diff --git a/src/duality/duality.h b/src/duality/duality.h
index 479c90a29..e35c97b50 100755
--- a/src/duality/duality.h
+++ b/src/duality/duality.h
@@ -29,6 +29,8 @@ using namespace stl_ext;
 
 namespace Duality {
 
+  class implicant_solver;
+
   /* Generic operations on Z3 formulas */
 
   struct Z3User {
@@ -80,6 +82,8 @@ namespace Duality {
 
       Term SubstAtom(hash_map<ast, Term> &memo, const expr &t, const expr &atom, const expr &val);
 
+      Term CloneQuantAndSimp(const expr &t, const expr &body);
+
       Term RemoveRedundancy(const Term &t);
 
       Term IneqToEq(const Term &t);
@@ -100,6 +104,9 @@ namespace Duality {
 
       FuncDecl RenumberPred(const FuncDecl &f, int n);
 
+    Term ExtractStores(hash_map<ast, Term> &memo, const Term &t, std::vector<expr> &cnstrs, hash_map<ast,expr> &renaming);
+
+
 protected:
 
       void SummarizeRec(hash_set<ast> &memo, std::vector<expr> &lits, int &ops, const Term &t);
@@ -195,6 +202,9 @@ protected:
 	   /** Is this a background constant? */
 	   virtual bool is_constant(const func_decl &f) = 0;
 
+	   /** Get the constants in the background vocabulary */
+	   virtual hash_set<func_decl> &get_constants() = 0;
+
            /** Assert a background axiom. */
            virtual void assert_axiom(const expr &axiom) = 0;
 
@@ -288,6 +298,11 @@ protected:
 	  return bckg.find(f) != bckg.end();
 	}
 
+	/** Get the constants in the background vocabulary */
+	virtual hash_set<func_decl> &get_constants(){
+	  return bckg;
+	}
+
         ~iZ3LogicSolver(){
           // delete ictx;
           delete islvr;
@@ -598,6 +613,8 @@ protected:
       void FixCurrentState(Edge *root);
     
       void FixCurrentStateFull(Edge *edge, const expr &extra);
+      
+      void FixCurrentStateFull(Edge *edge, const std::vector<expr> &assumps, const hash_map<ast,expr> &renaming);
 
       /** Declare a constant in the background theory. */
 
@@ -940,10 +957,12 @@ protected:
       Term UnderapproxFormula(const Term &f, hash_set<ast> &dont_cares);
 
       void ImplicantFullRed(hash_map<ast,int> &memo, const Term &f, std::vector<Term> &lits,
-			    hash_set<ast> &done, hash_set<ast> &dont_cares);
+			    hash_set<ast> &done, hash_set<ast> &dont_cares, bool extensional = true);
 
-      Term UnderapproxFullFormula(const Term &f, hash_set<ast> &dont_cares);
+    public:
+      Term UnderapproxFullFormula(const Term &f, bool extensional = true);
 
+    protected:
       Term ToRuleRec(Edge *e,  hash_map<ast,Term> &memo, const Term &t, std::vector<expr> &quants);
 
       hash_map<ast,Term> resolve_ite_memo;
@@ -984,6 +1003,8 @@ protected:
 
       void AddEdgeToSolver(Edge *edge);
 
+      void AddEdgeToSolver(implicant_solver &aux_solver, Edge *edge);
+
       void AddToProofCore(hash_set<ast> &core);
 
       void GetGroundLitsUnderQuants(hash_set<ast> *memo, const Term &f, std::vector<Term> &res, int under);
@@ -1049,13 +1070,40 @@ protected:
       
     public:
       
-      struct Counterexample {
+      class Counterexample {
+      private:
 	RPFP *tree;
 	RPFP::Node *root;
+      public:
 	Counterexample(){
 	  tree = 0;
 	  root = 0;
 	}
+	Counterexample(RPFP *_tree, RPFP::Node *_root){
+	  tree = _tree;
+	  root = _root;
+	}
+	~Counterexample(){
+	  if(tree) delete tree;
+	}
+	void swap(Counterexample &other){
+	  std::swap(tree,other.tree);
+	  std::swap(root,other.root);
+	}
+	void set(RPFP *_tree, RPFP::Node *_root){
+	  if(tree) delete tree;
+	  tree = _tree;
+	  root = _root;
+	}
+	void clear(){
+	  if(tree) delete tree;
+	  tree = 0;
+	}
+	RPFP *get_tree() const {return tree;}
+	RPFP::Node *get_root() const {return root;}
+      private:
+	Counterexample &operator=(const Counterexample &);
+	Counterexample(const Counterexample &);
       };
       
       /** Solve the problem. You can optionally give an old
@@ -1065,7 +1113,7 @@ protected:
       
       virtual bool Solve() = 0;
       
-      virtual Counterexample GetCounterexample() = 0;
+      virtual Counterexample &GetCounterexample() = 0;
       
       virtual bool SetOption(const std::string &option, const std::string &value) = 0;
       
@@ -1073,7 +1121,7 @@ protected:
 	  is chiefly useful for abstraction refinement, when we want to
 	  solve a series of similar problems. */
 
-      virtual void LearnFrom(Counterexample &old_cex) = 0;
+      virtual void LearnFrom(Solver *old_solver) = 0;
 
       virtual ~Solver(){}
 
diff --git a/src/duality/duality_rpfp.cpp b/src/duality/duality_rpfp.cpp
index 5751fa890..f3deee225 100755
--- a/src/duality/duality_rpfp.cpp
+++ b/src/duality/duality_rpfp.cpp
@@ -410,6 +410,33 @@ namespace Duality {
     return res;
   }
 
+  Z3User::Term Z3User::ExtractStores(hash_map<ast, Term> &memo, const Term &t, std::vector<expr> &cnstrs, hash_map<ast,expr> &renaming)
+  {
+    std::pair<ast,Term> foo(t,expr(ctx));
+    std::pair<hash_map<ast,Term>::iterator, bool> bar = memo.insert(foo);
+    Term &res = bar.first->second;
+    if(!bar.second) return res;
+    if (t.is_app()) {
+      func_decl f = t.decl();
+      std::vector<Term> args;
+      int nargs = t.num_args();
+      for(int i = 0; i < nargs; i++)
+	args.push_back(ExtractStores(memo, t.arg(i),cnstrs,renaming));
+      res = f(args.size(),&args[0]);
+      if(f.get_decl_kind() == Store){
+	func_decl fresh = ctx.fresh_func_decl("@arr", res.get_sort());
+	expr y = fresh();
+	expr equ = ctx.make(Equal,y,res);
+	cnstrs.push_back(equ);
+	renaming[y] = res;
+	res = y;
+      }
+    }
+    else res = t;
+    return res;
+  }
+
+
   bool Z3User::IsLiteral(const expr &lit, expr &atom, expr &val){
     if(!(lit.is_quantifier() && IsClosedFormula(lit))){
       if(!lit.is_app())
@@ -523,6 +550,25 @@ namespace Duality {
       return foo;
   }
 
+  Z3User::Term Z3User::CloneQuantAndSimp(const expr &t, const expr &body){
+    if(t.is_quantifier_forall() && body.is_app() && body.decl().get_decl_kind() == And){
+      int nargs = body.num_args();
+      std::vector<expr> args(nargs);
+      for(int i = 0; i < nargs; i++)
+	args[i] = CloneQuantAndSimp(t, body.arg(i));
+      return ctx.make(And,args);
+    }
+    if(!t.is_quantifier_forall() && body.is_app() && body.decl().get_decl_kind() == Or){
+      int nargs = body.num_args();
+      std::vector<expr> args(nargs);
+      for(int i = 0; i < nargs; i++)
+	args[i] = CloneQuantAndSimp(t, body.arg(i));
+      return ctx.make(Or,args);
+    }
+    return clone_quantifier(t,body);
+  }
+
+
   Z3User::Term Z3User::SubstAtom(hash_map<ast, Term> &memo, const expr &t, const expr &atom, const expr &val){
     std::pair<ast,Term> foo(t,expr(ctx));
     std::pair<hash_map<ast,Term>::iterator, bool> bar = memo.insert(foo);
@@ -1832,7 +1878,7 @@ namespace Duality {
   }
 
   void RPFP::ImplicantFullRed(hash_map<ast,int> &memo, const Term &f, std::vector<Term> &lits,
-			      hash_set<ast> &done, hash_set<ast> &dont_cares){
+			      hash_set<ast> &done, hash_set<ast> &dont_cares, bool extensional){
     if(done.find(f) != done.end())
       return; /* already processed */
     if(f.is_app()){
@@ -1840,7 +1886,7 @@ namespace Duality {
       decl_kind k = f.decl().get_decl_kind();
       if(k == Implies || k == Iff || k == And || k == Or || k == Not){
 	for(int i = 0; i < nargs; i++)
-	  ImplicantFullRed(memo,f.arg(i),lits,done,dont_cares);
+	  ImplicantFullRed(memo,f.arg(i),lits,done,dont_cares, extensional);
 	goto done;
       }
     }
@@ -1848,6 +1894,15 @@ namespace Duality {
       if(dont_cares.find(f) == dont_cares.end()){
 	int b = SubtermTruth(memo,f);
 	if(b != 0 && b != 1) goto done;
+	if(f.is_app() && f.decl().get_decl_kind() == Equal && f.arg(0).is_array()){
+	  if(b == 1 && !extensional){
+	    expr x = dualModel.eval(f.arg(0)); expr y = dualModel.eval(f.arg(1));
+	    if(!eq(x,y))
+	      b = 0;
+	  }
+	  if(b == 0)
+	    goto done;
+	}
 	expr bv = (b==1) ? f : !f;
 	lits.push_back(bv);
       }
@@ -1969,12 +2024,16 @@ namespace Duality {
     return conjoin(lits);
   }
 
