diff --git a/src/duality/duality.h b/src/duality/duality.h
index cc6d81b1a..b29a6a610 100644
--- a/src/duality/duality.h
+++ b/src/duality/duality.h
@@ -98,7 +98,7 @@ namespace Duality {
       bool IsClosedFormula(const Term &t);
 
       Term AdjustQuantifiers(const Term &t);
-private:
+protected:
 
       void SummarizeRec(hash_set<ast> &memo, std::vector<expr> &lits, int &ops, const Term &t);
       int CountOperatorsRec(hash_set<ast> &memo, const Term &t);
@@ -309,7 +309,7 @@ private:
 
       LogicSolver *ls;
         
-    private:
+    protected:
       int nodeCount;
       int edgeCount;
       
@@ -324,7 +324,7 @@ private:
       
     public:
       model dualModel;
-    private:
+    protected:
       literals dualLabels;
       std::list<stack_entry> stack;
       std::vector<Term> axioms; // only saved here for printing purposes
@@ -829,7 +829,7 @@ private:
        */
       void ComputeProofCore();
 
-    private:
+    protected:
       
       void ClearProofCore(){
 	if(proof_core)
@@ -947,6 +947,8 @@ private:
 
       expr SimplifyOr(std::vector<expr> &lits);
 
+      expr SimplifyAnd(std::vector<expr> &lits);
+
       void SetAnnotation(Node *root, const expr &t);
 
       void AddEdgeToSolver(Edge *edge);
@@ -959,9 +961,11 @@ private:
     
       expr NegateLit(const expr &f);
 
+      expr GetEdgeFormula(Edge *e, int persist, bool with_children, bool underapprox);
     };
     
-    /** RPFP solver base class. */
+
+  /** RPFP solver base class. */
 
     class Solver {
       
@@ -1044,3 +1048,54 @@ namespace std {
     }
   };
 }
+
+namespace Duality {
+    /** Caching version of RPFP. Instead of asserting constraints, returns assumption literals */
+
+    class RPFP_caching : public RPFP {
+  public:
+
+      /** appends assumption literals for edge to lits. if with_children is true,
+	  includes that annotation of the edge's children. 
+       */ 
+      void AssertEdgeCache(Edge *e, std::vector<Term> &lits, bool with_children = false);
+      
+      /** appends assumption literals for node to lits */
+      void AssertNodeCache(Node *, std::vector<Term> lits);
+
+      /** check assumption lits, and return core */
+      check_result CheckCore(const std::vector<Term> &assumps, std::vector<Term> &core);
+      
+      /** Clone another RPFP into this one, keeping a map */
+      void Clone(RPFP *other);
+
+      /** Get the clone of a node */
+      Node *GetNodeClone(Node *other_node);
+
+      /** Get the clone of an edge */
+      Edge *GetEdgeClone(Edge *other_edge);
+
+      /** Try to strengthen the parent of an edge */
+      void GeneralizeCache(Edge *edge);
+
+      /** Try to propagate some facts from children to parents of edge.
+	  Return true if success. */
+      bool PropagateCache(Edge *edge);
+
+      /** Construct a caching RPFP using a LogicSolver */
+      RPFP_caching(LogicSolver *_ls) : RPFP(_ls) {}
+
+  protected:
+      hash_map<ast,expr> AssumptionLits;
+      hash_map<Node *, Node *> NodeCloneMap;
+      hash_map<Edge *, Edge *> EdgeCloneMap;
+      
+      void GetAssumptionLits(const expr &fmla, std::vector<expr> &lits, hash_map<ast,expr> *opt_map = 0);
+
+      void GreedyReduceCache(std::vector<expr> &assumps, std::vector<expr> &core);
+
+      void FilterCore(std::vector<expr> &core, std::vector<expr> &full_core);
+
+    };
+
+}
diff --git a/src/duality/duality_profiling.cpp b/src/duality/duality_profiling.cpp
index bec32c51a..3b392a91a 100755
--- a/src/duality/duality_profiling.cpp
+++ b/src/duality/duality_profiling.cpp
@@ -26,6 +26,7 @@ Revision History:
 #include <stdlib.h>
 
