X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fparamodulation%2Fsaturation.ml;h=8e67bc7a05cee8147a2f0a774f56f0fe7073d12e;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=00e266ce33fcd06fc17567ceb4d8eca526749f9c;hpb=43c2a5068c1ff5f838e0558bb60c21e316cab852;p=helm.git

diff --git a/helm/ocaml/paramodulation/saturation.ml b/helm/ocaml/paramodulation/saturation.ml
index 00e266ce3..8e67bc7a0 100644
--- a/helm/ocaml/paramodulation/saturation.ml
+++ b/helm/ocaml/paramodulation/saturation.ml
@@ -1,3 +1,28 @@
+(* Copyright (C) 2005, HELM Team.
+ * 
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ * 
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ * 
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA  02111-1307, USA.
+ * 
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
 open Inference;;
 open Utils;;
 
@@ -53,12 +78,6 @@ type goal = proof * Cic.metasenv * Cic.term;;
 type theorem = Cic.term * Cic.term * Cic.metasenv;;
 
 
-(*
-let symbols_of_equality (_, (_, left, right), _, _) =
-  TermSet.union (symbols_of_term left) (symbols_of_term right)
-;;
-*)
-
 let symbols_of_equality ((_, _, (_, left, right, _), _, _) as equality) =
   let m1 = symbols_of_term left in
   let m = 
@@ -71,10 +90,6 @@ let symbols_of_equality ((_, _, (_, left, right, _), _, _) as equality) =
            TermMap.add k v res)
       (symbols_of_term right) m1
   in
-(*   Printf.printf "symbols_of_equality %s:\n" *)
-(*     (string_of_equality equality); *)
-(*   TermMap.iter (fun k v -> Printf.printf "%s: %d\n" (CicPp.ppterm k) v) m; *)
-(*   print_newline (); *)
   m
 ;;
 
@@ -88,9 +103,6 @@ module OrderedEquality = struct
     | false ->
         let w1, _, (ty, left, right, _), _, a = eq1
         and w2, _, (ty', left', right', _), _, a' = eq2 in
-(*         let weight_of t = fst (weight_of_term ~consider_metas:false t) in *)
-(*         let w1 = (weight_of ty) + (weight_of left) + (weight_of right) *)
-(*         and w2 = (weight_of ty') + (weight_of left') + (weight_of right') in *)
         match Pervasives.compare w1 w2 with
         | 0 ->
             let res = (List.length a) - (List.length a') in
@@ -99,11 +111,6 @@ module OrderedEquality = struct
                 let res = Pervasives.compare (List.hd a) (List.hd a') in
                 if res <> 0 then res else Pervasives.compare eq1 eq2
               with Failure "hd" -> Pervasives.compare eq1 eq2
-(*               match a, a' with *)
-(*               | (Cic.Meta (i, _)::_), (Cic.Meta (j, _)::_) -> *)
-(*                   let res = Pervasives.compare i j in *)
-(*                   if res <> 0 then res else Pervasives.compare eq1 eq2 *)
-(*               | _, _ -> Pervasives.compare eq1 eq2 *)
             )
         | res -> res
 end
@@ -111,13 +118,15 @@ end
 module EqualitySet = Set.Make(OrderedEquality);;
 
 
+(**
+   selects one equality from passive. The selection strategy is a combination
+   of weight, age and goal-similarity
+*)
 let select env goals passive (active, _) =
   processed_clauses := !processed_clauses + 1;
-
   let goal =
     match (List.rev goals) with (_, goal::_)::_ -> goal | _ -> assert false
   in
-  
   let (neg_list, neg_set), (pos_list, pos_set), passive_table = passive in
   let remove eq l =
     List.filter (fun e -> e <> eq) l
@@ -135,8 +144,6 @@ let select env goals passive (active, _) =
       | [], hd::tl ->
           let passive_table =
             Indexing.remove_index passive_table hd
-(*             if !use_fullred then Indexing.remove_index passive_table hd *)
-(*             else passive_table *)
           in
           (Positive, hd),
           (([], neg_set), (tl, EqualitySet.remove hd pos_set), passive_table)
@@ -147,67 +154,43 @@ let select env goals passive (active, _) =
       let cardinality map =
         TermMap.fold (fun k v res -> res + v) map 0
       in
-(*       match active with *)
-(*       | (Negative, e)::_ -> *)
-(*           let symbols = symbols_of_equality e in *)
       let symbols =
         let _, _, term = goal in
         symbols_of_term term
       in
-          let card = cardinality symbols in
-          let foldfun k v (r1, r2) = 
-            if TermMap.mem k symbols then
-              let c = TermMap.find k symbols in
-              let c1 = abs (c - v) in
-              let c2 = v - c1 in
-              r1 + c2, r2 + c1
-            else
-              r1, r2 + v
-          in
-          let f equality (i, e) =
-            let common, others =
-              TermMap.fold foldfun (symbols_of_equality equality) (0, 0)
-            in
-            let c = others + (abs (common - card)) in
-            if c < i then (c, equality)
-(*             else if c = i then *)
-(*               match OrderedEquality.compare equality e with *)
-(*               | -1 -> (c, equality) *)
-(*               | res -> (i, e) *)
-            else (i, e)
-          in
-          let e1 = EqualitySet.min_elt pos_set in
-          let initial =
-            let common, others = 
-              TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
-            in
-            (others + (abs (common - card))), e1
-          in
-          let _, current = EqualitySet.fold f pos_set initial in
-(*           Printf.printf "\nsymbols-based selection: %s\n\n" *)
-(*             (string_of_equality ~env current); *)
-          let passive_table =
-            Indexing.remove_index passive_table current
-(*             if !use_fullred then Indexing.remove_index passive_table current *)
-(*             else passive_table *)
-          in
-          (Positive, current),
-          (([], neg_set),
-           (remove current pos_list, EqualitySet.remove current pos_set),
-           passive_table)
-(*       | _ -> *)
-(*           let current = EqualitySet.min_elt pos_set in *)
-(*           let passive_table = *)
-(*             Indexing.remove_index passive_table current *)
-(* (\*             if !use_fullred then Indexing.remove_index passive_table current *\) *)
-(* (\*             else passive_table *\) *)
-(*           in *)
-(*           let passive = *)
-(*             (neg_list, neg_set), *)
-(*             (remove current pos_list, EqualitySet.remove current pos_set), *)
-(*             passive_table *)
-(*           in *)
-(*           (Positive, current), passive *)
+      let card = cardinality symbols in
+      let foldfun k v (r1, r2) = 
+        if TermMap.mem k symbols then
+          let c = TermMap.find k symbols in
+          let c1 = abs (c - v) in
+          let c2 = v - c1 in
+          r1 + c2, r2 + c1
+        else
+          r1, r2 + v
+      in
+      let f equality (i, e) =
+        let common, others =
+          TermMap.fold foldfun (symbols_of_equality equality) (0, 0)
+        in
+        let c = others + (abs (common - card)) in
+        if c < i then (c, equality)
+        else (i, e)
+      in
+      let e1 = EqualitySet.min_elt pos_set in
+      let initial =
+        let common, others = 
+          TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
+        in
+        (others + (abs (common - card))), e1
+      in
+      let _, current = EqualitySet.fold f pos_set initial in
+      let passive_table =
+        Indexing.remove_index passive_table current
+      in
+      (Positive, current),
+      (([], neg_set),
+       (remove current pos_list, EqualitySet.remove current pos_set),
+       passive_table)
     )
   | _ ->
       symbols_counter := !symbols_ratio;
@@ -218,8 +201,6 @@ let select env goals passive (active, _) =
           (neg_list, neg_set),
           (remove current pos_list, EqualitySet.remove current pos_set),
           Indexing.remove_index passive_table current
-(*           if !use_fullred then Indexing.remove_index passive_table current *)
-(*           else passive_table *)
         in
         (Positive, current), passive
       else
@@ -233,6 +214,7 @@ let select env goals passive (active, _) =
 ;;
 
 
+(* initializes the passive set of equalities *)
 let make_passive neg pos =
   let set_of equalities =
     List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities
@@ -240,11 +222,6 @@ let make_passive neg pos =
   let table =
       List.fold_left (fun tbl e -> Indexing.index tbl e)
         (Indexing.empty_table ()) pos
-(*     if !use_fullred then *)
-(*       List.fold_left (fun tbl e -> Indexing.index tbl e) *)
-(*         (Indexing.empty_table ()) pos *)
-(*     else *)
-(*       Indexing.empty_table () *)
   in
   (neg, set_of neg),
   (pos, set_of pos),
@@ -257,17 +234,15 @@ let make_active () =
 ;;
 