-  RPFP::Term RPFP::UnderapproxFullFormula(const Term &f, hash_set<ast> &dont_cares){
+  RPFP::Term RPFP::UnderapproxFullFormula(const Term &f, bool extensional){
+    hash_set<ast> dont_cares;
+    resolve_ite_memo.clear();
+    timer_start("UnderapproxFormula");
     /* first compute truth values of subterms */
     hash_map<ast,int> memo;
     hash_set<ast> done;
     std::vector<Term> lits;
-    ImplicantFullRed(memo,f,lits,done,dont_cares);
+    ImplicantFullRed(memo,f,lits,done,dont_cares, extensional);
+    timer_stop("UnderapproxFormula");
     /* return conjunction of literals */
     return conjoin(lits);
   }
@@ -2519,22 +2578,6 @@ namespace Duality {
     ConstrainEdgeLocalized(edge,eu);
   }
 
-  void RPFP::FixCurrentStateFull(Edge *edge, const expr &extra){
-    hash_set<ast> dont_cares;
-    resolve_ite_memo.clear();
-    timer_start("UnderapproxFormula");
-    Term dual = edge->dual.null() ? ctx.bool_val(true) : edge->dual;
-    for(unsigned i = 0; i < edge->constraints.size(); i++)
-      dual = dual && edge->constraints[i];
-    // dual = dual && extra;
-    Term eu = UnderapproxFullFormula(dual,dont_cares);
-    timer_stop("UnderapproxFormula");
-    ConstrainEdgeLocalized(edge,eu);
-  }
-
-  
-  
-
   void RPFP::GetGroundLitsUnderQuants(hash_set<ast> *memo, const Term &f, std::vector<Term> &res, int under){
     if(memo[under].find(f) != memo[under].end())
       return;
@@ -2817,7 +2860,91 @@ namespace Duality {
     return ctx.make(And,lits);
   }
 
-    // set up edge constraint in aux solver
+
+  /* This is a wrapper for a solver that is intended to compute
+     implicants from models. It works around a problem in Z3 with
+     models in the non-extensional array theory. It does this by
+     naming all of the store terms in a formula. That is, (store ...)
+     is replaced by "name" with an added constraint name = (store
+     ...). This allows us to determine from the model whether an array
+     equality is true or false (it is false if the two sides are
+     mapped to different function symbols, even if they have the same
+     contents).
+   */
+
+  struct implicant_solver {
+    RPFP *owner;
+    solver &aux_solver;
+    std::vector<expr> assumps, namings;
+    std::vector<int> assump_stack, naming_stack;
+    hash_map<ast,expr> renaming, renaming_memo;
+    
+    void add(const expr &e){
+      expr t = e;
+      if(!aux_solver.extensional_array_theory()){
+	unsigned i = namings.size();
+	t = owner->ExtractStores(renaming_memo,t,namings,renaming);
+	for(; i < namings.size(); i++)
+	  aux_solver.add(namings[i]);
+      }
+      assumps.push_back(t);
+      aux_solver.add(t);
+    }
+
+    void push() {
+      assump_stack.push_back(assumps.size());
+      naming_stack.push_back(namings.size());
+      aux_solver.push();
+    }
+
+    // When we pop the solver, we have to re-add any namings that were lost
+
+    void pop(int n) {
+      aux_solver.pop(n);
+      int new_assumps = assump_stack[assump_stack.size()-n];
+      int new_namings = naming_stack[naming_stack.size()-n];
+      for(unsigned i = new_namings; i < namings.size(); i++)
+	aux_solver.add(namings[i]);
+      assumps.resize(new_assumps);
+      namings.resize(new_namings);
+      assump_stack.resize(assump_stack.size()-1);
+      naming_stack.resize(naming_stack.size()-1);
+    }
+
+    check_result check() {
+      return aux_solver.check();
+    }
+
+    model get_model() {
+      return aux_solver.get_model();
+    }
+    
+    expr get_implicant() {
+      owner->dualModel = aux_solver.get_model();
+      expr dual = owner->ctx.make(And,assumps);
+      bool ext = aux_solver.extensional_array_theory();
+      expr eu = owner->UnderapproxFullFormula(dual,ext);
+      // if we renamed store terms, we have to undo
+      if(!ext)
+	eu = owner->SubstRec(renaming,eu);
+      return eu;
+    }
+    
+    implicant_solver(RPFP *_owner, solver &_aux_solver) 
+      : owner(_owner), aux_solver(_aux_solver)
+      {}
+  };
+
+  // set up edge constraint in aux solver
+  void RPFP::AddEdgeToSolver(implicant_solver &aux_solver, Edge *edge){
+    if(!edge->dual.null())
+      aux_solver.add(edge->dual);
+    for(unsigned i = 0; i < edge->constraints.size(); i++){
+      expr tl = edge->constraints[i];
+      aux_solver.add(tl);
+    }
+  }
+
   void RPFP::AddEdgeToSolver(Edge *edge){
     if(!edge->dual.null())
       aux_solver.add(edge->dual);
@@ -2828,47 +2955,66 @@ namespace Duality {
   }
 
   void RPFP::InterpolateByCases(Node *root, Node *node){
+    timer_start("InterpolateByCases");
     bool axioms_added = false;
-    aux_solver.push();
-    AddEdgeToSolver(node->Outgoing);
+    hash_set<ast> axioms_needed;
+    const std::vector<expr> &theory = ls->get_axioms();
+    for(unsigned i = 0; i < theory.size(); i++)
+      axioms_needed.insert(theory[i]);
+    implicant_solver is(this,aux_solver);
+    is.push();
+    AddEdgeToSolver(is,node->Outgoing);
     node->Annotation.SetEmpty();
     hash_set<ast> *core = new hash_set<ast>;
     core->insert(node->Outgoing->dual);
     while(1){
-      aux_solver.push();
+      is.push();
       expr annot = !GetAnnotation(node);
-      aux_solver.add(annot);
-      if(aux_solver.check() == unsat){
-	aux_solver.pop(1);
+      is.add(annot);
+      if(is.check() == unsat){
+	is.pop(1);
 	break;
       }
-      dualModel = aux_solver.get_model();
-      aux_solver.pop(1);
+      is.pop(1);
       Push();
-      FixCurrentStateFull(node->Outgoing,annot);
-       ConstrainEdgeLocalized(node->Outgoing,!GetAnnotation(node));
+      ConstrainEdgeLocalized(node->Outgoing,is.get_implicant());
+      ConstrainEdgeLocalized(node->Outgoing,!GetAnnotation(node)); //TODO: need this?
       check_result foo = Check(root);
-      if(foo != unsat)
+      if(foo != unsat){
+	slvr().print("should_be_unsat.smt2");
 	throw "should be unsat";
-      AddToProofCore(*core);
+      }
+      std::vector<expr> assumps, axioms_to_add;
+      slvr().get_proof().get_assumptions(assumps);
+      for(unsigned i = 0; i < assumps.size(); i++){
+	(*core).insert(assumps[i]);
+	if(axioms_needed.find(assumps[i]) != axioms_needed.end()){
+	  axioms_to_add.push_back(assumps[i]);
+	  axioms_needed.erase(assumps[i]);
+	}
+      }
+      // AddToProofCore(*core);
       Transformer old_annot = node->Annotation;
       SolveSingleNode(root,node);
 
       {
 	expr itp = GetAnnotation(node);
-	dualModel = aux_solver.get_model();
+	dualModel = is.get_model(); // TODO: what does this mean?
 	std::vector<expr> case_lits;
 	itp = StrengthenFormulaByCaseSplitting(itp, case_lits);
 	SetAnnotation(node,itp);
 	node->Annotation.Formula = node->Annotation.Formula.simplify();
       }
 
