;
+        inf.is_cc = false;
+        insert();
+    }
+
+    void ackerman::insert(app* a, app* b) {
+        if (a->get_id() > b->get_id())
+            std::swap(a, b);
+        inference& inf = *m_tmp_inference;
+        inf.a = a;
+        inf.b = b;
+        inf.c = nullptr;
+        inf.is_cc = true;
+        insert();
+    }
+
+    void ackerman::remove_from_queue(inference* inf) {
+        if (m_queue->m_next == m_queue) {
+            SASSERT(inf == m_queue);
+            m_queue = nullptr;
+            return;
+        }            
+        if (m_queue == inf) 
+            m_queue = inf->m_next;
+        auto* next = inf->m_next;
+        auto* prev = inf->m_prev;
+        prev->m_next = next;
+        next->m_prev = prev;        
+    }
+
+    void ackerman::push_to_front(inference* inf) {
+        if (!m_queue) {
+            m_queue = inf;
+        }
+        else if (m_queue != inf) {
+            auto* next = inf->m_next;
+            auto* prev = inf->m_prev;
+            prev->m_next = next;
+            next->m_prev = prev;
+            inf->m_prev = m_queue->m_prev;
+            inf->m_next = m_queue;
+            m_queue->m_prev = inf;
+        }
+    }
+
+    void ackerman::insert() {
+        inference* inf = m_tmp_inference;
+        inference* other = m_table.insert_if_not_there(inf);
+        if (other == inf) {
+            m.inc_ref(inf->a);
+            m.inc_ref(inf->b);
+            m.inc_ref(inf->c);
+        }
+        else 
+            new_tmp();        
+        other->m_count++;
+        push_to_front(other);
+    }
+
+    void ackerman::remove(inference* inf) {
+        remove_from_queue(inf);
+        m_table.erase(inf);
+        m.dec_ref(inf->a);
+        m.dec_ref(inf->b);
+        m.dec_ref(inf->c);
+        dealloc(inf);
+    }
+
+    void ackerman::new_tmp() {
+        m_tmp_inference = alloc(inference);
+        m_tmp_inference->m_next = m_tmp_inference->m_prev = m_tmp_inference;
+        m_tmp_inference->m_count = 0;
+    }
+
+    void ackerman::cg_conflict_eh(expr * n1, expr * n2) {
+        if (s.m_config.m_dack != DACK_ROOT)
+            return;
+        if (!is_app(n1) || !is_app(n2))
+            return;
+        app* a = to_app(n1);
+        app* b = to_app(n2);
+        if (a->get_decl() != b->get_decl() || a->get_num_args() != b->get_num_args())
+            return;
+        insert(a, b);
+        gc();
+    }
+
+    void ackerman::used_eq_eh(expr* a, expr* b, expr* c) {
+        if (!s.m_config.m_dack_eq)
+            return;
+        if (a == b || a == c || b == c)
+            return;
+        insert(a, b, c);
+        gc();
+    }
+        
+    void ackerman::used_cc_eh(app* a, app* b) {
+        if (s.m_config.m_dack != DACK_CR)
+            return;
+        SASSERT(a->get_decl() == b->get_decl());
+        SASSERT(a->get_num_args() == b->get_num_args());        
+        insert(a, b);
+        gc();
+    }
+
+    void ackerman::gc() {
+        m_num_propagations_since_last_gc++;
+        if (m_num_propagations_since_last_gc <= s.m_config.m_dack_gc) 
+            return;
+        m_num_propagations_since_last_gc = 0;
+        
+        while (m_table.size() > m_gc_threshold) 
+            remove(m_queue->m_prev);     
+
+        m_gc_threshold *= 110;
+        m_gc_threshold /= 100;
+        m_gc_threshold++;
+    }
+
+    void ackerman::propagate() {
+        SASSERT(s.s().at_base_lvl());
+        auto* n = m_queue;
+        inference* k = nullptr;
+        unsigned num_prop = static_cast<unsigned>(s.s().stats().m_conflict * s.m_config.m_dack_factor);
+        num_prop = std::min(num_prop, m_table.size());
+        for (unsigned i = 0; i < num_prop; ++i, n = k) {
+            k = n->m_next;
+            if (n->m_count < s.m_config.m_dack_threshold) 
+                continue;
+            if (n->is_cc) 
+                add_cc(n->a, n->b);
+            else 
+                add_eq(n->a, n->b, n->c);           
+            remove(n);
+        }
+    }
+
+    void ackerman::add_cc(expr* _a, expr* _b) {
+        app* a = to_app(_a);
+        app* b = to_app(_b);
+        sat::literal_vector lits;
+        unsigned sz = a->get_num_args();
+        for (unsigned i = 0; i < sz; ++i) {
+            expr_ref eq(m.mk_eq(a->get_arg(i), b->get_arg(i)), m);
+            sat::literal lit = s.internalize(eq, true, false);
+            lits.push_back(~lit);
+        }
+        expr_ref eq(m.mk_eq(a, b), m);
+        lits.push_back(s.internalize(eq, false, false));
+        s.s().mk_clause(lits, true);
+    }
+
+    void ackerman::add_eq(expr* a, expr* b, expr* c) {
+        sat::literal lits[3];
+        expr_ref eq1(m.mk_eq(a, c), m);
+        expr_ref eq2(m.mk_eq(b, c), m);
+        expr_ref eq3(m.mk_eq(a, b), m);
+        lits[0] = s.internalize(eq1, true, false);
+        lits[1] = s.internalize(eq2, true, false);
+        lits[2] = s.internalize(eq3, false, false);
+        s.s().mk_clause(3, lits, true);
+    }
+}
diff --git a/src/sat/smt/euf_ackerman.h b/src/sat/smt/euf_ackerman.h
new file mode 100644
index 000000000..eeed7639c
--- /dev/null
+++ b/src/sat/smt/euf_ackerman.h
@@ -0,0 +1,89 @@
+/*++
+Copyright (c) 2020 Microsoft Corporation
+
+Module Name:
+
+    euf_ackerman.h
+
+Abstract:
+
+    Ackerman reduction plugin for EUF
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2020-08-25
+
+--*/
+#pragma once
+
+#include "ast/euf/euf_egraph.h"
+#include "sat/smt/atom2bool_var.h"
+#include "sat/smt/sat_th.h"
+
+namespace euf {
+
+    class solver;
+
+    class ackerman {
+
+        struct inference {
+            bool is_cc;
+            expr* a, *b, *c;
+            inference* m_next{ nullptr };
+            inference* m_prev{ nullptr };
+            unsigned   m_count{ 0 };
+            inference():is_cc(false), a(nullptr), b(nullptr), c(nullptr) {}
+            inference(app* a, app* b):is_cc(true), a(a), b(b), c(nullptr) {}
+            inference(expr* a, expr* b, expr* c):is_cc(false), a(a), b(b), c(c) {}
+        };
+
+        struct inference_eq {
+            bool operator()(inference const* a, inference const* b) const {
+                return a->is_cc == b->is_cc && a->a == b->a && a->b == b->b && a->c == b->c;
+            }
+        };
+        
+        struct inference_hash {
+            unsigned operator()(inference const* a) const {