 
+(* adds to passive a list of equalities: new_neg is a list of negative
+   equalities, new_pos a list of positive equalities *)
 let add_to_passive passive (new_neg, new_pos) =
   let (neg_list, neg_set), (pos_list, pos_set), table = passive in
   let ok set equality = not (EqualitySet.mem equality set) in
   let neg = List.filter (ok neg_set) new_neg
   and pos = List.filter (ok pos_set) new_pos in
   let table =
-      List.fold_left (fun tbl e -> Indexing.index tbl e) table pos
-(*     if !use_fullred then *)
-(*       List.fold_left (fun tbl e -> Indexing.index tbl e) table pos *)
-(*     else *)
-(*       table *)
+    List.fold_left (fun tbl e -> Indexing.index tbl e) table pos
   in
   let add set equalities =
     List.fold_left (fun s e -> EqualitySet.add e s) set equalities
@@ -294,6 +269,8 @@ let size_of_active (active_list, _) =
 ;;
 
 
+(* removes from passive equalities that are estimated impossible to activate
+   within the current time limit *)
 let prune_passive howmany (active, _) passive =
   let (nl, ns), (pl, ps), tbl = passive in
   let howmany = float_of_int howmany
@@ -366,8 +343,6 @@ let prune_passive howmany (active, _) passive =
     else
       EqualitySet.empty, EqualitySet.empty
   in
-(*   let in_weight, ns = pickw in_weight ns in *)
-(*   let _, ps = pickw in_weight ps in *)
   let ns, ps = pickw in_weight ns ps in
   let rec picka w s l =
     if w > 0 then
@@ -385,21 +360,16 @@ let prune_passive howmany (active, _) passive =
   let in_age, ns, nl = picka in_age ns nl in
   let _, ps, pl = picka in_age ps pl in
   if not (EqualitySet.is_empty ps) then
-(*     maximal_weight := Some (weight_of_equality (EqualitySet.max_elt ps)); *)
     maximal_retained_equality := Some (EqualitySet.max_elt ps); 
   let tbl =
     EqualitySet.fold
       (fun e tbl -> Indexing.index tbl e) ps (Indexing.empty_table ())
-(*     if !use_fullred then *)
-(*       EqualitySet.fold *)
-(*         (fun e tbl -> Indexing.index tbl e) ps (Indexing.empty_table ()) *)
-(*     else *)
-(*       tbl *)
   in
   (nl, ns), (pl, ps), tbl  
 ;;
 
 
+(** inference of new equalities between current and some in active *)
 let infer env sign current (active_list, active_table) =
   let new_neg, new_pos = 
     match sign with
@@ -498,6 +468,7 @@ let contains_empty env (negative, positive) =
 ;;
 
 
+(** simplifies current using active and passive *)
 let forward_simplify env (sign, current) ?passive (active_list, active_table) =
   let pl, passive_table =
     match passive with
@@ -508,24 +479,6 @@ let forward_simplify env (sign, current) ?passive (active_list, active_table) =
         pn @ pp, Some pt
   in
   let all = if pl = [] then active_list else active_list @ pl in
-
-  (*   let rec find_duplicate sign current = function *)
-(*     | [] -> false *)
-(*     | (s, eq)::tl when s = sign -> *)
-(*         if meta_convertibility_eq current eq then true *)
-(*         else find_duplicate sign current tl *)
-(*     | _::tl -> find_duplicate sign current tl *)
-(*   in *)
-
-(*   let res =  *)
-(*     if sign = Positive then *)
-(*       Indexing.subsumption env active_table current *)
-(*     else *)
-(*       false *)
-(*   in *)
-(*   if res then *)
-(*     None *)
-(*   else *)
   
   let demodulate table current = 
     let newmeta, newcurrent =
@@ -533,7 +486,19 @@ let forward_simplify env (sign, current) ?passive (active_list, active_table) =
     maxmeta := newmeta;
     if is_identity env newcurrent then
       if sign = Negative then Some (sign, newcurrent)
-      else None
+      else (
+(* 	debug_print  *)
+(* 	  (lazy *)
+(* 	     (Printf.sprintf "\ncurrent was: %s\nnewcurrent is: %s\n" *)
+(* 		(string_of_equality current) *)
+(* 		(string_of_equality newcurrent))); *)
+(* 	debug_print *)
+(* 	  (lazy *)
+(* 	     (Printf.sprintf "active is: %s" *)
+(* 		(String.concat "\n"  *)
+(* 		   (List.map (fun (_, e) -> (string_of_equality e)) active_list)))); *)
+	None
+      )
     else
       Some (sign, newcurrent)
   in
@@ -560,34 +525,18 @@ let forward_simplify env (sign, current) ?passive (active_list, active_table) =
         None
       else
         match passive_table with
-        | None -> res
+        | None -> 
+	    if fst (Indexing.subsumption env active_table c) then
+	      None
+	    else
+	      res
         | Some passive_table ->
             if Indexing.in_index passive_table c then None
-            else res
-
-(*   | Some (s, c) -> if find_duplicate s c all then None else res *)
-
-(*         if s = Utils.Negative then *)
-(*           res *)
-(*         else *)
-(*           if Indexing.subsumption env active_table c then *)
-(*             None *)
-(*           else ( *)
-(*             match passive_table with *)
-(*             | None -> res *)
-(*             | Some passive_table -> *)
-(*                 if Indexing.subsumption env passive_table c then *)
-(*                   None *)
-(*                 else *)
-(*                   res *)
-(*           ) *)
-
-(*         let pred (sign, eq) = *)
-(*           if sign <> s then false *)
-(*           else subsumption env c eq *)
-(*         in *)
-(*         if List.exists pred all then None *)
-(*         else res *)
+            else 
+	      let r1, _ = Indexing.subsumption env active_table c in
+	      if r1 then None else
+		let r2, _ = Indexing.subsumption env passive_table c in 
+		if r2 then None else res
 ;;
 
 type fs_time_info_t = {
@@ -599,6 +548,7 @@ type fs_time_info_t = {
 let fs_time_info = { build_all = 0.; demodulate = 0.; subsumption = 0. };;
 
 
+(** simplifies new using active and passive *)
 let forward_simplify_new env (new_neg, new_pos) ?passive active =
   let t1 = Unix.gettimeofday () in
 
@@ -622,11 +572,6 @@ let forward_simplify_new env (new_neg, new_pos) ?passive active =
     maxmeta := newmeta;
     newtarget
   in
-(*   let f sign' target (sign, eq) = *)
-(*     if sign <> sign' then false *)
-(*     else subsumption env target eq  *)
-(*   in *)
-
   let t1 = Unix.gettimeofday () in
 
   let new_neg, new_pos =
@@ -661,22 +606,9 @@ let forward_simplify_new env (new_neg, new_pos) ?passive active =
         (fun e -> not ((fst (Indexing.subsumption env active_table e)) ||
                          (fst (Indexing.subsumption env passive_table e))))
   in
-
-  let t1 = Unix.gettimeofday () in
-
-(*   let new_neg, new_pos = *)
-(*     List.filter subs new_neg, *)
-(*     List.filter subs new_pos *)
-(*   in *)
-
-(*   let new_neg, new_pos =  *)
-(*     (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg, *)
-(*      List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos) *)
-(*   in *)
-
-  let t2 = Unix.gettimeofday () in
-  fs_time_info.subsumption <- fs_time_info.subsumption +. (t2 -. t1);
-
+(*   let t1 = Unix.gettimeofday () in *)
+(*   let t2 = Unix.gettimeofday () in *)
+(*   fs_time_info.subsumption <- fs_time_info.subsumption +. (t2 -. t1); *)
   let is_duplicate =
     match passive_table with
     | None ->
@@ -686,18 +618,11 @@ let forward_simplify_new env (new_neg, new_pos) ?passive active =
            not ((Indexing.in_index active_table e) ||
                   (Indexing.in_index passive_table e)))
   in
-  new_neg, List.filter is_duplicate new_pos
-
-(*   new_neg, new_pos *)
-
-(*   let res = *)
-(*     (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg, *)
-(*      List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos) *)
-(*   in *)
-(*   res *)
+  new_neg, List.filter subs (List.filter is_duplicate new_pos)
 ;;
 
 
+(** simplifies active usign new *)
 let backward_simplify_active env new_pos new_table min_weight active =
   let active_list, active_table = active in
   let active_list, newa = 
@@ -726,8 +651,7 @@ let backward_simplify_active env new_pos new_table min_weight active =
            res, tbl
          else if (is_identity env eq) || (find eq res) then (
            res, tbl
-         ) (* else if (find eq res) then *)
-(*            res, tbl *)
+         ) 
          else
            (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
       active_list ([], Indexing.empty_table ()),
@@ -746,12 +670,12 @@ let backward_simplify_active env new_pos new_table min_weight active =
 ;;
 