 #include "duality_wrapper.h"
+#include "iz3profiling.h"
 
 namespace Duality {
   
@@ -103,6 +104,7 @@ namespace Duality {
       output_time(*pfs, it->second.t);
       (*pfs) << std::endl;
     }
+    profiling::print(os); // print the interpolation stats
   }
   
   void timer_start(const char *name){
diff --git a/src/duality/duality_rpfp.cpp b/src/duality/duality_rpfp.cpp
index 162175721..a95561f5d 100644
--- a/src/duality/duality_rpfp.cpp
+++ b/src/duality/duality_rpfp.cpp
@@ -519,6 +519,20 @@ namespace Duality {
       const expr &lit = args[i];
       expr atom, val;
       if(IsLiteral(lit,atom,val)){
+	if(atom.is_app() && atom.decl().get_decl_kind() == Equal)
+	  if(pol ? eq(val,ctx.bool_val(true)) : eq(val,ctx.bool_val(false))){
+	    expr lhs = atom.arg(0), rhs = atom.arg(1);
+	    if(lhs.is_numeral())
+	      std::swap(lhs,rhs);
+	    if(rhs.is_numeral() && lhs.is_app()){
+	      for(unsigned j = 0; j < args.size(); j++)
+		if(j != i){
+		  smemo.clear();
+		  smemo[lhs] = rhs;
+		  args[j] = SubstRec(smemo,args[j]);
+		}
+	    }
+	  }
 	for(unsigned j = 0; j < args.size(); j++)
 	  if(j != i){
 	    smemo.clear();
@@ -711,6 +725,39 @@ namespace Duality {
 #endif    
 
 
+  expr RPFP::GetEdgeFormula(Edge *e, int persist, bool with_children, bool underapprox)
+  {
+    if (e->dual.null()) {
+      timer_start("ReducedDualEdge");
+      e->dual = ReducedDualEdge(e);
+      timer_stop("ReducedDualEdge");
+      timer_start("getting children");
+      if(with_children)
+	for(unsigned i = 0; i < e->Children.size(); i++)
+	  e->dual = e->dual && GetAnnotation(e->Children[i]);
+      if(underapprox){
+	std::vector<expr> cus(e->Children.size());
+	for(unsigned i = 0; i < e->Children.size(); i++)
+	  cus[i] = !UnderapproxFlag(e->Children[i]) || GetUnderapprox(e->Children[i]);
+	expr cnst =  conjoin(cus);
+	e->dual = e->dual && cnst;
+      }
+      timer_stop("getting children");
+      timer_start("Persisting");
+      std::list<stack_entry>::reverse_iterator it = stack.rbegin();
+      for(int i = 0; i < persist && it != stack.rend(); i++)
+	it++;
+      if(it != stack.rend())
+	it->edges.push_back(e);
+      timer_stop("Persisting");
+      //Console.WriteLine("{0}", cnst);
+    }
+    return e->dual;
+    timer_start("solver add");
+    slvr.add(e->dual);
+    timer_stop("solver add");
+  }
+
   /** For incremental solving, asserts the constraint associated
    * with this edge in the SMT context. If this edge is removed,
    * you must pop the context accordingly. The second argument is
@@ -732,41 +779,40 @@ namespace Duality {
   {
     if(eq(e->F.Formula,ctx.bool_val(true)) && (!with_children || e->Children.empty()))
       return;
-    if (e->dual.null())
-      {
-	timer_start("ReducedDualEdge");
-	e->dual = ReducedDualEdge(e);
-	timer_stop("ReducedDualEdge");
-	timer_start("getting children");
-	if(with_children)
-	  for(unsigned i = 0; i < e->Children.size(); i++)
-	    e->dual = e->dual && GetAnnotation(e->Children[i]);
-	if(underapprox){
-	  std::vector<expr> cus(e->Children.size());
-	  for(unsigned i = 0; i < e->Children.size(); i++)
-	    cus[i] = !UnderapproxFlag(e->Children[i]) || GetUnderapprox(e->Children[i]);
-	  expr cnst =  conjoin(cus);
-	  e->dual = e->dual && cnst;
-	}
-	timer_stop("getting children");
-	timer_start("Persisting");
-	std::list<stack_entry>::reverse_iterator it = stack.rbegin();
-	for(int i = 0; i < persist && it != stack.rend(); i++)
-	  it++;
-	if(it != stack.rend())
-	  it->edges.push_back(e);
-#if 0
-	if(persist != 0)
-	  Z3_persist_ast(ctx,e->dual,persist);
-#endif
-	timer_stop("Persisting");
-	//Console.WriteLine("{0}", cnst);
-      }
+    expr fmla = GetEdgeFormula(e, persist, with_children, underapprox);
     timer_start("solver add");
     slvr.add(e->dual);
     timer_stop("solver add");
   }
 