+                SASSERT(a->a && a->b);
+                return mk_mix(a->a->get_id(), a->b->get_id(), a->c ? a->c->get_id() : 0);
+            }
+        };
+
+        typedef hashtable<inference*, inference_hash, inference_eq> table_t;
+
+        solver&       s;
+        ast_manager&  m;
+        table_t       m_table;
+        inference*    m_queue { nullptr };
+        inference*    m_tmp_inference { nullptr };
+        unsigned      m_gc_threshold { 1 };
+        unsigned      m_propagate_threshold { 0 };
+        unsigned      m_num_propagations_since_last_gc { 0 };
+ 
+        void reset();
+        void new_tmp();
+        void insert(expr* a, expr* b, expr* lca);
+        void insert(app* a, app* b);
+        void insert();
+        void remove(inference* inf);
+        void add_cc(expr* a, expr* b);
+        void add_eq(expr* a, expr* b, expr* c);        
+        void gc();
+        void push_to_front(inference* inf);        
+        void remove_from_queue(inference* inf);
+
+    public:
+        ackerman(solver& s, ast_manager& m);
+        ~ackerman();
+
+        void cg_conflict_eh(expr * n1, expr * n2);
+                   
+        void used_eq_eh(expr* a, expr* b, expr* lca);
+        
+        void used_cc_eh(app* a, app* b);
+
+        void propagate();
+    };
+
+};
diff --git a/src/sat/smt/euf_model.cpp b/src/sat/smt/euf_model.cpp
new file mode 100644
index 000000000..048030636
--- /dev/null
+++ b/src/sat/smt/euf_model.cpp
@@ -0,0 +1,138 @@
+/*++
+Copyright (c) 2020 Microsoft Corporation
+
+Module Name:
+
+    euf_model.cpp
+
+Abstract:
+
+    Model building for EUF solver plugin.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2020-08-25
+
+--*/
+
+#include "ast/ast_pp.h"
+#include "sat/smt/euf_solver.h"
+#include "model/value_factory.h"
+
+namespace euf {
+
+    void solver::update_model(model_ref& mdl) {
+        deps_t deps;
+        expr_ref_vector values(m);
+        collect_dependencies(deps);
+        deps.topological_sort();
+        dependencies2values(deps, values, mdl);
+        values2model(deps, values, mdl);
+    }
+
+    sat::th_model_builder* solver::get_model_builder(expr* e) const {
+        if (is_app(e))
+            return get_model_builder(to_app(e)->get_decl());
+        return nullptr;
+    }
+
+    sat::th_model_builder* solver::get_model_builder(func_decl* f) const {
+        return m_id2model_builder.get(f->get_family_id(), nullptr);
+    }
+
+    bool solver::include_func_interp(func_decl* f) const {
+        if (f->get_family_id() == null_family_id)
+            return true;
+        sat::th_model_builder* mb = get_model_builder(f);
+        return mb && mb->include_func_interp(f);
+    }
+
+    void solver::collect_dependencies(deps_t& deps) {
+        for (enode* n : m_egraph.nodes()) {
+            if (n->num_args() == 0) {
+                deps.insert(n, nullptr);
+                continue;
+            }
+            auto* mb = get_model_builder(n->get_owner());
+            if (mb)
+                mb->add_dep(n, deps);
+            else
+                deps.insert(n, nullptr);
+        }
+    }
+
+    void solver::dependencies2values(deps_t& deps, expr_ref_vector& values, model_ref const& mdl) {
+        user_sort_factory user_sort(m);
+        for (enode* n : deps.top_sorted()) {
+            unsigned id = n->get_root_id();
+            if (values.get(id, nullptr))
+                continue;
+            expr* e = n->get_owner();
+            values.reserve(id + 1);
+            if (m.is_bool(e) && is_uninterp_const(e) && mdl->get_const_interp(to_app(e)->get_decl())) {
+                values.set(id, mdl->get_const_interp(to_app(e)->get_decl()));
+                continue;
+            }
+            // model of s() must have been fixed.
+            if (m.is_bool(e)) {
+                switch (s().value(m_expr2var.to_bool_var(e))) {
+                case l_true:
+                    values.set(id, m.mk_true());
+                    break;
+                case l_false:
+                    values.set(id, m.mk_false());
+                    break;
+                default:
+                    break;
+                }
+                continue;
+            }
+            auto* mb = get_model_builder(e);
+            if (mb) 
+                mb->add_value(n, values);
+            else if (m.is_uninterp(m.get_sort(e))) {
+                expr* v = user_sort.get_fresh_value(m.get_sort(e));
+                values.set(id, v);
+            }
+            else {
+                IF_VERBOSE(1, verbose_stream() << "no model values created for " << mk_pp(e, m) << "\n");
+            }                
+        }
+    }
+
+    void solver::values2model(deps_t const& deps, expr_ref_vector const& values, model_ref& mdl) {
+        ptr_vector<expr> args;
+        for (enode* n : deps.top_sorted()) {
+            expr* e = n->get_owner();
+            if (!is_app(e))
+                continue;
+            app* a = to_app(e);
+            func_decl* f = a->get_decl();
+            if (!include_func_interp(f))
+                continue;
+            if (m.is_bool(e) && is_uninterp_const(e) && mdl->get_const_interp(f))
+                continue;
+            expr* v = values.get(n->get_root_id());
+            unsigned arity = f->get_arity();
+            if (arity == 0) 
+                mdl->register_decl(f, v);
+            else {
+                auto* fi = mdl->get_func_interp(f);
+                if (!fi) {                    
+                    fi = alloc(func_interp, m, arity);
+                    mdl->register_decl(f, fi);
+                }
+                args.reset();
+                for (enode* arg : enode_args(n)) 
+                    args.push_back(values.get(arg->get_root_id()));
+                if (!fi->get_entry(args.c_ptr()))
+                    fi->insert_new_entry(args.c_ptr(), v);
+            }
+        }
+    }
+
+    void solver::register_macros(model& mdl) {
+        // TODO
+    }
+
+}
diff --git a/src/sat/euf/euf_solver.cpp b/src/sat/smt/euf_solver.cpp
similarity index 83%
rename from src/sat/euf/euf_solver.cpp
rename to src/sat/smt/euf_solver.cpp
index ed5129a52..7846a6436 100644
--- a/src/sat/euf/euf_solver.cpp
+++ b/src/sat/smt/euf_solver.cpp
@@ -16,15 +16,19 @@ Author:
 --*/
 