+      for(unsigned i = 0; i < axioms_to_add.size(); i++)
+	is.add(axioms_to_add[i]);
+      
       if(node->Annotation.IsEmpty()){
 	if(!axioms_added){
 	  // add the axioms in the off chance they are useful
 	  const std::vector<expr> &theory = ls->get_axioms();
 	  for(unsigned i = 0; i < theory.size(); i++)
-	    aux_solver.add(theory[i]);
+	    is.add(theory[i]);
 	  axioms_added = true;
 	}
 	else {
@@ -2886,7 +3032,8 @@ namespace Duality {
     if(proof_core)
       delete proof_core; // shouldn't happen
     proof_core = core;
-    aux_solver.pop(1);
+    is.pop(1);
+    timer_stop("InterpolateByCases");
   }
 
   void RPFP::Generalize(Node *root, Node *node){
@@ -3187,7 +3334,7 @@ namespace Duality {
 	func_decl f = t.decl();
 	std::vector<Term> args;
 	int nargs = t.num_args();
-	if(nargs == 0)
+	if(nargs == 0 && f.get_decl_kind() == Uninterpreted)
 	  ls->declare_constant(f);  // keep track of background constants
 	for(int i = 0; i < nargs; i++)
 	  args.push_back(SubstBoundRec(memo, subst, level, t.arg(i)));
diff --git a/src/duality/duality_solver.cpp b/src/duality/duality_solver.cpp
index 6079e17d9..d59309c00 100755
--- a/src/duality/duality_solver.cpp
+++ b/src/duality/duality_solver.cpp
@@ -54,6 +54,7 @@ Revision History:
 // #define KEEP_EXPANSIONS
 // #define USE_CACHING_RPFP
 // #define PROPAGATE_BEFORE_CHECK
+#define NEW_STRATIFIED_INLINING	
 
 #define USE_RPFP_CLONE
 #define USE_NEW_GEN_CANDS
@@ -82,7 +83,7 @@ namespace Duality {
       rpfp = _rpfp;
     }
     virtual void Extend(RPFP::Node *node){}
-    virtual void Update(RPFP::Node *node, const RPFP::Transformer &update){}
+    virtual void Update(RPFP::Node *node, const RPFP::Transformer &update, bool eager){}
     virtual void Bound(RPFP::Node *node){}
     virtual void Expand(RPFP::Edge *edge){}
     virtual void AddCover(RPFP::Node *covered, std::vector<RPFP::Node *> &covering){}
@@ -94,6 +95,7 @@ namespace Duality {
     virtual void UpdateUnderapprox(RPFP::Node *node, const RPFP::Transformer &update){}
     virtual void Reject(RPFP::Edge *edge, const std::vector<RPFP::Node *> &Children){}
     virtual void Message(const std::string &msg){}
+    virtual void Depth(int){}
     virtual ~Reporter(){}
   };
 
@@ -124,6 +126,7 @@ namespace Duality {
       rpfp = _rpfp;
       reporter = 0;
       heuristic = 0;
+      unwinding = 0;
       FullExpand = false;
       NoConj = false;
       FeasibleEdges = true;
@@ -131,6 +134,7 @@ namespace Duality {
       Report = false;
       StratifiedInlining = false;
       RecursionBound = -1;
+      BatchExpand = false;
       {
 	scoped_no_proof no_proofs_please(ctx.m());
 #ifdef USE_RPFP_CLONE
@@ -151,6 +155,7 @@ namespace Duality {
 #ifdef USE_NEW_GEN_CANDS
       delete gen_cands_rpfp;
 #endif
+      if(unwinding) delete unwinding;
     }
 
 #ifdef USE_RPFP_CLONE
@@ -249,6 +254,19 @@ namespace Duality {
       virtual void Done() {}
     };
     
+    /** The Proposer class proposes conjectures eagerly. These can come
+       from any source, including predicate abstraction, templates, or
+       previous solver runs. The proposed conjectures are checked
+       with low effort when the unwinding is expanded.
+    */
+
+    class Proposer {
+    public:
+      /** Given a node in the unwinding, propose some conjectures */
+      virtual std::vector<RPFP::Transformer> &Propose(Node *node) = 0;
+      virtual ~Proposer(){};
+    };
+
 
     class Covering; // see below
 
@@ -278,6 +296,7 @@ namespace Duality {
     hash_map<Node *, Node *> underapprox_map; // maps underapprox nodes to the nodes they approximate
     int last_decisions;
     hash_set<Node *> overapproxes;
+    std::vector<Proposer *> proposers;
 
 #ifdef BOUNDED
     struct Counter {
@@ -292,24 +311,22 @@ namespace Duality {
     virtual bool Solve(){
       reporter = Report ? CreateStdoutReporter(rpfp) : new Reporter(rpfp);
 #ifndef LOCALIZE_CONJECTURES
-      heuristic = !cex.tree ? new Heuristic(rpfp) : new ReplayHeuristic(rpfp,cex);
+      heuristic = !cex.get_tree() ? new Heuristic(rpfp) : new ReplayHeuristic(rpfp,cex);
 #else
-      heuristic = !cex.tree ? (Heuristic *)(new LocalHeuristic(rpfp))
+      heuristic = !cex.get_tree() ? (Heuristic *)(new LocalHeuristic(rpfp))
 	: (Heuristic *)(new ReplayHeuristic(rpfp,cex));
 #endif
-      cex.tree = 0; // heuristic now owns it
+      cex.clear(); // in case we didn't use it for heuristic
+      if(unwinding) delete unwinding;
       unwinding = new RPFP(rpfp->ls);
       unwinding->HornClauses = rpfp->HornClauses;
       indset = new Covering(this);
       last_decisions = 0;
       CreateEdgesByChildMap();
-      CreateLeaves();
 #ifndef TOP_DOWN
-      if(!StratifiedInlining){
-        if(FeasibleEdges)NullaryCandidates();
-        else InstantiateAllEdges();
-      }
+      void CreateInitialUnwinding();
 #else
+      CreateLeaves();
       for(unsigned i = 0; i < leaves.size(); i++)
 	if(!SatisfyUpperBound(leaves[i]))
 	  return false;
@@ -321,11 +338,29 @@ namespace Duality {
       //  print_profile(std::cout);
       delete indset;
       delete heuristic;
-      delete unwinding;
+      // delete unwinding; // keep the unwinding for future mining of predicates
       delete reporter;
+      for(unsigned i = 0; i < proposers.size(); i++)
+	delete proposers[i];
       return res;
     }
 
+    void CreateInitialUnwinding(){
+      if(!StratifiedInlining){
+	CreateLeaves();
+        if(FeasibleEdges)NullaryCandidates();
+        else InstantiateAllEdges();
+      }
+      else {
+#ifdef NEW_STRATIFIED_INLINING	
+
+#else
+	CreateLeaves();
+#endif
+      }
+      
+    }
+
     void Cancel(){
       // TODO
     }
@@ -346,15 +381,19 @@ namespace Duality {
     }
 #endif
 
-    virtual void LearnFrom(Counterexample &old_cex){
-      cex = old_cex;
+    virtual void LearnFrom(Solver *other_solver){
+      // get the counterexample as a guide
+      cex.swap(other_solver->GetCounterexample());
+
+      // propose conjectures based on old unwinding
+      Duality *old_duality = dynamic_cast<Duality *>(other_solver);
+      if(old_duality)
+	proposers.push_back(new HistoryProposer(old_duality,this));
     }
 
-    /** Return the counterexample */
-    virtual Counterexample GetCounterexample(){
-      Counterexample res = cex;
-      cex.tree = 0; // Cex now belongs to caller
-      return res;
+    /** Return a reference to the counterexample */
+    virtual Counterexample &GetCounterexample(){
+      return cex;
     }
 
     // options
@@ -365,6 +404,7 @@ namespace Duality {
     bool Report;         // spew on stdout
     bool StratifiedInlining; // Do stratified inlining as preprocessing step
     int RecursionBound;  // Recursion bound for bounded verification
+    bool BatchExpand;
     
     bool SetBoolOption(bool &opt, const std::string &value){
       if(value == "0") {
@@ -403,6 +443,9 @@ namespace Duality {
       if(option == "stratified_inlining"){
         return SetBoolOption(StratifiedInlining,value);
       }
+      if(option == "batch_expand"){
+        return SetBoolOption(BatchExpand,value);
+      }
       if(option == "recursion_bound"){
         return SetIntOption(RecursionBound,value);
       }
@@ -514,7 +557,11 @@ namespace Duality {
 	c.Children.resize(edge->Children.size());
 	for(unsigned j = 0; j < c.Children.size(); j++)
 	  c.Children[j] = leaf_map[edge->Children[j]];
-	Extend(c);
+	Node *new_node;
+	Extend(c,new_node);
+#ifdef EARLY_EXPAND
+	TryExpandNode(new_node);
+#endif
       }
       for(Unexpanded::iterator it = unexpanded.begin(), en = unexpanded.end(); it != en; ++it)
 	indset->Add(*it);
@@ -766,16 +813,14 @@ namespace Duality {
     }
 