 
+(** simplifies passive using new *)
 let backward_simplify_passive env new_pos new_table min_weight passive =
   let (nl, ns), (pl, ps), passive_table = passive in
   let f sign equality (resl, ress, newn) =
     let ew, _, _, _, _ = equality in
     if ew < min_weight then
-(*       let _ = debug_print (lazy (Printf.sprintf "OK: %d %d" ew min_weight)) in *)
       equality::resl, ress, newn
     else
       match forward_simplify env (sign, equality) (new_pos, new_table) with
@@ -795,15 +719,18 @@ let backward_simplify env new' ?passive active =
 ;;
 
 
+(* returns an estimation of how many equalities in passive can be activated
+   within the current time limit *)
 let get_selection_estimate () =
   elapsed_time := (Unix.gettimeofday ()) -. !start_time;
-(*   !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *)
+  (*   !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *)
   int_of_float (
     ceil ((float_of_int !processed_clauses) *.
             ((!time_limit (* *. 2. *)) /. !elapsed_time -. 1.)))
 ;;
 
 
+(** initializes the set of goals *)
 let make_goals goal =
   let active = []
   and passive = [0, [goal]] in
@@ -811,11 +738,9 @@ let make_goals goal =
 ;;
 
 
+(** initializes the set of theorems *)
 let make_theorems theorems =
   theorems, []
-(*   let active = [] *)
-(*   and passive = theorems in *)
-(*   active, passive *)
 ;;
 
 
@@ -832,7 +757,8 @@ let activate_theorem (active, passive) =
   | [] -> false, (active, passive)
 ;;
 
-  
+
+(** simplifies a goal with equalities in active and passive *)  
 let simplify_goal env goal ?passive (active_list, active_table) =
   let pl, passive_table =
     match passive with
@@ -858,13 +784,6 @@ let simplify_goal env goal ?passive (active_list, active_table) =
         let changed', goal = demodulate passive_table goal in
         (changed || changed'), goal
   in
-  let _ =
-    let p, _, t = goal in
-    debug_print
-      (lazy
-         (Printf.sprintf "Goal after demodulation: %s, %s"
-            (string_of_proof p) (CicPp.ppterm t)))
-  in
   changed, goal
 ;;
 
@@ -921,18 +840,16 @@ let simplify_theorems env theorems ?passive (active_list, active_table) =
   | None ->
       let p_theorems = List.map (mapfun active_table) p_theorems in
       List.fold_left (foldfun active_table) ([], p_theorems) a_theorems
-(*       List.map (demodulate active_table) theorems *)
   | Some passive_table ->
       let p_theorems = List.map (mapfun active_table) p_theorems in
       let p_theorems, a_theorems =
         List.fold_left (foldfun active_table) ([], p_theorems) a_theorems in
       let p_theorems = List.map (mapfun passive_table) p_theorems in
       List.fold_left (foldfun passive_table) ([], p_theorems) a_theorems
-(*       let theorems = List.map (demodulate active_table) theorems in *)
-(*       List.map (demodulate passive_table) theorems *)
 ;;
 
 
+(* applies equality to goal to see if the goal can be closed *)
 let apply_equality_to_goal env equality goal =
   let module C = Cic in
   let module HL = HelmLibraryObjects in
@@ -974,123 +891,49 @@ let apply_equality_to_goal env equality goal =
 ;;
 
 
-(*
-let apply_to_goal env theorems active (depth, goals) =
-  let _ =
-    debug_print ("apply_to_goal: " ^ (string_of_int (List.length goals)))
-  in
-  let metasenv, context, ugraph = env in
-  let goal = List.hd goals in
-  let proof, metas, term = goal in
-(*   debug_print *)
-(*     (Printf.sprintf "apply_to_goal with goal: %s" (CicPp.ppterm term)); *)
-  let newmeta = CicMkImplicit.new_meta metasenv [] in
-  let metasenv = (newmeta, context, term)::metasenv @ metas in
-  let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
-  let status =
-    ((None, metasenv, Cic.Meta (newmeta, irl), term), newmeta)
-  in
-  let rec aux = function
-    | [] -> false, [] (* goals *) (* None *)
-    | (theorem, thmty, _)::tl ->
-        try
-          let subst_in, (newproof, newgoals) =
-            PrimitiveTactics.apply_tac_verbose ~term:theorem status
-          in
-          if newgoals = [] then
-            let _, _, p, _ = newproof in
-            let newp =
-              let rec repl = function
-                | Inference.ProofGoalBlock (_, gp) ->
-                    Inference.ProofGoalBlock (Inference.BasicProof p, gp)
-                | Inference.NoProof -> Inference.BasicProof p
-                | Inference.BasicProof _ -> Inference.BasicProof p
-                | Inference.SubProof (t, i, p2) ->
-                    Inference.SubProof (t, i, repl p2)
-                | _ -> assert false
-              in
-              repl proof
-            in
-            true, [[newp, metas, term]] (* Some newp *)
-          else if List.length newgoals = 1 then
-            let _, menv, p, _ = newproof in
-            let irl =
-              CicMkImplicit.identity_relocation_list_for_metavariable context
-            in
-            let goals =
-              List.map
-                (fun i ->
-                   let _, _, ty = CicUtil.lookup_meta i menv in
-                   let proof =
-                     Inference.SubProof
-                       (p, i, Inference.BasicProof (Cic.Meta (i, irl)))
-                   in (proof, menv, ty))
-                newgoals
-            in
-            let res, others = aux tl in
-            if res then (true, others) else (false, goals::others)
-          else
-            aux tl
-        with ProofEngineTypes.Fail msg ->
-          (*     debug_print ("FAIL!!:" ^ msg); *)
-          aux tl
-  in
-  let r, l =
-    if Inference.term_is_equality term then
-      let rec appleq = function
-        | [] -> false, []
-        | (Positive, equality)::tl ->
-            let ok, _, newproof = apply_equality_to_goal env equality goal in
-            if ok then true, [(depth, [newproof, metas, term])] else appleq tl
-        | _::tl -> appleq tl
-      in
-      let al, _ = active in
-      appleq al
-    else
-      false, []
-  in
-  if r = true then r, l else
-    let r, l = aux theorems in
-    if r = true then
-      r, List.map (fun l -> (depth+1, l)) l
-    else
-      r, (depth, goals)::(List.map (fun l -> (depth+1, l)) l)
-;;
-*)
-
 
-let new_meta () =
-  incr maxmeta; !maxmeta
+let new_meta metasenv =
+  let m = CicMkImplicit.new_meta metasenv [] in
+  incr maxmeta;
+  while !maxmeta <= m do incr maxmeta done;
+  !maxmeta
 ;;
 