 #include "ast/pb_decl_plugin.h"
-#include "sat/smt/sat_smt.h"
-#include "sat/ba/ba_solver.h"
-#include "sat/ba/ba_internalize.h"
-#include "sat/euf/euf_solver.h"
-#include "sat/sat_solver.h"
 #include "tactic/tactic_exception.h"
+#include "sat/sat_solver.h"
+#include "sat/smt/sat_smt.h"
+#include "sat/smt/ba_solver.h"
+#include "sat/smt/ba_internalize.h"
+#include "sat/smt/euf_solver.h"
 
 namespace euf {
 
+    void solver::updt_params(params_ref const& p) {
+        m_config.updt_params(p);
+    }
+
     /**
     * retrieve extension that is associated with Boolean variable.
     */
@@ -55,9 +59,10 @@ namespace euf {
                 auto* ba = alloc(sat::ba_solver);
                 ba->set_solver(m_solver);
                 add_extension(pb.get_family_id(), ba);
-                auto* bai = alloc(sat::ba_internalize, *ba, s(), m);
+                auto* bai = alloc(sat::ba_internalize, *ba, s(), si, m);
                 m_id2internalize.setx(pb.get_family_id(), bai, nullptr);
                 m_internalizers.push_back(bai);
+                m_decompilers.push_back(alloc(sat::ba_decompile, *ba, s(), m));
                 ba->push_scopes(s().num_scopes());
                 return ba;
             }
@@ -74,12 +79,12 @@ namespace euf {
     void solver::get_antecedents(literal l, ext_justification_idx idx, literal_vector& r) {
         auto* ext = sat::index_base::to_extension(idx);
         if (ext == this)
-            get_antecedents(l, *euf_base::from_idx(idx), r);
+            get_antecedents(l, *constraint::from_idx(idx), r);
         else
             ext->get_antecedents(l, idx, r);
     }
 
-    void solver::get_antecedents(literal l, euf_base& j, literal_vector& r) {
+    void solver::get_antecedents(literal l, constraint& j, literal_vector& r) {
         m_explain.reset();
         euf::enode* n = nullptr;
         bool sign = false;
@@ -90,6 +95,8 @@ namespace euf {
             sign = l.sign() != p.second;
         }
 
+        // init_ackerman();
+
         switch (j.id()) {
         case 0:
             SASSERT(m_egraph.inconsistent());
@@ -144,6 +151,9 @@ namespace euf {
         }
         for (euf::enode* eq : m_egraph.new_eqs()) {
             bool_var v = m_expr2var.to_bool_var(eq->get_owner());
+            expr* a = nullptr, *b = nullptr;
+            if (s().value(v) == l_false && m_ackerman && m.is_eq(eq->get_owner(), a, b))
+                m_ackerman->cg_conflict_eh(a, b);
             s().assign(literal(v, false), sat::justification::mk_ext_justification(s().scope_lvl(), m_eq_idx.to_index()));
         }
         for (euf::enode* p : m_egraph.new_lits()) {
@@ -152,7 +162,10 @@ namespace euf {
             SASSERT(m.is_bool(e));
             SASSERT(m.is_true(p->get_root()->get_owner()) || sign);
             bool_var v = m_expr2var.to_bool_var(e);
-            s().assign(literal(v, sign), sat::justification::mk_ext_justification(s().scope_lvl(), m_lit_idx.to_index()));
+            literal lit(v, sign);
+            if (s().value(lit) == l_false && m_ackerman) 
+                m_ackerman->cg_conflict_eh(p->get_owner(), p->get_root()->get_owner());
+            s().assign(lit, sat::justification::mk_ext_justification(s().scope_lvl(), m_lit_idx.to_index()));
         }
     }
 
@@ -204,6 +217,8 @@ namespace euf {
     void solver::simplify() {
         for (auto* e : m_extensions)
             e->simplify();
+        if (m_ackerman)
+            m_ackerman->propagate();
     }
 
     void solver::clauses_modifed() {
@@ -243,12 +258,14 @@ namespace euf {
         m_egraph.collect_statistics(st);
         for (auto* e : m_extensions)
             e->collect_statistics(st);
+        st.update("euf dynack", m_stats.m_num_dynack);
     }
 
     solver* solver::copy_core() {
         ast_manager& to = m_translate ? m_translate->to() : m;
         atom2bool_var& a2b = m_translate_expr2var ? *m_translate_expr2var : m_expr2var;
-        auto* r = alloc(solver, to, a2b);
+        auto* r = alloc(solver, to, a2b, si);
+        r->m_config = m_config;
         std::function<void*(void*)> copy_justification = [&](void* x) { return (void*)(r->base_ptr() + ((unsigned*)x - base_ptr())); };
         r->m_egraph.copy_from(m_egraph, copy_justification);
         return r;
@@ -325,6 +342,23 @@ namespace euf {
         return w; 
     }
 