+  // caching verion of above
+  void RPFP_caching::AssertEdgeCache(Edge *e, std::vector<Term> &lits, bool with_children){
+    if(eq(e->F.Formula,ctx.bool_val(true)) && (!with_children || e->Children.empty()))
+      return;
+    expr fmla = GetEdgeFormula(e, 0, with_children, false);
+    GetAssumptionLits(fmla,lits);
+  }
+      
+  void RPFP_caching::GetAssumptionLits(const expr &fmla, std::vector<expr> &lits, hash_map<ast,expr> *opt_map){
+    std::vector<expr> conjs;
+    CollectConjuncts(fmla,conjs);
+    for(unsigned i = 0; i < conjs.size(); i++){
+      const expr &conj = conjs[i];
+      std::pair<ast,Term> foo(conj,expr(ctx));
+      std::pair<hash_map<ast,Term>::iterator, bool> bar = AssumptionLits.insert(foo);
+      Term &res = bar.first->second;
+      if(bar.second){
+	func_decl pred = ctx.fresh_func_decl("@alit", ctx.bool_sort());
+	res = pred();
+	slvr.add(ctx.make(Implies,res,conj));
+	//	std::cout << res << ": " << conj << "\n";
+      }
+      if(opt_map)
+	(*opt_map)[res] = conj;
+      lits.push_back(res);
+    }
+  }
+
   void RPFP::ConstrainParent(Edge *parent, Node *child){
     ConstrainEdgeLocalized(parent,GetAnnotation(child));
   } 
@@ -786,6 +832,53 @@ namespace Duality {
       }
   }
 
+  // caching version of above
+  void RPFP_caching::AssertNodeCache(Node *n, std::vector<Term> lits){
+    if (n->dual.null())
+      {
+	n->dual = GetUpperBound(n);
+	stack.back().nodes.push_back(n);
+	GetAssumptionLits(n->dual,lits);
+      }
+  }
+  
+  /** Clone another RPFP into this one, keeping a map */
+  void RPFP_caching::Clone(RPFP *other){
+    for(unsigned i = 0; i < other->nodes.size(); i++)
+      NodeCloneMap[other->nodes[i]] = CloneNode(other->nodes[i]);
+    for(unsigned i = 0; i < other->edges.size(); i++){
+      Edge *edge = other->edges[i];
+      std::vector<Node *> cs;
+      for(unsigned j = 0; j < edge->Children.size(); j++)
+	// cs.push_back(NodeCloneMap[edge->Children[j]]);
+	cs.push_back(CloneNode(edge->Children[j]));
+      EdgeCloneMap[edge] = CreateEdge(NodeCloneMap[edge->Parent],edge->F,cs);
+    }
+  }
+  
+  /** Get the clone of a node */
+  RPFP::Node *RPFP_caching::GetNodeClone(Node *other_node){
+    return NodeCloneMap[other_node];
+  }
+  
+  /** Get the clone of an edge */
+  RPFP::Edge *RPFP_caching::GetEdgeClone(Edge *other_edge){
+    return EdgeCloneMap[other_edge];
+  }  
+
+  /** check assumption lits, and return core */
+  check_result RPFP_caching::CheckCore(const std::vector<Term> &assumps, std::vector<Term> &core){
+    core.resize(assumps.size());
+    unsigned core_size;
+    check_result res = slvr.check(assumps.size(),(expr *)&assumps[0],&core_size,&core[0]);
+    if(res == unsat)
+      core.resize(core_size);
+    else
+      core.clear();
+    return res;
+  }
+  
+      
   /** Assert a constraint on an edge in the SMT context. 
    */
 