 
+(* applies a theorem or an equality to goal, returning a list of subgoals or
+   an indication of failure *)
 let apply_to_goal env theorems ?passive active goal =
   let metasenv, context, ugraph = env in
   let proof, metas, term = goal in
-  debug_print
-    (lazy
-       (Printf.sprintf "apply_to_goal with goal: %s"
-          (* (string_of_proof proof)  *)(CicPp.ppterm term)));
+  (*   debug_print *)
+  (*     (lazy *)
+  (*        (Printf.sprintf "apply_to_goal with goal: %s" *)
+  (*           (\* (string_of_proof proof)  *\)(CicPp.ppterm term))); *)
   let status =
     let irl =
       CicMkImplicit.identity_relocation_list_for_metavariable context in
     let proof', newmeta =
       let rec get_meta = function
-        | SubProof (t, i, _) -> t, i
+        | SubProof (t, i, p) ->
+            let t', i' = get_meta p in
+            if i' = -1 then t, i else t', i'
         | ProofGoalBlock (_, p) -> get_meta p
-        | _ ->
-            let n = new_meta () in (* CicMkImplicit.new_meta metasenv [] in *)
-            Cic.Meta (n, irl), n
+        | _ -> Cic.Implicit None, -1
       in
-      get_meta proof
+      let p, m = get_meta proof in
+      if m = -1 then
+        let n = new_meta (metasenv @ metas) in
+        Cic.Meta (n, irl), n
+      else
+        p, m
     in
-(*     let newmeta = CicMkImplicit.new_meta metasenv [] in *)
     let metasenv = (newmeta, context, term)::metasenv @ metas in
-    ((None, metasenv, Cic.Meta (newmeta, irl), term), newmeta)
-(*     ((None, metasenv, proof', term), newmeta) *)
+    let bit = new_meta metasenv, context, term in 
+    let metasenv' = bit::metasenv in
+    ((None, metasenv', Cic.Meta (newmeta, irl), term), newmeta)
   in
   let rec aux = function
-    | [] -> `No (* , [], [] *)
+    | [] -> `No
     | (theorem, thmty, _)::tl ->
         try
           let subst, (newproof, newgoals) =
@@ -1112,10 +955,6 @@ let apply_to_goal env theorems ?passive active goal =
             in
             let _, m = status in
             let subst = List.filter (fun (i, _) -> i = m) subst in
-(*             debug_print *)
-(*               (lazy *)
-(*                  (Printf.sprintf "m = %d\nsubst = %s\n" *)
-(*                     m (print_subst subst))); *)
             `Ok (subst, [newp, metas, term])
           else
             let _, menv, p, _ = newproof in
@@ -1131,9 +970,7 @@ let apply_to_goal env theorems ?passive active goal =
                        | SubProof (t, i, p) ->
                            SubProof (t, i, gp p)
                        | ProofGoalBlock (sp1, sp2) ->
-(*                            SubProof (p, i, sp) *)
                            ProofGoalBlock (sp1, gp sp2)
-(*                            gp sp *)
                        | BasicProof _
                        | NoProof ->
                            SubProof (p, i, BasicProof (Cic.Meta (i, irl)))
@@ -1141,13 +978,8 @@ let apply_to_goal env theorems ?passive active goal =
                            ProofSymBlock (s, gp sp)
                        | ProofBlock (s, u, nt, t, pe, sp) ->
                            ProofBlock (s, u, nt, t, pe, gp sp)
-(*                        | _ -> assert false *)
                      in gp proof
                    in
-                   debug_print
-                     (lazy
-                        (Printf.sprintf "new sub goal: %s"
-                           (* (string_of_proof p')  *)(CicPp.ppterm ty)));
                    (p', menv, ty))
                 newgoals
             in
@@ -1161,23 +993,16 @@ let apply_to_goal env theorems ?passive active goal =
                    Pervasives.compare (weight t1) (weight t2))
                 goals
             in
-(*             debug_print *)
-(*               (lazy *)
-(*                  (Printf.sprintf "\nGoOn with subst: %s" (print_subst subst))); *)
             let best = aux tl in
             match best with
             | `Ok (_, _) -> best
             | `No -> `GoOn ([subst, goals])
-            | `GoOn sl(* , subst', goals' *) ->
-(*                 if (List.length goals') < (List.length goals) then best *)
-(*                 else `GoOn, subst, goals *)
-                `GoOn ((subst, goals)::sl)
+            | `GoOn sl -> `GoOn ((subst, goals)::sl)
         with ProofEngineTypes.Fail msg ->
           aux tl
   in
   let r, s, l =
     if Inference.term_is_equality term then
-(*       let _ = debug_print (lazy "OK, is equality!!") in *)
       let rec appleq_a = function
         | [] -> false, [], []
         | (Positive, equality)::tl ->
@@ -1203,117 +1028,147 @@ let apply_to_goal env theorems ?passive active goal =
 ;;
 
 
-let apply_to_goal_conj env theorems ?passive active (depth, goals) =
-  let rec aux = function
-    | goal::tl ->
-        let propagate_subst subst (proof, metas, term) =
-(*           debug_print *)
-(*             (lazy *)
-(*                (Printf.sprintf "\npropagate_subst:\n%s\n%s, %s\n" *)
-(*                   (print_subst subst) (string_of_proof proof) *)
-(*                   (CicPp.ppterm term))); *)
-          let rec repl = function
-            | NoProof -> NoProof
-            | BasicProof t ->
-                BasicProof (CicMetaSubst.apply_subst subst t)
-            | ProofGoalBlock (p, pb) ->
-(*                 debug_print (lazy "HERE"); *)
-                let pb' = repl pb in
-                ProofGoalBlock (p, pb')
-            | SubProof (t, i, p) ->
-                let t' = CicMetaSubst.apply_subst subst t in
-(*                 debug_print *)
-(*                   (lazy *)
-(*                      (Printf.sprintf *)
-(*                         "SubProof %d\nt = %s\nsubst = %s\nt' = %s\n" *)
-(*                         i (CicPp.ppterm t) (print_subst subst) *)
-(*                         (CicPp.ppterm t'))); *)
-                let p = repl p in
-                SubProof (t', i, p)
-            | ProofSymBlock (ens, p) -> ProofSymBlock (ens, repl p)
-            | ProofBlock (s, u, nty, t, pe, p) ->
-                ProofBlock (subst @ s, u, nty, t, pe, p)
-          in (repl proof, metas, term)
-        in
-        let r = apply_to_goal env theorems ?passive active goal in (
-          match r with
-          | `No -> `No (depth, goals)
-          | `GoOn sl (* (subst, gl) *) ->
-(*               let tl = List.map (propagate_subst subst) tl in *)
-(*               debug_print (lazy "GO ON!!!"); *)
-              let l =
-                List.map
-                  (fun (s, gl) ->
-                     (depth+1, gl @ (List.map (propagate_subst s) tl))) sl
+(* sorts a conjunction of goals in order to detect earlier if it is
+   unsatisfiable. Non-predicate goals are placed at the end of the list *)
+let sort_goal_conj (metasenv, context, ugraph) (depth, gl) =
+  let gl = 
+    List.stable_sort
+      (fun (_, e1, g1) (_, e2, g2) ->
+         let ty1, _ =
+           CicTypeChecker.type_of_aux' (e1 @ metasenv) context g1 ugraph 
+         and ty2, _ =
+           CicTypeChecker.type_of_aux' (e2 @ metasenv) context g2 ugraph
+         in
+         let prop1 =
+           let b, _ =
+             CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty1 ugraph
+           in
+           if b then 0 else 1
+         and prop2 =
+           let b, _ =
+             CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty2 ugraph
+           in
+           if b then 0 else 1
+         in
+         if prop1 = 0 && prop2 = 0 then
+           let e1 = if Inference.term_is_equality g1 then 0 else 1
+           and e2 = if Inference.term_is_equality g2 then 0 else 1 in
+           e1 - e2
+         else
+           prop1 - prop2)
+      gl
+  in
+  (depth, gl)
+;;
+
+
+let is_meta_closed goals =
+  List.for_all (fun (_, _, g) -> CicUtil.is_meta_closed g) goals
+;;
+
+
+(* applies a series of theorems/equalities to a conjunction of goals *)
+let rec apply_to_goal_conj env theorems ?passive active (depth, goals) =
+  let aux (goal, r) tl =
+    let propagate_subst subst (proof, metas, term) =
+      let rec repl = function
+        | NoProof -> NoProof
+        | BasicProof t ->
+            BasicProof (CicMetaSubst.apply_subst subst t)
+        | ProofGoalBlock (p, pb) ->
+            let pb' = repl pb in
+            ProofGoalBlock (p, pb')
+        | SubProof (t, i, p) ->
+            let t' = CicMetaSubst.apply_subst subst t in
+            let p = repl p in
+            SubProof (t', i, p)
+        | ProofSymBlock (ens, p) -> ProofSymBlock (ens, repl p)
+        | ProofBlock (s, u, nty, t, pe, p) ->
+            ProofBlock (subst @ s, u, nty, t, pe, p)
+      in (repl proof, metas, term)
+    in
+    (* let r = apply_to_goal env theorems ?passive active goal in *) (
+      match r with
+      | `No -> `No (depth, goals)
+      | `GoOn sl ->
+          let l =
+            List.map
+              (fun (s, gl) ->
+                 let tl = List.map (propagate_subst s) tl in
+                 sort_goal_conj env (depth+1, gl @ tl)) sl
+          in
+          `GoOn l
+      | `Ok (subst, gl) ->
+          if tl = [] then
+            `Ok (depth, gl)
+          else
+            let p, _, _ = List.hd gl in
+            let subproof =
+              let rec repl = function
+                | SubProof (_, _, p) -> repl p
+                | ProofGoalBlock (p1, p2) ->
+                    ProofGoalBlock (repl p1, repl p2)
+                | p -> p
               in
-(*               debug_print *)
-(*                 (lazy *)
-(*                    (Printf.sprintf "%s\n" *)
-(*                       (String.concat "; " *)
-(*                          (List.map *)
-(*                             (fun (s, gl) -> *)
-(*                                (Printf.sprintf "[%s]" *)
-(*                                   (String.concat "; " *)
-(*                                      (List.map *)
-(*                                         (fun (p, _, g) -> *)
-(*                                            (Printf.sprintf "<%s, %s>" *)
-(*                                               (string_of_proof p) *)
-(*                                               (CicPp.ppterm g))) gl)))) l)))); *)
-              `GoOn l (* (depth+1, gl @ tl) *)
-          | `Ok (subst, gl) ->
-              if tl = [] then
-(*                 let _ = *)
-(*                   let p, _, t = List.hd gl in *)
-(*                   debug_print *)
-(*                     (lazy *)
-(*                        (Printf.sprintf "OK: %s, %s\n" *)
-(*                           (string_of_proof p) (CicPp.ppterm t))) *)
-(*                 in *)
-                `Ok (depth, gl)
-              else
-                let p, _, _ = List.hd gl in
-                let subproof =
-                  let rec repl = function
-                    | SubProof (_, _, p) -> repl p
-                    | ProofGoalBlock (p1, p2) ->
-                        ProofGoalBlock (repl p1, repl p2)
-                    | p -> p
-                  in
-                  build_proof_term (repl p)
-                in
-                let i = 
-                  let rec get_meta = function
-                    | SubProof (_, i, p) -> max i (get_meta p)
-                    | ProofGoalBlock (_, p) -> get_meta p
-                    | _ -> -1 (* assert false *)
-                  in
-                  get_meta p
-                in
-                let subst =
-                  let _, (context, _, _) = List.hd subst in
-                  [i, (context, subproof, Cic.Implicit None)]
-                in
-                let tl = List.map (propagate_subst subst) tl in
-                `GoOn ([depth+1, tl])
-        )
-    | _ -> assert false
+              build_proof_term (repl p)
+            in
+            let i = 
+              let rec get_meta = function
+                | SubProof (_, i, p) ->
+                    let i' = get_meta p in
+                    if i' = -1 then i else i'
+(*                         max i (get_meta p) *)
+                | ProofGoalBlock (_, p) -> get_meta p
+                | _ -> -1
+              in
+              get_meta p
+            in
+            let subst =
+              let _, (context, _, _) = List.hd subst in
+              [i, (context, subproof, Cic.Implicit None)]
+            in
+            let tl = List.map (propagate_subst subst) tl in
+            let conj = sort_goal_conj env (depth(* +1 *), tl) in
+            `GoOn ([conj])
+    )
   in
-  debug_print
-    (lazy
-       (Printf.sprintf "apply_to_goal_conj (%d, [%s])"
-          depth
-          (String.concat "; "
-             (List.map (fun (_, _, t) -> CicPp.ppterm t) goals))));
-  if depth > !maxdepth || (List.length goals) > !maxwidth then (
-    debug_print
-      (lazy (Printf.sprintf "Pruning because depth = %d, width = %d"
-               depth (List.length goals)));
+  if depth > !maxdepth || (List.length goals) > !maxwidth then 
     `No (depth, goals)
-  ) else
-    aux goals
+  else
+    let rec search_best res = function
+      | [] -> res
+      | goal::tl ->
+          let r = apply_to_goal env theorems ?passive active goal in
+          match r with
+          | `Ok _ -> (goal, r)
+          | `No -> search_best res tl
+          | `GoOn l ->
+              let newres = 
+                match res with
+                | _, `Ok _ -> assert false
+                | _, `No -> goal, r
+                | _, `GoOn l2 ->
+                    if (List.length l) < (List.length l2) then goal, r else res
+              in
+              search_best newres tl
+    in
+    let hd = List.hd goals in
+    let res = hd, (apply_to_goal env theorems ?passive active hd) in
+    let best =
+      match res with
+      | _, `Ok _ -> res
+      | _, _ -> search_best res (List.tl goals)
+    in
+    let res = aux best (List.filter (fun g -> g != (fst best)) goals) in
+    match res with
+    | `GoOn ([conj]) when is_meta_closed (snd conj) &&
+        (List.length (snd conj)) < (List.length goals)->
+        apply_to_goal_conj env theorems ?passive active conj
+    | _ -> res
 ;;
 