+    void solver::init_ackerman() {
+        if (m_ackerman) 
+            return;
+        if (m_config.m_dack == DACK_DISABLED)
+            return;
+        m_ackerman = alloc(ackerman, *this, m);
+        std::function<void(expr*,expr*,expr*)> used_eq = [&](expr* a, expr* b, expr* lca) {
+            m_ackerman->used_eq_eh(a, b, lca);
+        };
+        std::function<void(app*,app*)> used_cc = [&](app* a, app* b) {
+            m_ackerman->used_cc_eh(a, b);
+        };
+        m_egraph.set_used_eq(used_eq);
+        m_egraph.set_used_cc(used_cc);
+    }
+
+
     sat::th_internalizer* solver::get_internalizer(expr* e) {
         if (is_app(e))
             return m_id2internalize.get(to_app(e)->get_family_id(), nullptr);
@@ -334,25 +368,19 @@ namespace euf {
         }
         return nullptr;
     }
-
-    sat::th_model_builder* solver::get_model_builder(expr* e) {
-        if (is_app(e))
-            return m_id2model_builder.get(to_app(e)->get_family_id(), nullptr);
-        return nullptr;
-    }
    
-    sat::literal solver::internalize(sat::sat_internalizer& si, expr* e, bool sign, bool root) {
+    sat::literal solver::internalize(expr* e, bool sign, bool root) {
         auto* ext = get_internalizer(e);
         if (ext)
-            return ext->internalize(si, e, sign, root);
+            return ext->internalize(e, sign, root);
         if (!m_true) {
-            m_true = visit(si, m.mk_true());
-            m_false = visit(si, m.mk_false());
+            m_true  = visit(m.mk_true());
+            m_false = visit(m.mk_false());
         }
         SASSERT(!si.is_bool_op(e));
         sat::scoped_stack _sc(m_stack);
         unsigned sz = m_stack.size();
-        euf::enode* n = visit(si, e);
+        euf::enode* n = visit(e);
         while (m_stack.size() > sz) {
         loop:
             if (!m.inc())
@@ -368,7 +396,7 @@ namespace euf {
             while (fr.m_idx < num) {
                 expr* arg = to_app(e)->get_arg(fr.m_idx);
                 fr.m_idx++;
-                n = visit(si, arg);
+                n = visit(arg);
                 if (!n)
                     goto loop;
             }
@@ -376,13 +404,13 @@ namespace euf {
             for (unsigned i = 0; i < num; ++i)
                 m_args.push_back(m_egraph.find(to_app(e)->get_arg(i)));
             n = m_egraph.mk(e, num, m_args.c_ptr());
-            attach_bool_var(si, n);
+            attach_bool_var(n);
         }        
         SASSERT(m_egraph.find(e));
         return literal(m_expr2var.to_bool_var(e), sign);
     }
 
-    euf::enode* solver::visit(sat::sat_internalizer& si, expr* e) {
+    euf::enode* solver::visit(expr* e) {
         euf::enode* n = m_egraph.find(e);
         if (n)
             return n;
@@ -399,11 +427,11 @@ namespace euf {
             return nullptr;
         }
         n = m_egraph.mk(e, 0, nullptr);
-        attach_bool_var(si, n);
+        attach_bool_var(n);
         return n;
     }
 
-    void solver::attach_bool_var(sat::sat_internalizer& si, euf::enode* n) {
+    void solver::attach_bool_var(euf::enode* n) {
         expr* e = n->get_owner();
         if (m.is_bool(e)) {
             sat::bool_var v = si.add_bool_var(e);
@@ -420,6 +448,18 @@ namespace euf {
         m_bool_var_trail.push_back(v);
     }
 
+    bool solver::to_formulas(std::function<expr_ref(sat::literal)>& l2e, expr_ref_vector& fmls) {
+        for (auto* th : m_decompilers) {            
+            if (!th->to_formulas(l2e, fmls))
+                return false;
+        }
+        for (euf::enode* n : m_egraph.nodes()) {
+            if (!n->is_root()) 
+                fmls.push_back(m.mk_eq(n->get_owner(), n->get_root()->get_owner()));            
+        }
+        return true;
+    }
+
     bool solver::extract_pb(std::function<void(unsigned sz, literal const* c, unsigned k)>& card,
                             std::function<void(unsigned sz, literal const* c, unsigned const* coeffs, unsigned k)>& pb) {
         if (m_true)
diff --git a/src/sat/euf/euf_solver.h b/src/sat/smt/euf_solver.h
similarity index 55%
rename from src/sat/euf/euf_solver.h
rename to src/sat/smt/euf_solver.h
index f2aa26059..537a0b665 100644
--- a/src/sat/euf/euf_solver.h
+++ b/src/sat/smt/euf_solver.h
@@ -17,12 +17,14 @@ Author:
 #pragma once
 
 #include "util/scoped_ptr_vector.h"
-#include "sat/sat_extension.h"
-#include "ast/euf/euf_egraph.h"
 #include "ast/ast_translation.h"
+#include "ast/euf/euf_egraph.h"
+#include "smt/params/smt_params.h"
+#include "tactic/model_converter.h"
+#include "sat/sat_extension.h"
 #include "sat/smt/atom2bool_var.h"
 #include "sat/smt/sat_th.h"
-#include "tactic/model_converter.h"
+#include "sat/smt/euf_ackerman.h"
 
 namespace euf {
     typedef sat::literal literal;
@@ -31,66 +33,89 @@ namespace euf {
     typedef sat::literal_vector literal_vector;
     typedef sat::bool_var bool_var;
 
-    class euf_base : public sat::index_base {
+    class constraint : public sat::index_base {
         unsigned m_id;
     public:
-        euf_base(sat::extension* e, unsigned id) :
+        constraint(sat::extension* e, unsigned id) :
             index_base(e), m_id(id)
         {}
         unsigned id() const { return m_id; }
-        static euf_base* from_idx(size_t z) { return reinterpret_cast<euf_base*>(z); }
+        static constraint* from_idx(size_t z) { return reinterpret_cast<constraint*>(z); }
     };
 
-    class solver : public sat::extension, public sat::th_internalizer {
-        ast_manager& m;
-        atom2bool_var&        m_expr2var;
-        euf::egraph           m_egraph;
-        sat::solver*          m_solver;
-        sat::lookahead*       m_lookahead;
-        ast_translation*      m_translate;
-        atom2bool_var*        m_translate_expr2var;
+    class solver : public sat::extension, public sat::th_internalizer, public sat::th_decompile {
+        typedef top_sort<euf::enode> deps_t;
+        friend class ackerman;
+        struct stats {
+            unsigned m_num_dynack;
+            stats() { reset(); }
+            void reset() { memset(this, 0, sizeof(*this)); }
+        };
 
