diff --git a/src/ast/euf/euf_enode.cpp b/src/ast/euf/euf_enode.cpp
index 0a495cb20..038325790 100644
--- a/src/ast/euf/euf_enode.cpp
+++ b/src/ast/euf/euf_enode.cpp
@@ -142,4 +142,13 @@ namespace euf {
                 return false;
         return true;
     }
+
+    unsigned enode::class_generation() {
+        unsigned gen = m_generation;
+        
+        for (enode* n : enode_class(this)) 
+            gen = std::min(n->generation(), gen);
+        return gen;
+    }
+
 }
diff --git a/src/ast/euf/euf_enode.h b/src/ast/euf/euf_enode.h
index 398b38775..c8f32ba4f 100644
--- a/src/ast/euf/euf_enode.h
+++ b/src/ast/euf/euf_enode.h
@@ -149,6 +149,7 @@ namespace euf {
         void     set_table_id(unsigned t) { m_table_id = t; }
 
         unsigned generation() const { return m_generation; }
+        unsigned class_generation();
 
         void mark1() { m_mark1 = true; }
         void unmark1() { m_mark1 = false; }
diff --git a/src/sat/smt/euf_model.cpp b/src/sat/smt/euf_model.cpp
index cc0107e30..554f44a3c 100644
--- a/src/sat/smt/euf_model.cpp
+++ b/src/sat/smt/euf_model.cpp
@@ -215,6 +215,10 @@ namespace euf {
         return m_values2root;
     }
 
+    expr* solver::node2value(enode* n) const {
+        return m_values.get(n->get_root_id(), nullptr);
+    }
+
     void solver::validate_model(model& mdl) {
         for (enode* n : m_egraph.nodes()) {
             expr* e = n->get_expr();
diff --git a/src/sat/smt/euf_solver.h b/src/sat/smt/euf_solver.h
index 9d62ae4f4..4d583515b 100644
--- a/src/sat/smt/euf_solver.h
+++ b/src/sat/smt/euf_solver.h
@@ -306,6 +306,7 @@ namespace euf {
         bool check_model(sat::model const& m) const override;
         unsigned max_var(unsigned w) const override;
 
+        // proof
         bool use_drat() { return s().get_config().m_drat && (init_drat(), true); }
         sat::drat& get_drat() { return s().get_drat(); }
         void drat_bool_def(sat::bool_var v, expr* n);
@@ -345,6 +346,7 @@ namespace euf {
         // model construction
         void update_model(model_ref& mdl);
         obj_map<expr, enode*> const& values2root();
+        expr* node2value(enode* n) const;
 
         // diagnostics
         func_decl_ref_vector const& unhandled_functions() { return m_unhandled_functions; }
diff --git a/src/sat/smt/q_solver.cpp b/src/sat/smt/q_solver.cpp
index 243734ca6..df3e10d8d 100644
--- a/src/sat/smt/q_solver.cpp
+++ b/src/sat/smt/q_solver.cpp
@@ -183,4 +183,25 @@ namespace q {
         ctx.push(insert_ref2_map<euf::solver, ast_manager, sort, expr>(m, m_unit_table, s, val));
         return val;
     }
+
+    unsigned solver::get_max_generation(expr* e) const {
+        unsigned g = 0;
+        expr_fast_mark1 mark;
+        m_todo.push_back(e);
+        while (!m_todo.empty()) {
+            e = m_todo.back();
+            m_todo.pop_back();
+            if (mark.is_marked(e))
+                continue;
+            mark.mark(e);
+            euf::enode* n = ctx.get_egraph().find(e);
+            if (n) 
+                g = std::max(g, n->generation());
+            else if (is_app(e)) 
+                for (expr* arg : *to_app(e))
+                    m_todo.push_back(arg);
+        }
+        return g;
+    }
+
 }
diff --git a/src/sat/smt/q_solver.h b/src/sat/smt/q_solver.h
index 9cbe98f14..410e1a70c 100644
--- a/src/sat/smt/q_solver.h
+++ b/src/sat/smt/q_solver.h
@@ -44,6 +44,7 @@ namespace q {
         flat_table             m_flat;
         sat::literal_vector    m_universal;
         obj_map<sort, expr*>   m_unit_table;
+        mutable ptr_vector<expr> m_todo;
 
         sat::literal instantiate(quantifier* q, bool negate, std::function<expr* (quantifier*, unsigned)>& mk_var);
         sat::literal skolemize(quantifier* q);
@@ -75,5 +76,7 @@ namespace q {
         ast_manager& get_manager() { return m; }
         sat::literal_vector const& universal() const { return m_universal; }
         quantifier* flatten(quantifier* q);
+
+        unsigned get_max_generation(expr* e) const;
     };
 }
diff --git a/src/sat/smt/sat_th.cpp b/src/sat/smt/sat_th.cpp
index 55f8c1bfc..c52fc13ce 100644
--- a/src/sat/smt/sat_th.cpp
+++ b/src/sat/smt/sat_th.cpp
@@ -221,6 +221,10 @@ namespace euf {
         return n;
     }
 
+    unsigned th_euf_solver::random() {
+        return ctx.s().rand()();
+    }
+
     size_t th_propagation::get_obj_size(unsigned num_lits, unsigned num_eqs) {
         return sat::constraint_base::obj_size(sizeof(th_propagation) + sizeof(sat::literal) * num_lits + sizeof(enode_pair) * num_eqs);
     }
diff --git a/src/sat/smt/sat_th.h b/src/sat/smt/sat_th.h
index e2a0d59c6..b887e6da2 100644
--- a/src/sat/smt/sat_th.h
+++ b/src/sat/smt/sat_th.h
@@ -187,6 +187,8 @@ namespace euf {
         bool is_root(theory_var v) const { return var2enode(v)->is_root(); }
         void push() override { m_num_scopes++; }
         void pop(unsigned n) override;
+
+        unsigned random();
     };