 
+(*
 module OrderedGoals = struct
   type t = int * (Inference.proof * Cic.metasenv * Cic.term) list
 
@@ -1336,26 +1191,16 @@ module OrderedGoals = struct
              ) else
                false) l1 l2
       in !res
-(*       let res = Pervasives.compare g1 g2 in *)
-(*       let _ = *)
-(*         let print_goals (d, gl) =  *)
-(*           let gl' = List.map (fun (_, _, t) -> CicPp.ppterm t) gl in *)
-(*           Printf.sprintf "%d, [%s]" d (String.concat "; " gl') *)
-(*         in *)
-(*         debug_print *)
-(*           (lazy *)
-(*              (Printf.sprintf "comparing g1:%s and g2:%s, res: %d\n" *)
-(*                 (print_goals g1) (print_goals g2) res)) *)
-(*       in *)
-(*       res *)
 end
 
 module GoalsSet = Set.Make(OrderedGoals);;
 
 
 exception SearchSpaceOver;;
+*)
 
 
+(*
 let apply_to_goals env is_passive_empty theorems active goals =
   debug_print (lazy "\n\n\tapply_to_goals\n\n");
   let add_to set goals =
@@ -1382,46 +1227,11 @@ let apply_to_goals env is_passive_empty theorems active goals =
             in
             true, GoalsSet.singleton newgoals
         | `GoOn newgoals ->
-(*             let print_set set msg =  *)
-(*               debug_print *)
-(*                 (lazy *)
-(*                    (Printf.sprintf "%s:\n%s" msg *)
-(*                       (String.concat "\n" *)
-(*                          (GoalsSet.fold *)
-(*                             (fun (d, gl) l -> *)
-(*                                let gl' = *)
-(*                                  List.map (fun (_, _, t) -> CicPp.ppterm t) gl *)
-(*                                in *)
-(*                                let s = *)
-(*                                  Printf.sprintf "%d, [%s]" d *)
-(*                                    (String.concat "; " gl') *)
-(*                                in *)
-(*                                s::l) set [])))) *)
-(*             in *)
-
-(*             let r, s = *)
-(*               try aux set tl with SearchSpaceOver -> false, GoalsSet.empty *)
-(*             in  *)
-(*             if r then *)
-(*               r, s *)
-(*             else  *)
-            
             let set' = add_to set (goals::tl) in
-(*             print_set set "SET BEFORE"; *)
-(*             let n = GoalsSet.cardinal set in *)
             let set' = add_to set' newgoals in
-(*             print_set set "SET AFTER"; *)
-(*             let m = GoalsSet.cardinal set in *)
-(*             if n < m then *)
             false, set'
-(*             else *)
-(*               let _ = print_set set "SET didn't change" in *)
-(*               aux set tl *)
         | `No newgoals ->
             aux set tl
-(*             let set = add_to set (newgoals::goals::tl) in *)
-(*             let res, set = aux set tl in *)
-(*             res, set *)
   in
   let n = List.length goals in
   let res, goals = aux (add_to GoalsSet.empty goals) goals in
@@ -1433,75 +1243,84 @@ let apply_to_goals env is_passive_empty theorems active goals =
   else
     res, goals
 ;;
+*)
+
+
+(* sorts the list of passive goals to minimize the search for a proof (doesn't
+   work that well yet...) *)
+let sort_passive_goals goals =
+  List.stable_sort
+    (fun (d1, l1) (d2, l2) ->
+       let r1 = d2 - d1 
+       and r2 = (List.length l1) - (List.length l2) in
+       let foldfun ht (_, _, t) = 
+         let _ = List.map (fun i -> Hashtbl.replace ht i 1) (metas_of_term t)
+         in ht
+       in
+       let m1 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l1)
+       and m2 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l2)
+       in let r3 = m1 - m2 in
+       if r3 <> 0 then r3
+       else if r2 <> 0 then r2 
+       else r1)
+    (*          let _, _, g1 = List.hd l1 *)
+(*          and _, _, g2 = List.hd l2 in *)
+(*          let e1 = if Inference.term_is_equality g1 then 0 else 1 *)
+(*          and e2 = if Inference.term_is_equality g2 then 0 else 1 *)
+(*          in let r4 = e1 - e2 in *)
+(*          if r4 <> 0 then r3 else r1) *)
+    goals
+;;
 