-        euf::enode*           m_true;
-        euf::enode*           m_false;
-        svector<euf::enode_bool_pair> m_var2node;
-        ptr_vector<unsigned>  m_explain;
-        euf::enode_vector     m_args;
-        svector<sat::frame>   m_stack;
-        unsigned              m_num_scopes { 0 };
-        unsigned_vector       m_bool_var_trail;
-        unsigned_vector       m_bool_var_lim;
-        scoped_ptr_vector<sat::extension> m_extensions;
-        ptr_vector<sat::extension>        m_id2extension;
-        ptr_vector<sat::th_internalizer>  m_id2internalize;
-        scoped_ptr_vector<sat::th_internalizer>        m_internalizers;
-        scoped_ptr_vector<sat::th_model_builder>       m_model_builders;
-        ptr_vector<sat::th_model_builder>              m_id2model_builder;
-        euf_base              m_conflict_idx, m_eq_idx, m_lit_idx;
+        ast_manager&          m;
+        atom2bool_var&        m_expr2var;
+        sat::sat_internalizer& si;
+        smt_params            m_config;
+        euf::egraph           m_egraph;
+        stats                 m_stats;
+        sat::solver*          m_solver { nullptr };
+        sat::lookahead*       m_lookahead { nullptr };
+        ast_translation*      m_translate { nullptr };
+        atom2bool_var*        m_translate_expr2var { nullptr };
+        scoped_ptr<ackerman>  m_ackerman;
+
+        euf::enode*           m_true { nullptr };
+        euf::enode*           m_false { nullptr };
+        svector<euf::enode_bool_pair>                   m_var2node;
+        ptr_vector<unsigned>                            m_explain;
+        euf::enode_vector                               m_args;
+        svector<sat::frame>                             m_stack;
+        unsigned                                        m_num_scopes { 0 };
+        unsigned_vector                                 m_bool_var_trail;
+        unsigned_vector                                 m_bool_var_lim;
+        scoped_ptr_vector<sat::extension>               m_extensions;
+        ptr_vector<sat::extension>                      m_id2extension;
+        ptr_vector<sat::th_internalizer>                m_id2internalize;
+        scoped_ptr_vector<sat::th_internalizer>         m_internalizers;
+        scoped_ptr_vector<sat::th_model_builder>        m_model_builders;
+        ptr_vector<sat::th_model_builder>               m_id2model_builder;
+        scoped_ptr_vector<sat::th_decompile>            m_decompilers;
+        constraint              m_conflict_idx, m_eq_idx, m_lit_idx;
 
         sat::solver& s() { return *m_solver; }
         unsigned * base_ptr() { return reinterpret_cast<unsigned*>(this); }
-        euf::enode* visit(sat::sat_internalizer& si, expr* e);
-        void attach_bool_var(sat::sat_internalizer& si, euf::enode* n);
+
+        // internalization
+        sat::th_internalizer* get_internalizer(expr* e);
+        euf::enode* visit(expr* e);
+        void attach_bool_var(euf::enode* n);
         void attach_bool_var(sat::bool_var v, bool sign, euf::enode* n);
         solver* copy_core();
+
+        // extensions
         sat::extension* get_extension(sat::bool_var v);
         sat::extension* get_extension(expr* e);
         void add_extension(family_id fid, sat::extension* e);
-        sat::th_internalizer* get_internalizer(expr* e);
+        void init_ackerman();
 
-        sat::th_model_builder* get_model_builder(expr* e);
+        // model building
+        bool include_func_interp(func_decl* f) const;
+        sat::th_model_builder* get_model_builder(expr* e) const;
+        sat::th_model_builder* get_model_builder(func_decl* f) const;
+        void register_macros(model& mdl);
+        void dependencies2values(deps_t& deps, expr_ref_vector& values, model_ref const& mdl);
+        void collect_dependencies(deps_t& deps);        
+        void values2model(deps_t const& deps, expr_ref_vector const& values, model_ref& mdl);
 
+        // solving
         void propagate();
-        void get_antecedents(literal l, euf_base& j, literal_vector& r);
-
-        void dependencies2values(sat::th_dependencies& deps, expr_ref_vector& values);
-        void collect_dependencies(sat::th_dependencies& deps);        
-        void sort_dependencies(sat::th_dependencies& deps);
+        void get_antecedents(literal l, constraint& j, literal_vector& r);
 
     public:
-        solver(ast_manager& m, atom2bool_var& expr2var):
+       solver(ast_manager& m, atom2bool_var& expr2var, sat::sat_internalizer& si, params_ref const& p = params_ref()):
             m(m),
             m_expr2var(expr2var),
+            si(si),
             m_egraph(m),
             m_solver(nullptr),
             m_lookahead(nullptr),
@@ -101,9 +126,13 @@ namespace euf {
             m_conflict_idx(this, 0),
             m_eq_idx(this, 1),
             m_lit_idx(this, 2)
-        {}
+        {
+            updt_params(p);
+        }
+
         ~solver() override {}
 
+        void updt_params(params_ref const& p);
         void set_solver(sat::solver* s) override { m_solver = s; }
         void set_lookahead(sat::lookahead* s) override { m_lookahead = s; }
         struct scoped_set_translate {
@@ -143,11 +172,9 @@ namespace euf {
         bool extract_pb(std::function<void(unsigned sz, literal const* c, unsigned k)>& card,
                         std::function<void(unsigned sz, literal const* c, unsigned const* coeffs, unsigned k)>& pb) override;
 
-
-        sat::literal internalize(sat::sat_internalizer& si, expr* e, bool sign, bool root) override;
-        model_converter* get_model();
-
-        
-
+        bool to_formulas(std::function<expr_ref(sat::literal)>& l2e, expr_ref_vector& fmls);
+        sat::literal internalize(expr* e, bool sign, bool root) override;
+        void update_model(model_ref& mdl);
+       
     };
 };
diff --git a/src/sat/smt/sat_th.cpp b/src/sat/smt/sat_th.cpp
deleted file mode 100644
index 22c59fd2e..000000000
--- a/src/sat/smt/sat_th.cpp
+++ /dev/null
@@ -1,37 +0,0 @@
-/*++
-Copyright (c) 2020 Microsoft Corporation
-
-Module Name:
-
-    sat_th.cpp
-
-Abstract:
-
-    Theory plugins
-
-Author:
-
-    Nikolaj Bjorner (nbjorner) 2020-08-25
-
---*/
-#include "sat/smt/sat_th.h"
-#include "util/top_sort.h"
-
-namespace sat {
-    
-    /*
-     * \brief add dependency: dst depends on src.
-     */
-    void th_dependencies::add(euf::enode* src, euf::enode* dst) {
-        
-    }
-    
-    /*
-     * \brief sort dependencies.
-     */
-    void th_dependencies::sort() {
-        top_sort<euf::enode> top;
-        
-    }
-
-}
diff --git a/src/sat/smt/sat_th.h b/src/sat/smt/sat_th.h
index 9c0f92dd7..1497ee6b5 100644
--- a/src/sat/smt/sat_th.h
+++ b/src/sat/smt/sat_th.h
@@ -16,33 +16,26 @@ Author:
 --*/
 #pragma once
 