 
-    /* For stratified inlining, we need a topological sort of the
-	nodes. */
-
     hash_map<Node *, int> TopoSort;
     int TopoSortCounter;
+    std::vector<Edge *> SortedEdges;
     
     void DoTopoSortRec(Node *node){
       if(TopoSort.find(node) != TopoSort.end())
 	return;
-      TopoSort[node] = TopoSortCounter++;  // just to break cycles
+      TopoSort[node] = INT_MAX;  // just to break cycles
       Edge *edge = node->Outgoing; // note, this is just *one* outgoing edge
       if(edge){
 	std::vector<Node *> &chs = edge->Children;
@@ -783,22 +828,81 @@ namespace Duality {
 	  DoTopoSortRec(chs[i]);
       }
       TopoSort[node] = TopoSortCounter++;
+      SortedEdges.push_back(edge);
     }
 
     void DoTopoSort(){
       TopoSort.clear();
+      SortedEdges.clear();
       TopoSortCounter = 0;
       for(unsigned i = 0; i < nodes.size(); i++)
 	DoTopoSortRec(nodes[i]);
     }
 
+    
+    int StratifiedLeafCount;
+
+#ifdef NEW_STRATIFIED_INLINING	
+
+    /** Stratified inlining builds an initial layered unwinding before
+	switching to the LAWI strategy. Currently the number of layers
+	is one. Only nodes that are the targets of back edges are
+	consider to be leaves. This assumes we have already computed a
+	topological sort.
+    */
+
+    bool DoStratifiedInlining(){
+      DoTopoSort();
+      int depth = 1; // TODO: make this an option
+      std::vector<hash_map<Node *,Node *> > unfolding_levels(depth+1);
+      for(int level = 1; level <= depth; level++)
+	for(unsigned i = 0; i < SortedEdges.size(); i++){
+	  Edge *edge = SortedEdges[i];
+	  Node *parent = edge->Parent;
+	  std::vector<Node *> &chs = edge->Children;
+	  std::vector<Node *> my_chs(chs.size());
+	  for(unsigned j = 0; j < chs.size(); j++){
+	    Node *child = chs[j];
+	    int ch_level = TopoSort[child] >= TopoSort[parent] ? level-1 : level;
+	    if(unfolding_levels[ch_level].find(child) == unfolding_levels[ch_level].end()){
+	      if(ch_level == 0) 
+		unfolding_levels[0][child] = CreateLeaf(child);
+	      else
+		throw InternalError("in levelized unwinding");
+	    }
+	    my_chs[j] = unfolding_levels[ch_level][child];
+	  }
+	  Candidate cand; cand.edge = edge; cand.Children = my_chs;
+	  Node *new_node;
+	  bool ok = Extend(cand,new_node);
+	  MarkExpanded(new_node); // we don't expand here -- just mark it done
+	  if(!ok) return false; // got a counterexample
+	  unfolding_levels[level][parent] = new_node;
+	}
+      return true;
+    }
+
+    Node *CreateLeaf(Node *node){
+      RPFP::Node *nchild = CreateNodeInstance(node);
+      MakeLeaf(nchild, /* do_not_expand = */ true);
+      nchild->Annotation.SetEmpty();
+      return nchild;
+    }      
+
+    void MarkExpanded(Node *node){
+      if(unexpanded.find(node) != unexpanded.end()){
+	unexpanded.erase(node);
+	insts_of_node[node->map].push_back(node);
+      }
+    }
+
+#else
+
     /** In stratified inlining, we build the unwinding from the bottom
 	down, trying to satisfy the node bounds. We do this as a pre-pass,
 	limiting the expansion. If we get a counterexample, we are done,
 	else we continue as usual expanding the unwinding upward.
     */
-    
-    int StratifiedLeafCount;
 
     bool DoStratifiedInlining(){
       timer_start("StratifiedInlining");
@@ -821,6 +925,8 @@ namespace Duality {
       return true;
     }
     
+#endif
+
     /** Here, we do the downward expansion for stratified inlining */
 
     hash_map<Node *, Node *> LeafMap, StratifiedLeafMap;
@@ -907,9 +1013,14 @@ namespace Duality {
 	}
 	Candidate cand = candidates.front();
 	candidates.pop_front();
-	if(CandidateFeasible(cand))
-	  if(!Extend(cand))
+	if(CandidateFeasible(cand)){
+	  Node *new_node;
+	  if(!Extend(cand,new_node))
 	    return false;
+#ifdef EARLY_EXPAND
+	  TryExpandNode(new_node);
+#endif
+	}
       }
     }
 
@@ -929,9 +1040,9 @@ namespace Duality {
 	
 
     Node *CreateUnderapproxNode(Node *node){
-      // cex.tree->ComputeUnderapprox(cex.root,0);
+      // cex.get_tree()->ComputeUnderapprox(cex.get_root(),0);
       RPFP::Node *under_node = CreateNodeInstance(node->map /* ,StratifiedLeafCount-- */);
-      under_node->Annotation.IntersectWith(cex.root->Underapprox);
+      under_node->Annotation.IntersectWith(cex.get_root()->Underapprox);
       AddThing(under_node->Annotation.Formula);
       Edge *e = unwinding->CreateLowerBoundEdge(under_node);
       under_node->Annotation.SetFull(); // allow this node to cover others
@@ -967,9 +1078,8 @@ namespace Duality {
 	ExpandNodeFromCoverFail(node);
       }
 #endif
-      if(_cex) *_cex = cex;
-      else delete cex.tree;    // delete the cex if not required
-      cex.tree = 0;
+      if(_cex) (*_cex).swap(cex); // return the cex if asked
+      cex.clear();                // throw away the useless cex
       node->Bound = save; // put back original bound
       timer_stop("ProveConjecture");
       return false;
@@ -1349,16 +1459,20 @@ namespace Duality {
       }
     }
 
-    bool UpdateNodeToNode(Node *node, Node *top){
-      if(!node->Annotation.SubsetEq(top->Annotation)){
-	reporter->Update(node,top->Annotation);
-	indset->Update(node,top->Annotation);
+    bool Update(Node *node, const RPFP::Transformer &fact, bool eager=false){
+      if(!node->Annotation.SubsetEq(fact)){
+	reporter->Update(node,fact,eager);
+	indset->Update(node,fact);
 	updated_nodes.insert(node->map);
-	node->Annotation.IntersectWith(top->Annotation);
+	node->Annotation.IntersectWith(fact);
 	return true;
       }
       return false;
     }
+    
+    bool UpdateNodeToNode(Node *node, Node *top){
+      return Update(node,top->Annotation);
+    }
 
     /** Update the unwinding solution, using an interpolant for the
 	derivation tree. */
@@ -1400,8 +1514,7 @@ namespace Duality {
       // std::cout << "decisions: " << (end_decs - start_decs)  << std::endl;
       last_decisions = end_decs - start_decs;
       if(res){
-	cex.tree = dt.tree;
-	cex.root = dt.top;
+	cex.set(dt.tree,dt.top); // note tree is now owned by cex
 	if(UseUnderapprox){
 	  UpdateWithCounterexample(node,dt.tree,dt.top);
 	}
@@ -1413,6 +1526,64 @@ namespace Duality {
       delete dtp;
       return !res;
     }
+    
+    /* For a given nod in the unwinding, get conjectures from the
+       proposers and check them locally. Update the node with any true
+       conjectures.
+     */
+
+    void DoEagerDeduction(Node *node){
+      for(unsigned i = 0; i < proposers.size(); i++){
+	const std::vector<RPFP::Transformer> &conjectures = proposers[i]->Propose(node);
+	for(unsigned j = 0; j < conjectures.size(); j++){ 
+	  const RPFP::Transformer &conjecture = conjectures[j];
+	  RPFP::Transformer bound(conjecture);
+	  std::vector<expr> conj_vec;
+	  unwinding->CollectConjuncts(bound.Formula,conj_vec);
+	  for(unsigned k = 0; k < conj_vec.size(); k++){
+	    bound.Formula = conj_vec[k];
+	    if(CheckEdgeCaching(node->Outgoing,bound) == unsat)
+	      Update(node,bound, /* eager = */ true);
+	    //else
+	    //std::cout << "conjecture failed\n";
+	  }
+	}
+      }
+    }
+
+      
+    check_result CheckEdge(RPFP *checker, Edge *edge){
+      Node *root = edge->Parent;
+      checker->Push();
+      checker->AssertNode(root);
+      checker->AssertEdge(edge,1,true);
+      check_result res = checker->Check(root);
+      checker->Pop(1);
+      return res;
+    }
+
+    check_result CheckEdgeCaching(Edge *unwinding_edge, const RPFP::Transformer &bound){
+
+      // use a dedicated solver for this edge
+      // TODO: can this mess be hidden somehow?
+
+      RPFP_caching *checker = gen_cands_rpfp; // TODO: a good choice?
+      Edge *edge = unwinding_edge->map; // get the edge in the original RPFP
+      RPFP_caching::scoped_solver_for_edge ssfe(checker,edge,true /* models */, true /*axioms*/);
+      Edge *checker_edge = checker->GetEdgeClone(edge);
+      
+      // copy the annotations and bound to the clone
+      Node *root = checker_edge->Parent;
+      root->Bound = bound;
+      for(unsigned j = 0; j < checker_edge->Children.size(); j++){
+	Node *oc = unwinding_edge->Children[j];
+	Node *nc = checker_edge->Children[j];
+	nc->Annotation = oc->Annotation;
+      }
+      
+      return CheckEdge(checker,checker_edge);
+    }
+
 