@@ -970,6 +1063,7 @@ namespace Duality {
 
   check_result RPFP::Check(Node *root, std::vector<Node *> underapproxes, std::vector<Node *> *underapprox_core )
         {
+	  timer_start("Check");
 	  ClearProofCore();
 	  // if (dualModel != null) dualModel.Dispose();
 	  check_result res;
@@ -1002,6 +1096,7 @@ namespace Duality {
             // check_result temp = slvr.check();
 	  }
 	  dualModel = slvr.get_model();
+	  timer_stop("Check");
 	  return res;
         }
 
@@ -1927,10 +2022,14 @@ namespace Duality {
       for(int i = 0; i < num_args; i++)
 	CollectConjuncts(f.arg(i),lits,false);
     }
-    else if(pos)
-      lits.push_back(f);
-    else
-      lits.push_back(!f);
+    else if(pos){
+      if(!eq(f,ctx.bool_val(true)))
+	lits.push_back(f);
+    }
+    else {
+      if(!eq(f,ctx.bool_val(false)))
+	lits.push_back(!f);
+    }
   }
 
   struct TermLt {
@@ -2253,6 +2352,45 @@ namespace Duality {
     }
   }
 
+  void RPFP_caching::FilterCore(std::vector<expr> &core, std::vector<expr> &full_core){
+    hash_set<ast> core_set;
+    std::copy(full_core.begin(),full_core.end(),std::inserter(core_set,core_set.begin()));
+    std::vector<expr> new_core;
+    for(unsigned i = 0; i < core.size(); i++)
+      if(core_set.find(core[i]) != core_set.end())
+	new_core.push_back(core[i]);
+    core.swap(new_core);
+  }
+
+  void RPFP_caching::GreedyReduceCache(std::vector<expr> &assumps, std::vector<expr> &core){
+    std::vector<expr> lits = assumps, full_core; 
+    std::copy(core.begin(),core.end(),std::inserter(lits,lits.end()));
+    
+    // verify
+    check_result res = CheckCore(lits,full_core);
+    if(res != unsat)
+      throw "should be unsat";
+    FilterCore(core,full_core);
+    
+    std::vector<expr> dummy;
+    if(CheckCore(full_core,dummy) != unsat)
+      throw "should be unsat";
+
+    for(unsigned i = 0; i < core.size(); ){
+      expr temp = core[i];
+      std::swap(core[i],core.back());
+      core.pop_back();
+      lits.resize(assumps.size());
+      std::copy(core.begin(),core.end(),std::inserter(lits,lits.end()));
+      res = CheckCore(lits,full_core);
+      if(res != unsat){
+	core.push_back(temp);
+	std::swap(core[i],core.back());
+	i++;
+      }
+    }
+  }
+
   expr RPFP::NegateLit(const expr &f){
     if(f.is_app() && f.decl().get_decl_kind() == Not)
       return f.arg(0);
@@ -2278,6 +2416,14 @@ namespace Duality {
     return ctx.make(Or,lits);
   }
 
+  expr RPFP::SimplifyAnd(std::vector<expr> &lits){
+    if(lits.size() == 0)
+      return ctx.bool_val(true);
+    if(lits.size() == 1)
+      return lits[0];
+    return ctx.make(And,lits);
+  }
+
     // set up edge constraint in aux solver
   void RPFP::AddEdgeToSolver(Edge *edge){
     if(!edge->dual.null())
@@ -2321,7 +2467,7 @@ namespace Duality {
 	std::vector<expr> case_lits;
 	itp = StrengthenFormulaByCaseSplitting(itp, case_lits);
 	SetAnnotation(node,itp);
-	node->Annotation.Formula.simplify();
+	node->Annotation.Formula = node->Annotation.Formula.simplify();
       }
 