+#include "util/top_sort.h"
 #include "sat/smt/sat_smt.h"
 #include "ast/euf/euf_egraph.h"
 
 namespace sat {
     
-
-    class th_dependencies {
-    public:
-        th_dependencies() {}
-        euf::enode * const* begin() const { return nullptr; }
-        euf::enode * const* end() const { return nullptr; }
-
-        /*
-         * \brief add dependency: dst depends on src.
-         */
-        void add(euf::enode* src, euf::enode* dst);
-
-        /*
-         * \brief sort dependencies.
-         */
-        void sort();
-    };
-
     class th_internalizer {
     public:
-        virtual literal internalize(sat_internalizer& si, expr* e, bool sign, bool root) = 0;
         virtual ~th_internalizer() {}
+
+        virtual literal internalize(expr* e, bool sign, bool root) = 0;
+
+
+    };
+
+    class th_decompile {
+    public:
+        virtual ~th_decompile() {}
+
+        virtual bool to_formulas(std::function<expr_ref(sat::literal)>& lit2expr, expr_ref_vector& fmls) = 0;
     };
 
     class th_model_builder {
@@ -59,7 +52,12 @@ namespace sat {
         /**
            \brief compute dependencies for node n
          */
-        virtual void add_dep(euf::enode* n, th_dependencies& dep) = 0;
+        virtual void add_dep(euf::enode* n, top_sort<euf::enode>& dep) = 0;
+
+        /**
+           \brief should function be included in model.
+        */
+        virtual bool include_func_interp(func_decl* f) const { return false; }
     };
 
 
diff --git a/src/sat/tactic/CMakeLists.txt b/src/sat/tactic/CMakeLists.txt
index 434fe854c..d1924d679 100644
--- a/src/sat/tactic/CMakeLists.txt
+++ b/src/sat/tactic/CMakeLists.txt
@@ -7,8 +7,6 @@ z3_add_component(sat_tactic
     tactic
     solver
     sat_smt
-    sat_ba
-    sat_euf
   TACTIC_HEADERS
     sat_tactic.h
 )
diff --git a/src/sat/tactic/goal2sat.cpp b/src/sat/tactic/goal2sat.cpp
index 8dcf2f0ee..c1c3343b1 100644
--- a/src/sat/tactic/goal2sat.cpp
+++ b/src/sat/tactic/goal2sat.cpp
@@ -35,9 +35,9 @@ Notes:
 #include "ast/for_each_expr.h"
 #include "sat/tactic/goal2sat.h"
 #include "sat/sat_cut_simplifier.h"
-#include "sat/ba/ba_internalize.h"
-#include "sat/ba/ba_solver.h"
-#include "sat/euf/euf_solver.h"
+#include "sat/smt/ba_internalize.h"
+#include "sat/smt/ba_solver.h"
+#include "sat/smt/euf_solver.h"
 #include "model/model_evaluator.h"
 #include "model/model_v2_pp.h"
 #include "tactic/tactic.h"
@@ -71,7 +71,6 @@ struct goal2sat::imp : public sat::sat_internalizer {
     bool                        m_default_external;
     bool                        m_xor_solver;
     bool                        m_euf;
-    bool                        m_is_lemma;
 
     
     imp(ast_manager & _m, params_ref const & p, sat::solver_core & s, atom2bool_var & map, dep2asm_map& dep2asm, bool default_external):
@@ -83,8 +82,7 @@ struct goal2sat::imp : public sat::sat_internalizer {
         m_dep2asm(dep2asm),
         m_trail(m),
         m_interpreted_atoms(m),
-        m_default_external(default_external),
-        m_is_lemma(false) {
+        m_default_external(default_external) {
         updt_params(p);
         m_true = sat::null_literal;
         m_aig = s.get_cut_simplifier();
@@ -107,21 +105,19 @@ struct goal2sat::imp : public sat::sat_internalizer {
         m_solver.add_clause(1, &l, false);
     }
 
-    void set_lemma_mode(bool f) { m_is_lemma = f; }
-
     void mk_clause(sat::literal l1, sat::literal l2) override {
         TRACE("goal2sat", tout << "mk_clause: " << l1 << " " << l2 << "\n";);
-        m_solver.add_clause(l1, l2, m_is_lemma);
+        m_solver.add_clause(l1, l2, false);
     }
 
     void mk_clause(sat::literal l1, sat::literal l2, sat::literal l3, bool is_lemma = false) override {
         TRACE("goal2sat", tout << "mk_clause: " << l1 << " " << l2 << " " << l3 << "\n";);
-        m_solver.add_clause(l1, l2, l3, m_is_lemma || is_lemma);
+        m_solver.add_clause(l1, l2, l3, is_lemma);
     }
 
     void mk_clause(unsigned num, sat::literal * lits) {
         TRACE("goal2sat", tout << "mk_clause: "; for (unsigned i = 0; i < num; i++) tout << lits[i] << " "; tout << "\n";);
-        m_solver.add_clause(num, lits, m_is_lemma);
+        m_solver.add_clause(num, lits, false);
     }
 
     sat::literal mk_true() {
@@ -444,7 +440,7 @@ struct goal2sat::imp : public sat::sat_internalizer {
         sat::extension* ext = m_solver.get_extension();
         euf::solver* euf = nullptr;
         if (!ext) {
-            euf = alloc(euf::solver, m, m_map);
+            euf = alloc(euf::solver, m, m_map, *this);
             m_solver.set_extension(euf);
             for (unsigned i = m_solver.num_scopes(); i-- > 0; )
                 euf->push();
@@ -454,7 +450,7 @@ struct goal2sat::imp : public sat::sat_internalizer {
         }
         if (!euf)
             throw default_exception("cannot convert to euf");
-        sat::literal lit = euf->internalize(*this, e, sign, root);
+        sat::literal lit = euf->internalize(e, sign, root);
         if (root)
             m_result_stack.reset();
         if (lit == sat::null_literal)
@@ -478,8 +474,8 @@ struct goal2sat::imp : public sat::sat_internalizer {
         }
         if (!ba)
             throw default_exception("cannot convert to pb");
-        sat::ba_internalize internalize(*ba, m_solver, m);
-        sat::literal lit = internalize.internalize(*this, t, sign, root);
+        sat::ba_internalize internalize(*ba, m_solver, *this, m);
+        sat::literal lit = internalize.internalize(t, sign, root);
         if (root)
             m_result_stack.reset();
         else 
@@ -735,7 +731,13 @@ bool goal2sat::has_unsupported_bool(goal const & g) {
     return test<unsupported_bool_proc>(g);
 }
 