     /* If the counterexample derivation is partial due to
        use of underapproximations, complete it. */
@@ -1421,10 +1592,7 @@ namespace Duality {
       DerivationTree dt(this,unwinding,reporter,heuristic,FullExpand); 
       bool res = dt.Derive(unwinding,node,UseUnderapprox,true); // build full tree
       if(!res) throw "Duality internal error in BuildFullCex";
-      if(cex.tree)
-	delete cex.tree;
-      cex.tree = dt.tree;
-      cex.root = dt.top;
+      cex.set(dt.tree,dt.top);
     }
     
     void UpdateBackEdges(Node *node){
@@ -1447,25 +1615,23 @@ namespace Duality {
     }
 
     /** Extend the unwinding, keeping it solved. */
-    bool Extend(Candidate &cand){
+    bool Extend(Candidate &cand, Node *&node){
       timer_start("Extend");
-      Node *node = CreateNodeInstance(cand.edge->Parent);
+      node = CreateNodeInstance(cand.edge->Parent);
       CreateEdgeInstance(cand.edge,node,cand.Children);
       UpdateBackEdges(node);
       reporter->Extend(node);
-      bool res = SatisfyUpperBound(node);
+      DoEagerDeduction(node); // first be eager...
+      bool res = SatisfyUpperBound(node); // then be lazy
       if(res) indset->CloseDescendants(node);
       else {
 #ifdef UNDERAPPROX_NODES
-	ExpandUnderapproxNodes(cex.tree, cex.root);
+	ExpandUnderapproxNodes(cex.get_tree(), cex.get_root());
 #endif
 	if(UseUnderapprox) BuildFullCex(node);
 	timer_stop("Extend");
 	return res;
       }
-#ifdef EARLY_EXPAND
-      TryExpandNode(node);
-#endif
       timer_stop("Extend");
       return res;
     }
@@ -1916,6 +2082,7 @@ namespace Duality {
 
 	stack.back().level = tree->slvr().get_scope_level();
 	bool was_sat = true;
+	int update_failures = 0;
 
 	while (true)
 	{
@@ -1924,6 +2091,7 @@ namespace Duality {
 	  unsigned slvr_level = tree->slvr().get_scope_level();
 	  if(slvr_level != stack.back().level)
 	    throw "stacks out of sync!";
+	  reporter->Depth(stack.size());
 
 	  //	  res = tree->Solve(top, 1);            // incremental solve, keep interpolants for one pop
 	  check_result foo = tree->Check(top);
@@ -1954,10 +2122,14 @@ namespace Duality {
 		  heuristic->Update(node->map); // make it less likely to expand this node in future
 	      }
 	      if(update_count == 0){
-		if(was_sat)
-		  throw "Help!";
+		if(was_sat){
+		  update_failures++;
+		  if(update_failures > 10)
+		    throw Incompleteness();
+		}
 		reporter->Message("backtracked without learning");
 	      }
+	      else update_failures = 0;
 	    }
 	    tree->ComputeProofCore(); // need to compute the proof core before popping solver
 	    bool propagated = false;
@@ -2011,7 +2183,7 @@ namespace Duality {
 	  }
 	  else {
 	    was_sat = true;
-	    tree->Push();

+	    tree->Push();
 	    std::vector<Node *> &expansions = stack.back().expansions;
 #ifndef NO_DECISIONS
 	    for(unsigned i = 0; i < expansions.size(); i++){
@@ -2022,11 +2194,16 @@ namespace Duality {
 	    if(tree->slvr().check() == unsat)
 	      throw "help!";
 #endif
-	    stack.push_back(stack_entry());
-	    stack.back().level = tree->slvr().get_scope_level();
-	    if(ExpandSomeNodes(false,1)){
-	      continue;
+	    int expand_max = 1;
+	    if(0&&duality->BatchExpand){
+	      int thing = stack.size() * 0.1;
+	      expand_max = std::max(1,thing);
+	      if(expand_max > 1)
+		std::cout << "foo!\n";
 	    }
+
+	    if(ExpandSomeNodes(false,expand_max))
+	      continue;
 	    while(stack.size() > 1){
 	      tree->Pop(1);	
 	      stack.pop_back();
@@ -2085,6 +2262,8 @@ namespace Duality {
       std::list<Node *> updated_nodes;
 
       virtual void ExpandNode(RPFP::Node *p){
+	stack.push_back(stack_entry());
+	stack.back().level = tree->slvr().get_scope_level();
 	stack.back().expansions.push_back(p);
 	DerivationTree::ExpandNode(p);
 	std::vector<Node *> &new_nodes = p->Outgoing->Children;
@@ -2442,7 +2621,7 @@ namespace Duality {
       }      
 
       bool ContainsCex(Node *node, Counterexample &cex){
-	expr val = cex.tree->Eval(cex.root->Outgoing,node->Annotation.Formula);
+	expr val = cex.get_tree()->Eval(cex.get_root()->Outgoing,node->Annotation.Formula);
 	return eq(val,parent->ctx.bool_val(true));
       }
 
@@ -2461,15 +2640,15 @@ namespace Duality {
 	  Node *other = insts[i];
 	  if(CouldCover(node,other)){
 	    reporter()->Forcing(node,other);
-	    if(cex.tree && !ContainsCex(other,cex))
+	    if(cex.get_tree() && !ContainsCex(other,cex))
 	      continue;
-	    if(cex.tree) {delete cex.tree; cex.tree = 0;}
+	    cex.clear();
 	    if(parent->ProveConjecture(node,other->Annotation,other,&cex))
 	      if(CloseDescendants(node))
 		return true;
 	  }
 	}
-	if(cex.tree) {delete cex.tree; cex.tree = 0;}
+	cex.clear();
 	return false;
       }
 #else
@@ -2568,13 +2747,12 @@ namespace Duality {
       Counterexample old_cex;
     public:
       ReplayHeuristic(RPFP *_rpfp, Counterexample &_old_cex)
-	: Heuristic(_rpfp), old_cex(_old_cex)
+	: Heuristic(_rpfp)
       {
+	old_cex.swap(_old_cex); // take ownership from caller
       }
 
       ~ReplayHeuristic(){
-	if(old_cex.tree)
-	  delete old_cex.tree;
       }
 
       // Maps nodes of derivation tree into old cex
@@ -2582,9 +2760,7 @@ namespace Duality {
       
       void Done() {
 	cex_map.clear();
-	if(old_cex.tree)
-	  delete old_cex.tree;
-	old_cex.tree = 0; // only replay once!
+	old_cex.clear();
       }
 
       void ShowNodeAndChildren(Node *n){
@@ -2606,7 +2782,7 @@ namespace Duality {
       }
 
       virtual void ChooseExpand(const std::set<RPFP::Node *> &choices, std::set<RPFP::Node *> &best, bool high_priority, bool best_only){
-	if(!high_priority || !old_cex.tree){
+	if(!high_priority || !old_cex.get_tree()){
 	  Heuristic::ChooseExpand(choices,best,false);
 	  return;
 	}
@@ -2615,7 +2791,7 @@ namespace Duality {
 	for(std::set<Node *>::iterator it = choices.begin(), en = choices.end(); it != en; ++it){
 	  Node *node = (*it);
 	  if(cex_map.empty())
-	    cex_map[node] = old_cex.root;  // match the root nodes
+	    cex_map[node] = old_cex.get_root();  // match the root nodes
 	  if(cex_map.find(node) == cex_map.end()){ // try to match an unmatched node
 	    Node *parent = node->Incoming[0]->Parent; // assumes we are a tree!
 	    if(cex_map.find(parent) == cex_map.end())
@@ -2641,7 +2817,7 @@ namespace Duality {
 	  Node *old_node = cex_map[node];
 	  if(!old_node)
 	    unmatched.insert(node);
-	  else if(old_cex.tree->Empty(old_node))
+	  else if(old_cex.get_tree()->Empty(old_node))
 	    unmatched.insert(node);
 	  else
 	    matched.insert(node);
@@ -2715,7 +2891,120 @@ namespace Duality {
       }
     };
 
+    /** This proposer class generates conjectures based on the
+	unwinding generated by a previous solver. The assumption is
+	that the provious solver was working on a different
+	abstraction of the same system. The trick is to adapt the
+	annotations in the old unwinding to the new predicates.  We
+	start by generating a map from predicates and parameters in
+	the old problem to the new. 
 