       if(node->Annotation.IsEmpty()){
@@ -2330,6 +2476,7 @@ namespace Duality {
 	  const std::vector<expr> &theory = ls->get_axioms();
 	  for(unsigned i = 0; i < theory.size(); i++)
 	    aux_solver.add(theory[i]);
+	  axioms_added = true;
 	}
 	else {
 	  std::cout << "bad in InterpolateByCase -- core:\n";
@@ -2350,6 +2497,7 @@ namespace Duality {
   }
 
   void RPFP::Generalize(Node *root, Node *node){
+    timer_start("Generalize");
     aux_solver.push();
     AddEdgeToSolver(node->Outgoing);
     expr fmla = GetAnnotation(node);
@@ -2359,8 +2507,103 @@ namespace Duality {
     aux_solver.pop(1);
     NegateLits(conjuncts);
     SetAnnotation(node,SimplifyOr(conjuncts));
+    timer_stop("Generalize");
   }
 
+
+  // caching version of above
+  void RPFP_caching::GeneralizeCache(Edge *edge){
+    timer_start("Generalize");
+    Node *node = edge->Parent;
+    std::vector<expr> assumps, core, conjuncts;
+    AssertEdgeCache(edge,assumps);
+    for(unsigned i = 0; i < edge->Children.size(); i++){
+      expr ass = GetAnnotation(edge->Children[i]);
+      std::vector<expr> clauses;
+      CollectConjuncts(ass.arg(1),clauses);
+      for(unsigned j = 0; j < clauses.size(); j++)
+	GetAssumptionLits(ass.arg(0) || clauses[j],assumps);
+    }
+    expr fmla = GetAnnotation(node);
+    assumps.push_back(fmla.arg(0).arg(0));
+    std::vector<expr> lits;
+    CollectConjuncts(!fmla.arg(1),lits);
+#if 0
+    for(unsigned i = 0; i < lits.size(); i++){
+      const expr &lit = lits[i];
+      if(lit.is_app() && lit.decl().get_decl_kind() == Equal){
+	lits[i] = ctx.make(Leq,lit.arg(0),lit.arg(1));
+	lits.push_back(ctx.make(Leq,lit.arg(1),lit.arg(0)));
+      }
+    }
+#endif
+    hash_map<ast,expr> lit_map;
+    for(unsigned i = 0; i < lits.size(); i++)
+      GetAssumptionLits(lits[i],core,&lit_map);
+    GreedyReduceCache(assumps,core);
+    for(unsigned i = 0; i < core.size(); i++)
+      conjuncts.push_back(lit_map[core[i]]); 
+    NegateLits(conjuncts);
+    SetAnnotation(node,SimplifyOr(conjuncts));
+    timer_stop("Generalize");
+  }
+
+  // caching version of above
+  bool RPFP_caching::PropagateCache(Edge *edge){
+    timer_start("PropagateCache");
+    bool some = false;
+    {
+      std::vector<expr> candidates, skip;
+      Node *node = edge->Parent;
+      CollectConjuncts(node->Annotation.Formula,skip);
+      for(unsigned i = 0; i < edge->Children.size(); i++){
+	Node *child = edge->Children[i];
+	if(child->map == node->map){
+	  CollectConjuncts(child->Annotation.Formula,candidates);
+	  break;
+	}
+      }
+      if(candidates.empty()) goto done;
+      hash_set<ast> skip_set;
+      std::copy(skip.begin(),skip.end(),std::inserter(skip_set,skip_set.begin()));
+      std::vector<expr> new_candidates;
+      for(unsigned i = 0; i < candidates.size(); i++)
+	if(skip_set.find(candidates[i]) == skip_set.end())
+	  new_candidates.push_back(candidates[i]);
+      candidates.swap(new_candidates);
+      if(candidates.empty()) goto done;
+      std::vector<expr> assumps, core, conjuncts;
+      AssertEdgeCache(edge,assumps);
+      for(unsigned i = 0; i < edge->Children.size(); i++){
+	expr ass = GetAnnotation(edge->Children[i]);
+	std::vector<expr> clauses;
+	CollectConjuncts(ass.arg(1),clauses);
+	for(unsigned j = 0; j < clauses.size(); j++)
+	  GetAssumptionLits(ass.arg(0) || clauses[j],assumps);
+      }
+      for(unsigned i = 0; i < candidates.size(); i++){
+	unsigned old_size = assumps.size();
+	node->Annotation.Formula = candidates[i];
+	expr fmla = GetAnnotation(node);
+	assumps.push_back(fmla.arg(0).arg(0));
+	GetAssumptionLits(!fmla.arg(1),assumps);
+	std::vector<expr> full_core; 
+	check_result res = CheckCore(assumps,full_core);
+	if(res == unsat)
+	  conjuncts.push_back(candidates[i]);
+	assumps.resize(old_size);
+      }
+      if(conjuncts.empty())
+	goto done;
+      SetAnnotation(node,SimplifyAnd(conjuncts));
+      some = true;
+    }
+  done:
+    timer_stop("PropagateCache");
+    return some;
+  }
+
+
   /** Push a scope. Assertions made after Push can be undone by Pop. */
 