-goal2sat::goal2sat():m_imp(nullptr), m_interpreted_atoms(nullptr) {
+goal2sat::goal2sat():
+    m_imp(nullptr), 
+    m_interpreted_atoms(nullptr) {
+}
+
+goal2sat::~goal2sat() {
+    dealloc(m_imp);
 }
 
 void goal2sat::collect_param_descrs(param_descrs & r) {
@@ -743,25 +745,18 @@ void goal2sat::collect_param_descrs(param_descrs & r) {
     r.insert("ite_extra", CPK_BOOL, "(default: true) add redundant clauses (that improve unit propagation) when encoding if-then-else formulas");
 }
 
-struct goal2sat::scoped_set_imp {
-    goal2sat * m_owner; 
-    scoped_set_imp(goal2sat * o, goal2sat::imp * i):m_owner(o) {
-        m_owner->m_imp = i;        
-    }
-    ~scoped_set_imp() {
-        m_owner->m_imp = nullptr;
-    }
-};
 
-
-void goal2sat::operator()(goal const & g, params_ref const & p, sat::solver_core & t, atom2bool_var & m, dep2asm_map& dep2asm, bool default_external, bool is_lemma) {
-    imp proc(g.m(), p, t, m, dep2asm, default_external);
-    scoped_set_imp set(this, &proc);
-    proc.set_lemma_mode(is_lemma);
-    proc(g);
-    dealloc(m_interpreted_atoms);
+void goal2sat::operator()(goal const & g, params_ref const & p, sat::solver_core & t, atom2bool_var & m, dep2asm_map& dep2asm, bool default_external) {
+    if (!m_imp) 
+        m_imp = alloc(imp, g.m(), p, t, m, dep2asm, default_external);
+        
+    (*m_imp)(g);
     m_interpreted_atoms = alloc(expr_ref_vector, g.m());
-    m_interpreted_atoms->append(proc.m_interpreted_atoms);
+    m_interpreted_atoms->append(m_imp->m_interpreted_atoms);
+    if (!t.get_extension()) {
+        dealloc(m_imp);
+        m_imp = nullptr;
+    }
 }
 
 void goal2sat::get_interpreted_atoms(expr_ref_vector& atoms) {
@@ -948,50 +943,6 @@ struct sat2goal::imp {
         return m_lit2expr.get(l.index());
     }
 
-    void assert_pb(ref<mc>& mc, goal& r, sat::ba_solver::pb const& p) {
-        pb_util pb(m);
-        ptr_buffer<expr> lits;
-        vector<rational> coeffs;
-        for (auto const& wl : p) {
-            lits.push_back(lit2expr(mc, wl.second));
-            coeffs.push_back(rational(wl.first));
-        }
-        rational k(p.k());
-        expr_ref fml(pb.mk_ge(p.size(), coeffs.c_ptr(), lits.c_ptr(), k), m);
-        
-        if (p.lit() != sat::null_literal) {
-            fml = m.mk_eq(lit2expr(mc, p.lit()), fml);            
-        }
-        r.assert_expr(fml);
-    }
-
-    void assert_card(ref<mc>& mc, goal& r, sat::ba_solver::card const& c) {
-        pb_util pb(m);
-        ptr_buffer<expr> lits;
-        for (sat::literal l : c) {
-            lits.push_back(lit2expr(mc, l));
-        }
-        expr_ref fml(pb.mk_at_least_k(c.size(), lits.c_ptr(), c.k()), m);
-        
-        if (c.lit() != sat::null_literal) {
-            fml = m.mk_eq(lit2expr(mc, c.lit()), fml);            
-        }
-        r.assert_expr(fml);
-    }
-
-    void assert_xor(ref<mc>& mc, goal & r, sat::ba_solver::xr const& x) {
-        ptr_buffer<expr> lits;
-        for (sat::literal l : x) {
-            lits.push_back(lit2expr(mc, l));
-        }
-        expr_ref fml(m.mk_xor(x.size(), lits.c_ptr()), m);
-        
-        if (x.lit() != sat::null_literal) {
-            fml = m.mk_eq(lit2expr(mc, x.lit()), fml);            
-        }
-        r.assert_expr(fml);
-    }
-
     void assert_clauses(ref<mc>& mc, sat::solver_core const & s, sat::clause_vector const& clauses, goal & r, bool asserted) {
         ptr_buffer<expr> lits;
         unsigned small_lbd = 3; // s.get_config().m_gc_small_lbd;
@@ -1008,10 +959,6 @@ struct sat2goal::imp {
         }
     }
 
-    sat::ba_solver* get_ba_solver(sat::solver_core const& s) {
-        return dynamic_cast<sat::ba_solver*>(s.get_extension());
-    }
-
     void operator()(sat::solver_core & s, atom2bool_var const & map, goal & r, ref<mc> & mc) {
         if (s.at_base_lvl() && s.inconsistent()) {
             r.assert_expr(m.mk_false());
@@ -1039,21 +986,21 @@ struct sat2goal::imp {
         // collect clauses
         assert_clauses(mc, s, s.clauses(), r, true);
 