+	HACK: mapping is done by cheesy name comparison.
+    */
+    
+    class HistoryProposer : public Proposer
+    {
+      Duality *old_solver;
+      Duality *new_solver;
+      hash_map<Node *, std::vector<RPFP::Transformer> > conjectures;
+
+    public:
+      /** Construct a history solver. */
+      HistoryProposer(Duality *_old_solver, Duality *_new_solver)
+	: old_solver(_old_solver), new_solver(_new_solver) {
+
+	// tricky: names in the axioms may have changed -- map them
+	hash_set<func_decl> &old_constants = old_solver->unwinding->ls->get_constants();
+	hash_set<func_decl> &new_constants = new_solver->rpfp->ls->get_constants();
+	hash_map<std::string,func_decl> cmap;
+        for(hash_set<func_decl>::iterator it = new_constants.begin(), en = new_constants.end(); it != en; ++it)
+	  cmap[GetKey(*it)] = *it;
+	hash_map<func_decl,func_decl> bckg_map;
+        for(hash_set<func_decl>::iterator it = old_constants.begin(), en = old_constants.end(); it != en; ++it){
+	  func_decl f = new_solver->ctx.translate(*it); // move to new context
+	  if(cmap.find(GetKey(f)) != cmap.end())
+	    bckg_map[f] = cmap[GetKey(f)];
+	  // else
+	  //  std::cout << "constant not matched\n";
+	}
+	
+	RPFP *old_unwinding = old_solver->unwinding;
+	hash_map<std::string, std::vector<Node *> > pred_match;
+
+	// index all the predicates in the old unwinding
+	for(unsigned i = 0; i < old_unwinding->nodes.size(); i++){
+	  Node *node = old_unwinding->nodes[i];
+	  std::string key = GetKey(node);
+	  pred_match[key].push_back(node);
+	}
+
+	// match with predicates in the new RPFP
+	RPFP *rpfp = new_solver->rpfp;
+	for(unsigned i = 0; i < rpfp->nodes.size(); i++){
+	  Node *node = rpfp->nodes[i];
+	  std::string key = GetKey(node);
+	  std::vector<Node *> &matches = pred_match[key];
+	  for(unsigned j = 0; j < matches.size(); j++)
+	    MatchNodes(node,matches[j],bckg_map);
+	}
+      }
+      
+      virtual std::vector<RPFP::Transformer> &Propose(Node *node){
+	return conjectures[node->map];
+      }
+
+      virtual ~HistoryProposer(){
+      };
+
+    private:
+      void MatchNodes(Node *new_node, Node *old_node, hash_map<func_decl,func_decl> &bckg_map){
+	if(old_node->Annotation.IsFull())
+	  return; // don't conjecture true!
+	hash_map<std::string, expr> var_match;
+	std::vector<expr> &new_params = new_node->Annotation.IndParams;
+	// Index the new parameters by their keys
+	for(unsigned i = 0; i < new_params.size(); i++)
+	  var_match[GetKey(new_params[i])] = new_params[i];
+	RPFP::Transformer &old = old_node->Annotation;
+	std::vector<expr> from_params = old.IndParams;
+	for(unsigned j = 0; j < from_params.size(); j++)
+	  from_params[j] = new_solver->ctx.translate(from_params[j]); // get in new context
+	std::vector<expr> to_params = from_params;
+	for(unsigned j = 0; j < to_params.size(); j++){
+	  std::string key = GetKey(to_params[j]);
+	  if(var_match.find(key) == var_match.end()){
+	    // std::cout << "unmatched parameter!\n";
+	    return;
+	  }
+	  to_params[j] = var_match[key];
+	}
+	expr fmla = new_solver->ctx.translate(old.Formula); // get in new context
+	fmla = new_solver->rpfp->SubstParams(old.IndParams,to_params,fmla); // substitute parameters
+	hash_map<ast,expr> memo;
+	fmla = new_solver->rpfp->SubstRec(memo,bckg_map,fmla); // substitute background constants
+	RPFP::Transformer new_annot = new_node->Annotation;
+	new_annot.Formula = fmla;
+	conjectures[new_node].push_back(new_annot);
+      }
+      
+      // We match names by removing suffixes beginning with double at sign
+
+      std::string GetKey(Node *node){
+	return GetKey(node->Name);
+      }
+
+      std::string GetKey(const expr &var){
+	return GetKey(var.decl());
+      }
+
+      std::string GetKey(const func_decl &f){
+	std::string name = f.name().str();
+	int idx = name.find("@@");
+	if(idx >= 0)
+	  name.erase(idx);
+	return name;
+      }
+    };
   };
 
 
@@ -2723,8 +3012,9 @@ namespace Duality {
     std::ostream &s;
   public:
     StreamReporter(RPFP *_rpfp, std::ostream &_s)
-      : Reporter(_rpfp), s(_s) {event = 0;}
+      : Reporter(_rpfp), s(_s) {event = 0; depth = -1;}
     int event;
+    int depth;
     void ev(){
       s << "[" << event++ << "]" ;
     }
@@ -2735,23 +3025,30 @@ namespace Duality {
 	s << " " << rps[i]->number;
       s << std::endl;
     }
-    virtual void Update(RPFP::Node *node, const RPFP::Transformer &update){
+    virtual void Update(RPFP::Node *node, const RPFP::Transformer &update, bool eager){
       ev(); s << "update " << node->number << " " << node->Name.name()  << ": ";
       rpfp->Summarize(update.Formula);
-      std::cout << std::endl;
+      if(depth > 0) s << " (depth=" << depth << ")";
+      if(eager) s << " (eager)";
+      s << std::endl;
     }
     virtual void Bound(RPFP::Node *node){
       ev(); s << "check " << node->number << std::endl;
     }
     virtual void Expand(RPFP::Edge *edge){
       RPFP::Node *node = edge->Parent;
-      ev(); s << "expand " << node->map->number << " " << node->Name.name() << std::endl;
+      ev(); s << "expand " << node->map->number << " " << node->Name.name();
+      if(depth > 0) s << " (depth=" << depth << ")";
+      s << std::endl;
+    }
+    virtual void Depth(int d){
+      depth = d;
     }
     virtual void AddCover(RPFP::Node *covered, std::vector<RPFP::Node *> &covering){
       ev(); s << "cover " << covered->Name.name() << ": " << covered->number << " by ";
       for(unsigned i = 0; i < covering.size(); i++)
-	std::cout << covering[i]->number << " ";
-      std::cout << std::endl;
+	s << covering[i]->number << " ";
+      s << std::endl;
     }
     virtual void RemoveCover(RPFP::Node *covered, RPFP::Node *covering){
       ev(); s << "uncover " << covered->Name.name() << ": " << covered->number << " by " << covering->number << std::endl;
@@ -2762,7 +3059,7 @@ namespace Duality {
     virtual void Conjecture(RPFP::Node *node, const RPFP::Transformer &t){
       ev(); s << "conjecture " << node->number << " " << node->Name.name() << ": ";
       rpfp->Summarize(t.Formula);
-      std::cout << std::endl;
+      s << std::endl;
     }
     virtual void Dominates(RPFP::Node *node, RPFP::Node *other){
       ev(); s << "dominates " << node->Name.name() << ": " << node->number << " > " << other->number << std::endl;
diff --git a/src/duality/duality_wrapper.cpp b/src/duality/duality_wrapper.cpp
index cf2c803cb..0f6198edd 100755
--- a/src/duality/duality_wrapper.cpp
+++ b/src/duality/duality_wrapper.cpp
@@ -37,16 +37,18 @@ Revision History:
 
 namespace Duality {
 
-  solver::solver(Duality::context& c, bool extensional, bool models) : object(c), the_model(c) {
+  solver::solver(Duality::context& c, bool _extensional, bool models) : object(c), the_model(c) {
     params_ref p;
     p.set_bool("proof", true); // this is currently useless
     if(models)
       p.set_bool("model", true); 
     p.set_bool("unsat_core", true); 
-    p.set_bool("mbqi",true);
+    bool mbqi = c.get_config().get().get_bool("mbqi",true);
+    p.set_bool("mbqi",mbqi); // just to test
     p.set_str("mbqi.id","itp"); // use mbqi for quantifiers in interpolants
     p.set_uint("mbqi.max_iterations",1); // use mbqi for quantifiers in interpolants
-    if(true || extensional)
+    extensional = mbqi && (true || _extensional);
+    if(extensional)
       p.set_bool("array.extensional",true);
     scoped_ptr<solver_factory> sf = mk_smt_solver_factory();
     m_solver = (*sf)(m(), p, true, true, true, ::symbol::null);
@@ -656,6 +658,18 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
     pp.display_smt2(std::cout, m_solver->get_assertion(n-1));
   }
 