 
+let print_goals goals = 
+  (String.concat "\n"
+     (List.map
+        (fun (d, gl) ->
+           let gl' =
+             List.map
+               (fun (p, _, t) ->
+                  (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl
+           in
+           Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
+;;
+
+
+(* tries to prove the first conjunction in goals with applications of
+   theorems/equalities, returning new sub-goals or an indication of success *)
 let apply_goal_to_theorems dbd env theorems ?passive active goals =
-(*   let theorems, _ = theorems in *)
-  let context_hyp, library_thms = theorems in
-  let thm_uris =
-    List.fold_left
-      (fun s (u, _, _, _) -> UriManager.UriSet.add u s)
-      UriManager.UriSet.empty library_thms
-  in
+  let theorems, _ = theorems in
   let a_goals, p_goals = goals in
   let goal = List.hd a_goals in
-  let rec aux = function
-    | [] -> false, (a_goals, p_goals)
-    | theorem::tl ->
-        let res = apply_to_goal_conj env [theorem] ?passive active goal in
-        match res with
-        | `Ok newgoals ->
-            true, ([newgoals], [])
-        | `No _ ->
-            aux tl
-(*             false, (a_goals, p_goals) *)
-        | `GoOn newgoals ->
-            let res, (ag, pg) = aux tl in
-            if res then
-              res, (ag, pg)
+  let not_in_active gl =
+    not
+      (List.exists
+         (fun (_, gl') ->
+            if (List.length gl) = (List.length gl') then
+              List.for_all2 (fun (_, _, g1) (_, _, g2) -> g1 = g2) gl gl'
             else
-              let newgoals =
-                List.filter
-                  (fun (d, gl) ->
-                     (d <= !maxdepth) && (List.length gl) <= !maxwidth)
-                  newgoals in
-              let p_goals = newgoals @ pg in
-              let p_goals =
-                List.stable_sort
-                  (fun (d1, l1) (d2, l2) -> (List.length l1) - (List.length l2))
-                  p_goals
-              in
-              res, (ag, p_goals)
+              false)
+         a_goals)
   in
-  let theorems =
-(*     let ty = *)
-(*       match goal with *)
-(*       | (_, (_, _, t)::_) -> t *)
-(*       | _ -> assert false *)
-(*     in *)
-(*     if CicUtil.is_meta_closed ty then *)
-(*       let _ =  *)
-(*         debug_print (lazy (Printf.sprintf "META CLOSED: %s" (CicPp.ppterm ty))) *)
-(*       in *)
-(*       let metasenv, context, ugraph = env in *)
-(*       let uris = *)
-(*         MetadataConstraints.sigmatch ~dbd (MetadataConstraints.signature_of ty) *)
-(*       in *)
-(*       let uris = List.sort (fun (i, _) (j, _) -> Pervasives.compare i j) uris in *)
-(*       let uris = *)
-(*         List.filter *)
-(*           (fun u -> UriManager.UriSet.mem u thm_uris) (List.map snd uris) *)
-(*       in *)
-(*       List.map *)
-(*         (fun u -> *)
-(*            let t = CicUtil.term_of_uri u in *)
-(*            let ty, _ = CicTypeChecker.type_of_aux' metasenv context t ugraph in *)
-(*            (t, ty, [])) *)
-(*         uris *)
-(*     else *)
-    List.map (fun (_, t, ty, m) -> (t, ty, m)) library_thms
+  let aux theorems =
+    let res = apply_to_goal_conj env theorems ?passive active goal in
+    match res with
+    | `Ok newgoals ->
+        true, ([newgoals], [])
+    | `No _ ->
+        false, (a_goals, p_goals)
+    | `GoOn newgoals ->
+        let newgoals =
+          List.filter
+            (fun (d, gl) ->
+               (d <= !maxdepth) && (List.length gl) <= !maxwidth &&
+                 not_in_active gl)
+            newgoals in
+        let p_goals = newgoals @ p_goals in
+        let p_goals = sort_passive_goals p_goals in
+        false, (a_goals, p_goals)
   in
-  aux (context_hyp @ theorems)
+  aux theorems
 ;;
 
 
@@ -1543,10 +1362,11 @@ let apply_theorem_to_goals env theorems active goals =
 ;;
 
 
+(* given-clause algorithm with lazy reduction strategy *)
 let rec given_clause dbd env goals theorems passive active =
   let goals = simplify_goals env goals active in
   let ok, goals = activate_goal goals in
-(*   let theorems = simplify_theorems env theorems active in *)
+  (*   let theorems = simplify_theorems env theorems active in *)
   if ok then
     let ok, goals = apply_goal_to_theorems dbd env theorems active goals in
     if ok then
@@ -1602,20 +1422,6 @@ and given_clause_aux dbd env goals theorems passive active =
   passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
 
   kept_clauses := (size_of_passive passive) + (size_of_active active);
-    
-(* (\*   let goals = simplify_goals env goals active in *\) *)
-(* (\*   let theorems = simplify_theorems env theorems active in  *\) *)
-(*   let is_passive_empty = passive_is_empty passive in *)
-(*   try *)
-(*     let ok, goals = false, [] in (\* apply_to_goals env is_passive_empty theorems active goals in *\) *)
-(*     if ok then *)
-(*       let proof = *)
-(*         match goals with *)
-(*         | (_, [proof, _, _])::_ -> Some proof *)
-(*         | _ -> assert false *)
-(*       in *)
-(*       ParamodulationSuccess (proof, env) *)
-(*     else *)
   match passive_is_empty passive with
   | true -> (* ParamodulationFailure *)
       given_clause dbd env goals theorems passive active
@@ -1634,7 +1440,7 @@ and given_clause_aux dbd env goals theorems passive active =
               (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                        (string_of_equality ~env current)));
             let _, proof, _, _, _  = current in
-            ParamodulationSuccess (Some proof (* current *), env)
+            ParamodulationSuccess (Some proof, env)
           ) else (            
             debug_print
               (lazy "\n================================================");
@@ -1654,7 +1460,7 @@ and given_clause_aux dbd env goals theorems passive active =
                 | Some goal -> let _, proof, _, _, _ = goal in Some proof
                 | None -> None
               in
-              ParamodulationSuccess (proof (* goal *), env)
+              ParamodulationSuccess (proof, env)
             else 
               let t1 = Unix.gettimeofday () in
               let new' = forward_simplify_new env new' active in
@@ -1688,27 +1494,6 @@ and given_clause_aux dbd env goals theorems passive active =
                         in
                         nn @ al @ pp, tbl
               in
-(*               let _ = *)
-(*                 Printf.printf "active:\n%s\n" *)
-(*                   (String.concat "\n" *)
-(*                      ((List.map *)
-(*                          (fun (s, e) -> (string_of_sign s) ^ " " ^ *)
-(*                             (string_of_equality ~env e)) (fst active)))); *)
-(*                 print_newline (); *)
-(*               in *)
-(*               let _ = *)
-(*                 match new' with *)
-(*                 | neg, pos -> *)
-(*                     Printf.printf "new':\n%s\n" *)
-(*                       (String.concat "\n" *)
-(*                          ((List.map *)
-(*                              (fun e -> "Negative " ^ *)
-(*                                 (string_of_equality ~env e)) neg) @ *)
-(*                             (List.map *)
-(*                                (fun e -> "Positive " ^ *)
-(*                                   (string_of_equality ~env e)) pos))); *)
-(*                     print_newline (); *)
-(*               in *)
               match contains_empty env new' with
               | false, _ -> 
                   let active =
@@ -1720,15 +1505,6 @@ and given_clause_aux dbd env goals theorems passive active =
                   in
                   let passive = add_to_passive passive new' in
                   let (_, ns), (_, ps), _ = passive in
-(*                   Printf.printf "passive:\n%s\n" *)
-(*                     (String.concat "\n" *)
-(*                        ((List.map (fun e -> "Negative " ^ *)
-(*                                      (string_of_equality ~env e)) *)
-(*                            (EqualitySet.elements ns)) @ *)
-(*                           (List.map (fun e -> "Positive " ^ *)
-(*                                        (string_of_equality ~env e)) *)
-(*                              (EqualitySet.elements ps)))); *)
-(*                   print_newline (); *)
                   given_clause dbd env goals theorems passive active
               | true, goal ->
                   let proof =
@@ -1737,35 +1513,29 @@ and given_clause_aux dbd env goals theorems passive active =
                         let _, proof, _, _, _ = goal in Some proof
                     | None -> None
                   in
-                  ParamodulationSuccess (proof (* goal *), env)
+                  ParamodulationSuccess (proof, env)
           )
-(*   with SearchSpaceOver -> *)
-(*     ParamodulationFailure *)
 ;;
 