   void RPFP::Push()
diff --git a/src/duality/duality_solver.cpp b/src/duality/duality_solver.cpp
index 6ef9d7746..7318b020d 100644
--- a/src/duality/duality_solver.cpp
+++ b/src/duality/duality_solver.cpp
@@ -44,7 +44,7 @@ Revision History:
 // #define TOP_DOWN
 // #define EFFORT_BOUNDED_STRAT
 #define SKIP_UNDERAPPROX_NODES
-
+#define USE_RPFP_CLONE
 
 namespace Duality {
 
@@ -115,8 +115,25 @@ namespace Duality {
       Report = false;
       StratifiedInlining = false;
       RecursionBound = -1;
+#ifdef USE_RPFP_CLONE
+      clone_ls = new RPFP::iZ3LogicSolver(ctx);
+      clone_rpfp = new RPFP_caching(clone_ls);
+      clone_rpfp->Clone(rpfp);
+#endif      
     }
 
+    ~Duality(){
+#ifdef USE_RPFP_CLONE
+      delete clone_rpfp;
+      delete clone_ls;
+#endif      
+    }
+
+#ifdef USE_RPFP_CLONE
+    RPFP::LogicSolver *clone_ls;
+    RPFP_caching *clone_rpfp;
+#endif      
+
     typedef RPFP::Node Node;
     typedef RPFP::Edge Edge;
 
@@ -1309,6 +1326,7 @@ namespace Duality {
       node. */
     bool SatisfyUpperBound(Node *node){
       if(node->Bound.IsFull()) return true;
+      Propagate();
       reporter->Bound(node);
       int start_decs = rpfp->CumulativeDecisions();
       DerivationTree *dtp = new DerivationTreeSlow(this,unwinding,reporter,heuristic,FullExpand);
@@ -1412,6 +1430,70 @@ namespace Duality {
       }
     }
 
+    // Propagate conjuncts up the unwinding
+    void Propagate(){
+      reporter->Message("beginning propagation");
+      timer_start("Propagate");
+      std::vector<Node *> sorted_nodes = unwinding->nodes;
+      std::sort(sorted_nodes.begin(),sorted_nodes.end(),std::less<Node *>()); // sorts by sequence number
+      hash_map<Node *,std::set<expr> > facts;
+      for(unsigned i = 0; i < sorted_nodes.size(); i++){
+	Node *node = sorted_nodes[i];
+	std::set<expr> &node_facts = facts[node->map];
+	if(!(node->Outgoing && indset->Contains(node)))
+	  continue;
+	std::vector<expr> conj_vec;
+	unwinding->CollectConjuncts(node->Annotation.Formula,conj_vec);
+	std::set<expr> conjs;
+	std::copy(conj_vec.begin(),conj_vec.end(),std::inserter(conjs,conjs.begin()));
+	if(!node_facts.empty()){
+	  RPFP *checker = new RPFP(rpfp->ls);
+	  slvr.push();
+	  Node *root = checker->CloneNode(node);
+	  Edge *edge = node->Outgoing;
+	  // checker->AssertNode(root);
+	  std::vector<Node *> cs;
+	  for(unsigned j = 0; j < edge->Children.size(); j++){
+	    Node *oc = edge->Children[j];
+	    Node *nc = checker->CloneNode(oc);
+	    nc->Annotation = oc->Annotation; // is this needed?
+	    cs.push_back(nc);
+	  }
+	  Edge *checker_edge = checker->CreateEdge(root,edge->F,cs); 
+	  checker->AssertEdge(checker_edge, 0, true, false);
+	  std::vector<expr> propagated;
+	  for(std::set<expr> ::iterator it = node_facts.begin(), en = node_facts.end(); it != en;){
+	    const expr &fact = *it;
+	    if(conjs.find(fact) == conjs.end()){
+	      root->Bound.Formula = fact;
+	      slvr.push();
+	      checker->AssertNode(root);
+	      check_result res = checker->Check(root);
+	      slvr.pop();
+	      if(res != unsat){
+		std::set<expr> ::iterator victim = it;
+		++it;
+		node_facts.erase(victim); // if it ain't true, nix it
+		continue;
+	      }
+	      propagated.push_back(fact);
+	    }
+	    ++it;
+	  }
+	  slvr.pop();
+	  for(unsigned i = 0; i < propagated.size(); i++){
+	    root->Annotation.Formula = propagated[i];
+	    UpdateNodeToNode(node,root);
+	  }
+	  delete checker;
+	}
+	for(std::set<expr> ::iterator it = conjs.begin(), en = conjs.end(); it != en; ++it){
+	  expr foo = *it;
+	  node_facts.insert(foo);
+	}
+      }
+      timer_stop("Propagate");
+    }
 