+  void solver::print(const char *filename) {
+    std::ofstream f(filename);
+    unsigned n = m_solver->get_num_assertions();
+    if(!n)
+      return;
+    ast_smt_pp pp(m());
+    for (unsigned i = 0; i < n-1; ++i)
+      pp.add_assumption(m_solver->get_assertion(i));
+    pp.display_smt2(f, m_solver->get_assertion(n-1));
+  }
+
+
   void solver::show_assertion_ids() {
 #if 0
     unsigned n = m_solver->get_num_assertions();
diff --git a/src/duality/duality_wrapper.h b/src/duality/duality_wrapper.h
index 90f1799a6..0861ab791 100755
--- a/src/duality/duality_wrapper.h
+++ b/src/duality/duality_wrapper.h
@@ -182,6 +182,7 @@ namespace Duality {
       void set(char const * param, char const * value) { m_config.set(param,value); }
       void set(char const * param, bool value) { m_config.set(param,value); }
       void set(char const * param, int value) { m_config.set(param,value); }
+      config &get_config() {return m_config;}
 
       symbol str_symbol(char const * s);
       symbol int_symbol(int n);
@@ -243,6 +244,9 @@ namespace Duality {
 
       sort_kind get_sort_kind(const sort &s);
 
+      expr translate(const expr &e);
+      func_decl translate(const func_decl &);
+
       void print_expr(std::ostream &s, const ast &e);
 
       fixedpoint mk_fixedpoint();
@@ -818,6 +822,7 @@ namespace Duality {
         model the_model;
 	bool canceled;
 	proof_gen_mode m_mode;
+	bool extensional;
     public:
         solver(context & c, bool extensional = false, bool models = true);
         solver(context & c, ::solver *s):object(c),the_model(c) { m_solver = s; canceled = false;}
@@ -921,6 +926,7 @@ namespace Duality {
 	unsigned get_scope_level(){ scoped_proof_mode spm(m(),m_mode); return m_solver->get_scope_level();}
 
 	void show();
+	void print(const char *filename);
 	void show_assertion_ids();
 
 	proof get_proof(){
@@ -928,6 +934,7 @@ namespace Duality {
 	  return proof(ctx(),m_solver->get_proof());
 	}
 
+	bool extensional_array_theory() {return extensional;}
     };
 
 #if 0
@@ -1370,6 +1377,20 @@ namespace Duality {
       return to_expr(a.raw());
     }
 
+    inline expr context::translate(const expr &e) {
+      ::expr *f = to_expr(e.raw());
+      if(&e.ctx().m() != &m()) // same ast manager -> no translation
+	throw "ast manager mismatch";
+      return cook(f);
+    }
+
+    inline func_decl context::translate(const func_decl &e) {
+      ::func_decl *f = to_func_decl(e.raw());
+      if(&e.ctx().m() != &m()) // same ast manager -> no translation
+	throw "ast manager mismatch";
+      return func_decl(*this,f);
+    }
+
     typedef double clock_t;
     clock_t current_time();
     inline void output_time(std::ostream &os, clock_t time){os << time;}
diff --git a/src/interp/iz3proof_itp.cpp b/src/interp/iz3proof_itp.cpp
index 6a150ad38..9352348f4 100755
--- a/src/interp/iz3proof_itp.cpp
+++ b/src/interp/iz3proof_itp.cpp
@@ -367,11 +367,17 @@ class iz3proof_itp_impl : public iz3proof_itp {
       }
       default:
 	{
-	  symb s = sym(itp2);
-	  if(s == sforall || s == sexists)
-	    res = make(s,arg(itp2,0),resolve_arith_rec2(memo, pivot1, conj1, arg(itp2,1)));
-	  else
+	  opr o = op(itp2);
+	  if(o == Uninterpreted){
+	    symb s = sym(itp2);
+	    if(s == sforall || s == sexists)
+	      res = make(s,arg(itp2,0),resolve_arith_rec2(memo, pivot1, conj1, arg(itp2,1)));
+	    else
+	      res = itp2;
+	  }
+	  else {
 	    res = itp2;
+	  }
 	}
       }
     }
@@ -403,11 +409,17 @@ class iz3proof_itp_impl : public iz3proof_itp {
       }
       default:
 	{
-	  symb s = sym(itp1);
-	  if(s == sforall || s == sexists)
-	    res = make(s,arg(itp1,0),resolve_arith_rec1(memo, neg_pivot_lit, arg(itp1,1), itp2));
-	  else
+	  opr o = op(itp1);
+	  if(o == Uninterpreted){
+	    symb s = sym(itp1);
+	    if(s == sforall || s == sexists)
+	      res = make(s,arg(itp1,0),resolve_arith_rec1(memo, neg_pivot_lit, arg(itp1,1), itp2));
+	    else
+	      res = itp1;
+	  }
+	  else {
 	    res = itp1;
+	  }
 	}
       }
     }
@@ -462,18 +474,20 @@ class iz3proof_itp_impl : public iz3proof_itp {
     std::pair<hash_map<ast,ast>::iterator,bool> bar = subst_memo.insert(foo);
     ast &res = bar.first->second;
     if(bar.second){
-      symb g = sym(e);
-      if(g == rotate_sum){
-	if(var == get_placeholder(arg(e,0))){
-	  res = e;
+      if(op(e) == Uninterpreted){
+	symb g = sym(e);
+	if(g == rotate_sum){
+	  if(var == get_placeholder(arg(e,0))){
+	    res = e;
+	  }
+	  else 
+	    res = make(rotate_sum,arg(e,0),subst_term_and_simp_rec(var,t,arg(e,1)));
+	  return res;
+	}
+	if(g == concat){
+	  res = e;
+	  return res;
 	}
-	else 
-	  res = make(rotate_sum,arg(e,0),subst_term_and_simp_rec(var,t,arg(e,1)));
-	return res;
-      }
-      if(g == concat){
-	res = e;
-	return res;
       }
       int nargs = num_args(e);
       std::vector<ast> args(nargs);
@@ -792,6 +806,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
      return simplify_sum(args);
   }
 
+
   ast simplify_rotate_eq2leq(const ast &pl, const ast &neg_equality, const ast &pf){
     if(pl == arg(pf,1)){
       ast cond = mk_true();
@@ -1034,6 +1049,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
       ast mc = z3_simplify(chain_side_proves(LitA,pref));
       Aproves = my_and(Aproves,mc);
     }
+    if(is_true(nc))
+      return itp;
     return make_normal(itp,nc);
   }
 
@@ -2616,6 +2633,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
     }
 
     hash_map<ast,ast>::iterator it = localization_map.find(e);
+
+    if(it != localization_map.end() && is_bool_type(get_type(e)) 
+       && !pv->ranges_intersect(pv->ast_scope(it->second),rng))
+      it = localization_map.end();  // prevent quantifiers over booleans
+
     if(it != localization_map.end()){
       pf = localization_pf_map[e];
       e = it->second;
diff --git a/src/muz/base/fixedpoint_params.pyg b/src/muz/base/fixedpoint_params.pyg
index e09e1307b..e201c2a19 100644
--- a/src/muz/base/fixedpoint_params.pyg
+++ b/src/muz/base/fixedpoint_params.pyg
@@ -74,6 +74,8 @@ def_module_params('fixedpoint',
 			  ('stratified_inlining', BOOL, False, 'DUALITY: Use stratified inlining'),
 			  ('recursion_bound', UINT, UINT_MAX, 'DUALITY: Recursion bound for stratified inlining'),
 			  ('profile', BOOL, False, 'DUALITY: profile run time'),
+			  ('mbqi', BOOL, True, 'DUALITY: use model-based quantifier instantion'),
+			  ('batch_expand', BOOL, False, 'DUALITY: use batch expansion'),
                           ('dump_aig', SYMBOL, '', 'Dump clauses in AIG text format (AAG) to the given file name'),
                           ))
 
diff --git a/src/muz/duality/duality_dl_interface.cpp b/src/muz/duality/duality_dl_interface.cpp
index 248aca163..587a184bc 100755
--- a/src/muz/duality/duality_dl_interface.cpp
+++ b/src/muz/duality/duality_dl_interface.cpp
@@ -64,20 +64,22 @@ namespace Duality {
     std::vector<expr> clauses;
     std::vector<std::vector<RPFP::label_struct> > clause_labels;
     hash_map<RPFP::Edge *,int> map;  // edges to clauses
+    Solver *old_rs;
     Solver::Counterexample cex;
 
     duality_data(ast_manager &_m) : ctx(_m,config(params_ref())) {
       ls = 0;
       rpfp = 0;
       status = StatusNull;
+      old_rs = 0;
     }
     ~duality_data(){
+      if(old_rs)
+	dealloc(old_rs);
       if(rpfp)
 	dealloc(rpfp);
       if(ls)
 	dealloc(ls);
-      if(cex.tree)
-	delete cex.tree;
     }
   };
 
@@ -132,15 +134,18 @@ lbool dl_interface::query(::expr * query) {
   m_ctx.ensure_opened();
 