 
+(** given-clause algorithm with full reduction strategy *)
 let rec given_clause_fullred dbd env goals theorems passive active =
   let goals = simplify_goals env goals ~passive active in
   let ok, goals = activate_goal goals in
 (*   let theorems = simplify_theorems env theorems ~passive active in *)
   if ok then
-    let _ =
-      let print_goals goals = 
-        (String.concat "\n"
-           (List.map
-              (fun (d, gl) ->
-                 let gl' =
-                   List.map
-                     (fun (p, _, t) ->
-                        (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl
-                 in
-                 Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
-      in
-      debug_print
-        (lazy
-           (Printf.sprintf "\ngoals = \nactive\n%s\npassive\n%s\n"
-              (print_goals (fst goals)) (print_goals (snd goals))))
-    in
+(*     let _ = *)
+(*       debug_print *)
+(*         (lazy *)
+(*            (Printf.sprintf "\ngoals = \nactive\n%s\npassive\n%s\n" *)
+(*               (print_goals (fst goals)) (print_goals (snd goals)))); *)
+(*       let current = List.hd (fst goals) in *)
+(*       let p, _, t = List.hd (snd current) in *)
+(*       debug_print *)
+(*         (lazy *)
+(*            (Printf.sprintf "goal activated:\n%s\n%s\n" *)
+(*               (CicPp.ppterm t) (string_of_proof p))); *)
+(*     in *)
     let ok, goals =
       apply_goal_to_theorems dbd env theorems ~passive active goals
     in
@@ -1819,35 +1589,8 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
 
   let time2 = Unix.gettimeofday () in
   passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
-    
+  
   kept_clauses := (size_of_passive passive) + (size_of_active active);
-
-(*   try *)
-(*     let ok, goals = apply_to_goals env is_passive_empty theorems active goals in *)
-(*     if ok then *)
-(*       let proof = *)
-(*         match goals with *)
-(*         | (_, [proof, _, _])::_ -> Some proof *)
-(*         | _ -> assert false *)
-(*       in *)
-(*       ParamodulationSuccess (proof, env) *)
-(*     else *)
-(*       let _ = *)
-(*         debug_print *)
-(*           (lazy ("new_goals: " ^ (string_of_int (List.length goals)))); *)
-(*         debug_print *)
-(*           (lazy *)
-(*              (String.concat "\n" *)
-(*                 (List.map *)
-(*                    (fun (d, gl) -> *)
-(*                       let gl' = *)
-(*                         List.map *)
-(*                           (fun (p, _, t) -> *)
-(*                              (\* (string_of_proof p) ^ ", " ^ *\) (CicPp.ppterm t)) gl *)
-(*                       in *)
-(*                       Printf.sprintf "%d: %s" d (String.concat "; " gl')) *)
-(*                    goals))); *)
-(*       in *)
   match passive_is_empty passive with
   | true -> (* ParamodulationFailure *)
       given_clause_fullred dbd env goals theorems passive active        
@@ -1866,7 +1609,7 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
               (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                        (string_of_equality ~env current)));
             let _, proof, _, _, _ = current in 
-            ParamodulationSuccess (Some proof (* current *), env)
+            ParamodulationSuccess (Some proof, env)
           ) else (
             debug_print
               (lazy "\n================================================");
@@ -1942,16 +1685,6 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
             match contains_empty env new' with
             | false, _ -> 
                 let passive = add_to_passive passive new' in
-(*                 let (_, ns), (_, ps), _ = passive in *)
-(*                 Printf.printf "passive:\n%s\n" *)
-(*                   (String.concat "\n" *)
-(*                      ((List.map (fun e -> "Negative " ^ *)
-(*                                    (string_of_equality ~env e)) *)
-(*                          (EqualitySet.elements ns)) @ *)
-(*                         (List.map (fun e -> "Positive " ^ *)
-(*                                      (string_of_equality ~env e)) *)
-(*                            (EqualitySet.elements ps)))); *)
-(*                 print_newline (); *)
                 given_clause_fullred dbd env goals theorems passive active
             | true, goal ->
                 let proof =
@@ -1959,14 +1692,11 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
                   | Some goal -> let _, proof, _, _, _ = goal in Some proof
                   | None -> None
                 in
-                ParamodulationSuccess (proof (* goal *), env)
+                ParamodulationSuccess (proof, env)
           )
-(*   with SearchSpaceOver -> *)
-(*     ParamodulationFailure *)
 ;;
 
 
-(* let given_clause_ref = ref given_clause;; *)
 