-        sat::ba_solver* ext = get_ba_solver(s);
+        auto* ext = s.get_extension();
         if (ext) {
-            for (auto* c : ext->constraints()) {
-                switch (c->tag()) {
-                case sat::ba_solver::card_t: 
-                    assert_card(mc, r, c->to_card());
-                    break;
-                case sat::ba_solver::pb_t: 
-                    assert_pb(mc, r, c->to_pb());
-                    break;
-                case sat::ba_solver::xr_t: 
-                    assert_xor(mc, r, c->to_xr());
-                    break;
-                }
+            std::function<expr_ref(sat::literal)> l2e = [&](sat::literal lit) {
+                return expr_ref(lit2expr(mc, lit), m);
+            };
+            expr_ref_vector fmls(m);
+            sat::ba_solver* ba = dynamic_cast<sat::ba_solver*>(ext);
+            if (ba) {                
+                sat::ba_decompile decompile(*ba, s, m);
+                decompile.to_formulas(l2e, fmls);
             }
+            else 
+                dynamic_cast<euf::solver*>(ext)->to_formulas(l2e, fmls);            
+            for (expr* f : fmls)
+                r.assert_expr(f);            
         }
     }
 
diff --git a/src/sat/tactic/goal2sat.h b/src/sat/tactic/goal2sat.h
index a4c9b90b0..40ccb2e9c 100644
--- a/src/sat/tactic/goal2sat.h
+++ b/src/sat/tactic/goal2sat.h
@@ -38,12 +38,11 @@ Notes:
 class goal2sat {
     struct imp;
     imp *  m_imp;
-    struct scoped_set_imp;
-    expr_ref_vector* m_interpreted_atoms;
+    scoped_ptr<expr_ref_vector> m_interpreted_atoms;
 
 public:
     goal2sat();
-    ~goal2sat() { dealloc(m_interpreted_atoms); }
+    ~goal2sat();
 
     typedef obj_map<expr, sat::literal> dep2asm_map;
 
@@ -61,7 +60,7 @@ public:
        \warning conversion throws a tactic_exception, if it is interrupted (by set_cancel),
        an unsupported operator is found, or memory consumption limit is reached (set with param :max-memory).
     */
-    void operator()(goal const & g, params_ref const & p, sat::solver_core & t, atom2bool_var & m, dep2asm_map& dep2asm, bool default_external = false, bool is_lemma = false);
+    void operator()(goal const & g, params_ref const & p, sat::solver_core & t, atom2bool_var & m, dep2asm_map& dep2asm, bool default_external = false);
 
     void get_interpreted_atoms(expr_ref_vector& atoms);
 
diff --git a/src/shell/dimacs_frontend.cpp b/src/shell/dimacs_frontend.cpp
index 3b82fbd52..9bc723f82 100644
--- a/src/shell/dimacs_frontend.cpp
+++ b/src/shell/dimacs_frontend.cpp
@@ -25,7 +25,6 @@ Revision History:
 #include "sat/dimacs.h"
 #include "sat/sat_params.hpp"
 #include "sat/sat_solver.h"
-#include "sat/ba/ba_solver.h"
 #include "sat/tactic/goal2sat.h"
 #include "ast/reg_decl_plugins.h"
 #include "tactic/tactic.h"
diff --git a/src/smt/params/CMakeLists.txt b/src/smt/params/CMakeLists.txt
index 4beec80f0..31b9b203d 100644
--- a/src/smt/params/CMakeLists.txt
+++ b/src/smt/params/CMakeLists.txt
@@ -11,8 +11,6 @@ z3_add_component(smt_params
     theory_seq_params.cpp
     theory_str_params.cpp
   COMPONENT_DEPENDENCIES
-    ast
-    bit_blaster
     pattern
   PYG_FILES
     smt_params_helper.pyg
diff --git a/src/smt/params/smt_params.h b/src/smt/params/smt_params.h
index 01d83403c..844a9a9b6 100644
--- a/src/smt/params/smt_params.h
+++ b/src/smt/params/smt_params.h
@@ -18,7 +18,6 @@ Revision History:
 --*/
 #pragma once
 
-#include "ast/ast.h"
 #include "smt/params/dyn_ack_params.h"
 #include "smt/params/qi_params.h"
 #include "smt/params/theory_arith_params.h"
diff --git a/src/smt/qi_queue.h b/src/smt/qi_queue.h
index e79b0cfb5..50ba2e1b9 100644
--- a/src/smt/qi_queue.h
+++ b/src/smt/qi_queue.h
@@ -22,8 +22,8 @@ Revision History:
 #include "smt/smt_quantifier_stat.h"
 #include "smt/smt_checker.h"
 #include "smt/smt_quantifier.h"
-#include "smt/params/qi_params.h"
 #include "smt/fingerprints.h"
+#include "smt/params/qi_params.h"
 #include "parsers/util/cost_parser.h"
 #include "smt/cost_evaluator.h"
 #include "smt/cached_var_subst.h"
diff --git a/src/util/top_sort.h b/src/util/top_sort.h
index ec9ee4668..0e4f97af1 100644
--- a/src/util/top_sort.h
+++ b/src/util/top_sort.h
@@ -18,11 +18,11 @@ Revision History:
 
 #pragma once
 
-#include "util/obj_hashtable.h"
-#include "util/vector.h"
 #include<algorithm>
 #include<type_traits>
 #include<memory.h>
+#include "util/obj_hashtable.h"
+#include "util/vector.h"
 #include "util/memory_manager.h"
 
 
@@ -52,12 +52,13 @@ class top_sort {
         else {
             m_dfs_num.insert(f, m_next_preorder++);        
             m_stack_S.push_back(f);
-            m_stack_P.push_back(f);  
-            for (T* g : *m_deps[f]) {
-                traverse(g);
-            }        
-            if (f == m_stack_P.back()) {
-                
+            m_stack_P.push_back(f);
+            if (m_deps[f]) { 
+                for (T* g : *m_deps[f]) {
+                    traverse(g);
+                }        
+            }
+            if (f == m_stack_P.back()) {                
                 p_id = m_top_sorted.size();            
                 T* s_f;
                 do {
@@ -94,7 +95,16 @@ public:
         m_deps.insert(t, s); 
     }
 
-    ptr_vector<T> const& top_sorted() { return m_top_sorted; }    
+    void add(T* t, T* s) {
+        T_set* tb = nullptr;
+        if (!m_deps.find(t, tb)) {
+            tb = alloc(T_set);
+            insert(s, tb);
+        }
+        t->insert(s);
+    }
+
+    ptr_vector<T> const& top_sorted() const { return m_top_sorted; }    
 
     obj_map<T, unsigned> const& partition_ids() const { return m_partition_id; }