   // if there is old data, get the cex and dispose (later)
-  Solver::Counterexample old_cex;
   duality_data *old_data = _d;
-  if(old_data)
-    old_cex = old_data->cex;
+  Solver *old_rs = 0;
+  if(old_data){
+    old_rs = old_data->old_rs;
+    old_rs->GetCounterexample().swap(old_data->cex);
+  }
 
   scoped_proof generate_proofs_please(m_ctx.get_manager());
 
   // make a new problem and solver
   _d = alloc(duality_data,m_ctx.get_manager());
+  _d->ctx.set("mbqi",m_ctx.get_params().mbqi());
   _d->ls = alloc(RPFP::iZ3LogicSolver,_d->ctx);
   _d->rpfp = alloc(RPFP,_d->ls);
 
@@ -195,8 +200,9 @@ lbool dl_interface::query(::expr * query) {
 
   Solver *rs = Solver::Create("duality", _d->rpfp);
 
-  rs->LearnFrom(old_cex); // new solver gets hints from old cex
-
+  if(old_rs)
+    rs->LearnFrom(old_rs); // new solver gets hints from old solver
+  
   // set its options
   IF_VERBOSE(1, rs->SetOption("report","1"););
   rs->SetOption("full_expand",m_ctx.get_params().full_expand() ? "1" : "0");
@@ -204,6 +210,7 @@ lbool dl_interface::query(::expr * query) {
   rs->SetOption("feasible_edges",m_ctx.get_params().feasible_edges() ? "1" : "0");
   rs->SetOption("use_underapprox",m_ctx.get_params().use_underapprox() ? "1" : "0");
   rs->SetOption("stratified_inlining",m_ctx.get_params().stratified_inlining() ? "1" : "0");
+  rs->SetOption("batch_expand",m_ctx.get_params().batch_expand() ? "1" : "0");
   unsigned rb = m_ctx.get_params().recursion_bound();
   if(rb != UINT_MAX){
     std::ostringstream os; os << rb;
@@ -229,15 +236,14 @@ lbool dl_interface::query(::expr * query) {
 
   // save the result and counterexample if there is one
   _d->status = ans ? StatusModel : StatusRefutation;
-  _d->cex = rs->GetCounterexample();
+  _d->cex.swap(rs->GetCounterexample()); // take ownership of cex
+  _d->old_rs = rs; // save this for later hints
   
   if(old_data){
-    old_data->cex.tree = 0; // we own it now
-    dealloc(old_data);
+    dealloc(old_data); // this deallocates the old solver if there is one
   }
 
-
-  dealloc(rs);
+  // dealloc(rs); this is now owned by data
 
   // true means the RPFP problem is SAT, so the query is UNSAT
   return ans ? l_false : l_true;
@@ -265,18 +271,16 @@ void dl_interface::reset_statistics() {
 
 static hash_set<func_decl> *local_func_decls;
 
-static void print_proof(dl_interface *d, std::ostream& out, Solver::Counterexample &cex) {
+  static void print_proof(dl_interface *d, std::ostream& out, RPFP *tree, RPFP::Node *root) {
   context &ctx = d->dd()->ctx;
-  RPFP::Node &node = *cex.root;
+  RPFP::Node &node = *root;
   RPFP::Edge &edge = *node.Outgoing;
   
   // first, prove the children (that are actually used)
 
   for(unsigned i = 0; i < edge.Children.size(); i++){
-    if(!cex.tree->Empty(edge.Children[i])){
-      Solver::Counterexample foo = cex;
-      foo.root = edge.Children[i];
-      print_proof(d,out,foo);
+    if(!tree->Empty(edge.Children[i])){
+      print_proof(d,out,tree,edge.Children[i]);
     }
   }
 
@@ -285,7 +289,7 @@ static void print_proof(dl_interface *d, std::ostream& out, Solver::Counterexamp
   out << "(step s!" << node.number;
   out << " (" << node.Name.name();
   for(unsigned i = 0; i < edge.F.IndParams.size(); i++)
-    out << " " << cex.tree->Eval(&edge,edge.F.IndParams[i]);
+    out << " " << tree->Eval(&edge,edge.F.IndParams[i]);
   out << ")\n";
 
   // print the rule number
@@ -307,8 +311,8 @@ static void print_proof(dl_interface *d, std::ostream& out, Solver::Counterexamp
       sort the_sort = t.get_quantifier_bound_sort(j);
       symbol name = t.get_quantifier_bound_name(j);
       expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort));
-      out << "    (= " << skolem << " " << cex.tree->Eval(&edge,skolem) << ")\n";
-      expr local_skolem = cex.tree->Localize(&edge,skolem);
+      out << "    (= " << skolem << " " << tree->Eval(&edge,skolem) << ")\n";
+      expr local_skolem = tree->Localize(&edge,skolem);
       (*local_func_decls).insert(local_skolem.decl());
     }
   }
@@ -316,7 +320,7 @@ static void print_proof(dl_interface *d, std::ostream& out, Solver::Counterexamp
   
   out << "  (labels";
   std::vector<symbol> labels;
-  cex.tree->GetLabels(&edge,labels);
+  tree->GetLabels(&edge,labels);
   for(unsigned j = 0; j < labels.size(); j++){
     out << " " << labels[j];
   }
@@ -328,7 +332,7 @@ static void print_proof(dl_interface *d, std::ostream& out, Solver::Counterexamp
   
   out << "  (ref ";
   for(unsigned i = 0; i < edge.Children.size(); i++){
-    if(!cex.tree->Empty(edge.Children[i]))
+    if(!tree->Empty(edge.Children[i]))
       out << " s!" << edge.Children[i]->number;
     else
       out << " true";
@@ -353,11 +357,11 @@ void dl_interface::display_certificate_non_const(std::ostream& out) {
     // negation of the query is the last clause -- prove it
     hash_set<func_decl> locals;
     local_func_decls = &locals;
-    print_proof(this,out,_d->cex);
+    print_proof(this,out,_d->cex.get_tree(),_d->cex.get_root());
     out << ")\n";
     out << "(model \n\"";
     ::model mod(m_ctx.get_manager());
-    model orig_model = _d->cex.tree->dualModel;
+    model orig_model = _d->cex.get_tree()->dualModel;
     for(unsigned i = 0; i < orig_model.num_consts(); i++){
       func_decl cnst = orig_model.get_const_decl(i);
       if(locals.find(cnst) == locals.end()){
@@ -428,10 +432,10 @@ model_ref dl_interface::get_model() {
   return md;
 }
   
-static proof_ref extract_proof(dl_interface *d, Solver::Counterexample &cex) {
+  static proof_ref extract_proof(dl_interface *d, RPFP *tree, RPFP::Node *root) {
   context &ctx = d->dd()->ctx;
   ast_manager &mgr = ctx.m();
-  RPFP::Node &node = *cex.root;
+  RPFP::Node &node = *root;
   RPFP::Edge &edge = *node.Outgoing;
   RPFP::Edge *orig_edge = edge.map;
   
@@ -453,21 +457,19 @@ static proof_ref extract_proof(dl_interface *d, Solver::Counterexample &cex) {
       sort the_sort = t.get_quantifier_bound_sort(j);
       symbol name = t.get_quantifier_bound_name(j);
       expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort));
-      expr val = cex.tree->Eval(&edge,skolem);
+      expr val = tree->Eval(&edge,skolem);
       expr_ref thing(ctx.uncook(val),mgr);
       substs[0].push_back(thing);
-      expr local_skolem = cex.tree->Localize(&edge,skolem);
+      expr local_skolem = tree->Localize(&edge,skolem);
       (*local_func_decls).insert(local_skolem.decl());
     }
   }
 
   svector<std::pair<unsigned, unsigned> > pos;
   for(unsigned i = 0; i < edge.Children.size(); i++){
-    if(!cex.tree->Empty(edge.Children[i])){
+    if(!tree->Empty(edge.Children[i])){
       pos.push_back(std::pair<unsigned,unsigned>(i+1,0));
-      Solver::Counterexample foo = cex;
-      foo.root = edge.Children[i];
-      proof_ref prem = extract_proof(d,foo);
+      proof_ref prem = extract_proof(d,tree,edge.Children[i]);
       prems.push_back(prem);
       substs.push_back(expr_ref_vector(mgr));
     }
@@ -476,7 +478,7 @@ static proof_ref extract_proof(dl_interface *d, Solver::Counterexample &cex) {
   func_decl f = node.Name;
   std::vector<expr> args;
   for(unsigned i = 0; i < edge.F.IndParams.size(); i++)
-    args.push_back(cex.tree->Eval(&edge,edge.F.IndParams[i]));
+    args.push_back(tree->Eval(&edge,edge.F.IndParams[i]));
   expr conc = f(args);
   
 
@@ -493,7 +495,7 @@ proof_ref dl_interface::get_proof() {
   if(_d->status == StatusRefutation){
     hash_set<func_decl> locals;
     local_func_decls = &locals;
-    return extract_proof(this,_d->cex);
+    return extract_proof(this,_d->cex.get_tree(),_d->cex.get_root());
   }
   else
     return proof_ref(m_ctx.get_manager());