     /** This class represents a derivation tree. */
     class DerivationTree {
@@ -1757,7 +1839,9 @@ namespace Duality {
 		tree->SolveSingleNode(top,node);
 		if(expansions.size() == 1 && NodeTooComplicated(node))
 		  SimplifyNode(node);
-		tree->Generalize(top,node);
+		else
+		  node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify();
+		Generalize(node);
 		if(RecordUpdate(node))
 		  update_count++;
 	      }
@@ -1791,7 +1875,14 @@ namespace Duality {
 		RemoveExpansion(node);
 	      }
 	      stack.pop_back();
-	      if(prev_level_used || stack.size() == 1) break;
+	      if(stack.size() == 1)break;
+	      if(prev_level_used){
+		Node *node = stack.back().expansions[0];
+		if(!Propagate(node)) break;
+		if(!RecordUpdate(node)) break; // shouldn't happen!
+		RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list
+		continue;
+	      }
 	      RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list
 	      std::vector<Node *> &unused_ex = stack.back().expansions;
 	      for(unsigned i = 0; i < unused_ex.size(); i++)
@@ -1833,8 +1924,10 @@ namespace Duality {
 
       void SimplifyNode(Node *node){
 	// have to destroy the old proof to get a new interpolant
+	timer_start("SimplifyNode");
 	tree->PopPush();
 	tree->InterpolateByCases(top,node);
+	timer_stop("SimplifyNode");
       }
 
       bool LevelUsedInProof(unsigned level){
@@ -1933,6 +2026,34 @@ namespace Duality {
 	throw "can't unmap node";
       }
 
+      void Generalize(Node *node){
+#ifndef USE_RPFP_CLONE
+	tree->Generalize(top,node);
+#else
+	RPFP_caching *clone_rpfp = duality->clone_rpfp;
+	Edge *clone_edge = clone_rpfp->GetEdgeClone(node->Outgoing->map);
+	Node *clone_node = clone_edge->Parent;
+	clone_node->Annotation = node->Annotation;
+	for(unsigned i = 0; i < clone_edge->Children.size(); i++)
+	  clone_edge->Children[i]->Annotation = node->map->Outgoing->Children[i]->Annotation;
+	clone_rpfp->GeneralizeCache(clone_edge);
+	node->Annotation = clone_node->Annotation;
+      }
+#endif
+
+      bool Propagate(Node *node){
+	RPFP_caching *clone_rpfp = duality->clone_rpfp;
+	Edge *clone_edge = clone_rpfp->GetEdgeClone(node->Outgoing->map);
+	Node *clone_node = clone_edge->Parent;
+	clone_node->Annotation = node->map->Annotation;
+	for(unsigned i = 0; i < clone_edge->Children.size(); i++)
+	  clone_edge->Children[i]->Annotation = node->map->Outgoing->Children[i]->Annotation;
+	bool res = clone_rpfp->PropagateCache(clone_edge);
+	if(res)
+	  node->Annotation = clone_node->Annotation;
+	return res;
+      }
+
     };
 
 
diff --git a/src/duality/duality_wrapper.cpp b/src/duality/duality_wrapper.cpp
index 55883202f..26bdf52d7 100644
--- a/src/duality/duality_wrapper.cpp
+++ b/src/duality/duality_wrapper.cpp
@@ -504,7 +504,10 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
 	  add(linear_assumptions[i][j]);
     }
     
-    check_result res = check();
+    check_result res = unsat;
+
+    if(!m_solver->get_proof())
+      res = check();
     
     if(res == unsat){
 
diff --git a/src/duality/duality_wrapper.h b/src/duality/duality_wrapper.h
index a36f93b40..fa4eca77b 100755
--- a/src/duality/duality_wrapper.h
+++ b/src/duality/duality_wrapper.h
@@ -1393,6 +1393,18 @@ namespace std {
   };
 }
 
+// to make Duality::ast usable in ordered collections
+namespace std {
+  template <>
+    class less<Duality::expr> {
+  public:
+    bool operator()(const Duality::expr &s, const Duality::expr &t) const {
+      // return s.raw() < t.raw();
+      return s.raw()->get_id() < t.raw()->get_id();
+    }
+  };
+}
+
 // to make Duality::func_decl hashable
 namespace hash_space {
   template <>
diff --git a/src/interp/iz3proof_itp.cpp b/src/interp/iz3proof_itp.cpp
index 75d14bca1..8b78a7135 100644
--- a/src/interp/iz3proof_itp.cpp
+++ b/src/interp/iz3proof_itp.cpp
@@ -2170,7 +2170,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
     for(unsigned i = 0; i < prem_cons.size(); i++){
       const ast &lit = prem_cons[i];
       if(get_term_type(lit) == LitA)
-	linear_comb(thing,coeffs[i],lit);
+	// Farkas rule seems to assume strict integer inequalities are rounded
+	linear_comb(thing,coeffs[i],lit,true /*round_off*/);
     }
     thing = simplify_ineq(thing);
     for(unsigned i = 0; i < prem_cons.size(); i++){
@@ -2195,9 +2196,9 @@ class iz3proof_itp_impl : public iz3proof_itp {
 
   /** Set P to P + cQ, where P and Q are linear inequalities. Assumes P is 0 <= y or 0 < y. */
 
-  void linear_comb(ast &P, const ast &c, const ast &Q){
+  void linear_comb(ast &P, const ast &c, const ast &Q, bool round_off = false){
     ast Qrhs;
-    bool strict = op(P) == Lt;
+    bool qstrict = false;
     if(is_not(Q)){
       ast nQ = arg(Q,0);
       switch(op(nQ)){
@@ -2209,11 +2210,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
 	break;
       case Geq:
 	Qrhs = make(Sub,arg(nQ,1),arg(nQ,0));
-	strict = true;
+	qstrict = true;
 	break;
       case Leq: 
 	Qrhs = make(Sub,arg(nQ,0),arg(nQ,1));
-	strict = true;
+	qstrict = true;
 	break;
       default:
 	throw proof_error();
@@ -2229,17 +2230,20 @@ class iz3proof_itp_impl : public iz3proof_itp {
 	break;
       case Lt:
 	Qrhs = make(Sub,arg(Q,1),arg(Q,0));
-	strict = true;
+	qstrict = true;
 	break;
       case Gt: 
 	Qrhs = make(Sub,arg(Q,0),arg(Q,1));
-	strict = true;
+	qstrict = true;
 	break;
       default:
 	throw proof_error();
       }
     }
     Qrhs = make(Times,c,Qrhs);
+    bool pstrict = op(P) == Lt, strict = pstrict || qstrict;
+    if(pstrict && qstrict && round_off)
+      Qrhs = make(Sub,Qrhs,make_int(rational(1)));
     if(strict)
       P = make(Lt,arg(P,0),make(Plus,arg(P,1),Qrhs));
     else