 let main dbd full term metasenv ugraph =
   let module C = Cic in
@@ -1983,23 +1713,25 @@ let main dbd full term metasenv ugraph =
   let lib_eq_uris, library_equalities, maxm =
     find_library_equalities dbd context (proof, goal') (maxm+2)
   in
+  let library_equalities = List.map snd library_equalities in
   maxmeta := maxm+2; (* TODO ugly!! *)
   let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
   let new_meta_goal, metasenv, type_of_goal =
     let _, context, ty = CicUtil.lookup_meta goal' metasenv in
-    Printf.printf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty);
-    print_newline ();
+    debug_print
+      (lazy
+         (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n\n" (CicPp.ppterm ty)));
     Cic.Meta (maxm+1, irl),
     (maxm+1, context, ty)::metasenv,
     ty
   in
-(*   let new_meta_goal = Cic.Meta (goal', irl) in *)
   let env = (metasenv, context, ugraph) in
+  let t1 = Unix.gettimeofday () in
   let theorems =
     if full then
       let theorems = find_library_theorems dbd env (proof, goal') lib_eq_uris in
       let context_hyp = find_context_hypotheses env eq_indexes in
-      context_hyp, theorems
+      context_hyp @ theorems, []
     else
       let refl_equal =
         let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
@@ -2007,8 +1739,12 @@ let main dbd full term metasenv ugraph =
       in
       let t = CicUtil.term_of_uri refl_equal in
       let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
-      [], [(refl_equal, t, ty, [])]
+      [(t, ty, [])], []
   in
+  let t2 = Unix.gettimeofday () in
+  debug_print
+    (lazy
+       (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
   let _ =
     debug_print
       (lazy
@@ -2016,93 +1752,72 @@ let main dbd full term metasenv ugraph =
             "Theorems:\n-------------------------------------\n%s\n"
             (String.concat "\n"
                (List.map
-                  (fun (_, t, ty, _) ->
+                  (fun (t, ty, _) ->
                      Printf.sprintf
                        "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty))
-                  (snd theorems)))))
+                  (fst theorems)))))
   in
   try
     let goal = Inference.BasicProof new_meta_goal, [], goal in
-(*     let term_equality = equality_of_term new_meta_goal goal in *)
-(*     let _, meta_proof, (eq_ty, left, right, ordering), _, _ = term_equality in *)
-(*     if is_identity env term_equality then *)
-(*       let proof = *)
-(*         Cic.Appl [Cic.MutConstruct (\* reflexivity *\) *)
-(*                     (HelmLibraryObjects.Logic.eq_URI, 0, 1, []); *)
-(*                   eq_ty; left] *)
-(*       in *)
-(*       let _ =  *)
-(*         Printf.printf "OK, found a proof!\n"; *)
-(*         let names = names_of_context context in *)
-(*         print_endline (PP.pp proof names) *)
-(*       in *)
-(*       () *)
-(*     else *)
-      let equalities =
-        let equalities = equalities @ library_equalities in
-        debug_print
-          (lazy 
-             (Printf.sprintf "equalities:\n%s\n"
-                (String.concat "\n"
-                   (List.map string_of_equality equalities))));
-        debug_print (lazy "SIMPLYFYING EQUALITIES...");
-        let rec simpl e others others_simpl =
-          let active = others @ others_simpl in
-          let tbl =
-            List.fold_left
-              (fun t (_, e) -> Indexing.index t e)
-              (Indexing.empty_table ()) active
-          in
-          let res = forward_simplify env e (active, tbl) in
-          match others with
-          | hd::tl -> (
-              match res with
-              | None -> simpl hd tl others_simpl
-              | Some e -> simpl hd tl (e::others_simpl)
-            )
-          | [] -> (
-              match res with
-              | None -> others_simpl
-              | Some e -> e::others_simpl
-            )
+    let equalities =
+      let equalities = equalities @ library_equalities in
+      debug_print
+        (lazy 
+           (Printf.sprintf "equalities:\n%s\n"
+              (String.concat "\n"
+                 (List.map string_of_equality equalities))));
+      debug_print (lazy "SIMPLYFYING EQUALITIES...");
+      let rec simpl e others others_simpl =
+        let active = others @ others_simpl in
+        let tbl =
+          List.fold_left
+            (fun t (_, e) -> Indexing.index t e)
+            (Indexing.empty_table ()) active
         in
-        match equalities with
-        | [] -> []
-        | hd::tl ->
-            let others = List.map (fun e -> (Positive, e)) tl in
-            let res =
-              List.rev (List.map snd (simpl (Positive, hd) others []))
-            in
-            debug_print
-              (lazy
-                 (Printf.sprintf "equalities AFTER:\n%s\n"
-                    (String.concat "\n"
-                       (List.map string_of_equality res))));
-            res
+        let res = forward_simplify env e (active, tbl) in
+        match others with
+        | hd::tl -> (
+            match res with
+            | None -> simpl hd tl others_simpl
+            | Some e -> simpl hd tl (e::others_simpl)
+          )
+        | [] -> (
+            match res with
+            | None -> others_simpl
+            | Some e -> e::others_simpl
+          )
       in
-      let active = make_active () in
-      let passive = make_passive [] (* [term_equality] *) equalities in
-      Printf.printf "\ncurrent goal: %s\n"
-        (let _, _, g = goal in CicPp.ppterm g);
-(*         (string_of_equality ~env term_equality); *)
-      Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
-      Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
-      Printf.printf "\nequalities:\n%s\n"
-        (String.concat "\n"
-           (List.map
-              (string_of_equality ~env)
-              (equalities @ library_equalities)));
+      match equalities with
+      | [] -> []
+      | hd::tl ->
+          let others = List.map (fun e -> (Positive, e)) tl in
+          let res =
+            List.rev (List.map snd (simpl (Positive, hd) others []))
+          in
+          debug_print
+            (lazy
+               (Printf.sprintf "equalities AFTER:\n%s\n"
+                  (String.concat "\n"
+                     (List.map string_of_equality res))));
+          res
+    in
+    let active = make_active () in
+    let passive = make_passive [] equalities in
+    Printf.printf "\ncurrent goal: %s\n"
+      (let _, _, g = goal in CicPp.ppterm g);
+    Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
+    Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
+    Printf.printf "\nequalities:\n%s\n"
+      (String.concat "\n"
+         (List.map
+            (string_of_equality ~env) equalities));
+(*             (equalities @ library_equalities))); *)
       print_endline "--------------------------------------------------";
       let start = Unix.gettimeofday () in
       print_endline "GO!";
       start_time := Unix.gettimeofday ();
-(*       let res = *)
-(*         (if !use_fullred then given_clause_fullred else given_clause) *)
-(*           env [0, [goal]] theorems passive active *)
-(*       in *)
       let res =
         let goals = make_goals goal in
-(*         and theorems = make_theorems theorems in *)
         (if !use_fullred then given_clause_fullred else given_clause)
           dbd env goals theorems passive active
       in
@@ -2111,8 +1826,7 @@ let main dbd full term metasenv ugraph =
         match res with
         | ParamodulationFailure ->
             Printf.printf "NO proof found! :-(\n\n"
-        | ParamodulationSuccess (Some proof (* goal *), env) ->
-(*             let proof = Inference.build_proof_term goal in          *)
+        | ParamodulationSuccess (Some proof, env) ->
             let proof = Inference.build_proof_term proof in
             Printf.printf "OK, found a proof!\n";
             (* REMEMBER: we have to instantiate meta_proof, we should use
@@ -2125,24 +1839,10 @@ let main dbd full term metasenv ugraph =
                 (fun m (_, _, _, menv, _) -> m @ menv) metasenv equalities
             in
             let _ =
-(*               Printf.printf "OK, found a proof!\n"; *)
-(*               (\* REMEMBER: we have to instantiate meta_proof, we should use *)
-(*                  apply  the "apply" tactic to proof and status  *)
-(*               *\) *)
-(*               let names = names_of_context context in *)
-(*               print_endline (PP.pp proof names); *)
               try
                 let ty, ug =
                   CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
                 in
-(*                 Printf.printf "OK, found a proof!\n"; *)
-(*                 (\* REMEMBER: we have to instantiate meta_proof, we should use *)
-(*                    apply  the "apply" tactic to proof and status  *)
-(*                 *\) *)
-(*                 let names = names_of_context context in *)
-(*                 print_endline (PP.pp proof names); *)
-                (*           print_endline (PP.ppterm proof); *)
-                
                 print_endline (string_of_float (finish -. start));
                 Printf.printf
                   "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n\n"
@@ -2228,10 +1928,13 @@ let saturate
   let ugraph = CicUniv.empty_ugraph in
   let env = (metasenv, context, ugraph) in
   let goal = Inference.BasicProof new_meta_goal, [], goal in
-  let res, time = 
+  let res, time =
+    let t1 = Unix.gettimeofday () in
     let lib_eq_uris, library_equalities, maxm =
       find_library_equalities dbd context (proof, goal') (maxm+2)
     in
+    let library_equalities = List.map snd library_equalities in
+    let t2 = Unix.gettimeofday () in
     maxmeta := maxm+2;
     let equalities =
       let equalities = equalities @ library_equalities in
@@ -2275,28 +1978,15 @@ let saturate
                      (List.map string_of_equality res))));
           res
     in
+    debug_print
+      (lazy
+         (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)));
+    let t1 = Unix.gettimeofday () in
     let theorems =
       if full then
-(*         let refl_eq = *)
-(*           let u = eq_XURI () in *)
-(*           let t = CicUtil.term_of_uri u in *)
-(*           let ty, _ = *)
-(*             CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in *)
-(*           (t, ty, []) *)
-(*         in *)
-(*         let le_S = *)
-(*           let u = UriManager.uri_of_string *)
-(*             "cic:/matita/nat/orders/le.ind#xpointer(1/1/2)" in *)
-(*           let t = CicUtil.term_of_uri u in *)
-(*           let ty, _ = *)
-(*             CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in *)
-(*           (t, ty, []) *)
-(*         in *)
-(*         let thms = refl_eq::le_S::[] in *)
-          let thms = find_library_theorems dbd env (proof, goal') lib_eq_uris in
+        let thms = find_library_theorems dbd env (proof, goal') lib_eq_uris in
         let context_hyp = find_context_hypotheses env eq_indexes in
-(*         context_hyp @ thms *)
-        (context_hyp, thms)
+        context_hyp @ thms, []
       else
         let refl_equal =
           let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
@@ -2304,8 +1994,9 @@ let saturate
         in
         let t = CicUtil.term_of_uri refl_equal in
         let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
-        [], [(refl_equal, t, ty, [])]
+        [(t, ty, [])], []
     in
+    let t2 = Unix.gettimeofday () in
     let _ =
       debug_print
         (lazy
@@ -2313,28 +2004,28 @@ let saturate
               "Theorems:\n-------------------------------------\n%s\n"
               (String.concat "\n"
                  (List.map
-                    (fun (_, t, ty, _) ->
+                    (fun (t, ty, _) ->
                        Printf.sprintf
                          "Term: %s, type: %s"
                          (CicPp.ppterm t) (CicPp.ppterm ty))
-                    (snd theorems)))))
+                    (fst theorems)))));
+      debug_print
+        (lazy
+           (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
     in
     let active = make_active () in
-    let passive = make_passive [(* term_equality *)] equalities in
+    let passive = make_passive [] equalities in
     let start = Unix.gettimeofday () in
-(*     let res = given_clause_fullred env [0, [goal]] theorems passive active in *)
     let res =
       let goals = make_goals goal in
-(*       and theorems = make_theorems theorems in *)
-        given_clause_fullred dbd env goals theorems passive active
+      given_clause_fullred dbd env goals theorems passive active
     in
     let finish = Unix.gettimeofday () in
     (res, finish -. start)
   in
   match res with
-  | ParamodulationSuccess (Some proof (* goal *), env) ->
+  | ParamodulationSuccess (Some proof, env) ->
       debug_print (lazy "OK, found a proof!");
-(*       let proof = Inference.build_proof_term goal in          *)
       let proof = Inference.build_proof_term proof in
       let names = names_of_context context in
       let newmetasenv =
@@ -2382,12 +2073,12 @@ let saturate
           debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
           debug_print (lazy (CicPp.pp proof names));
           raise (ProofEngineTypes.Fail
-                   "Found a proof, but it doesn't typecheck")
+                  (lazy "Found a proof, but it doesn't typecheck"))
       in
       debug_print (lazy (Printf.sprintf "\nTIME NEEDED: %.9f" time));
       newstatus          
   | _ ->
-      raise (ProofEngineTypes.Fail "NO proof found")
+      raise (ProofEngineTypes.Fail (lazy "NO proof found"))
 ;;
 
 (* dummy function called within matita to trigger linkage *)
@@ -2400,3 +2091,95 @@ if connect_to_auto then (
   AutoTactic.term_is_equality := Inference.term_is_equality;
 );;
 
+
+let retrieve_and_print dbd term metasenv ugraph = 
+  let module C = Cic in
+  let module T = CicTypeChecker in
+  let module PET = ProofEngineTypes in
+  let module PP = CicPp in
+  let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
+  let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
+  let proof, goals = status in
+  let goal' = List.nth goals 0 in
+  let uri, metasenv, meta_proof, term_to_prove = proof in
+  let _, context, goal = CicUtil.lookup_meta goal' metasenv in
+  let eq_indexes, equalities, maxm = find_equalities context proof in
+  let new_meta_goal, metasenv, type_of_goal =
+    let irl =
+      CicMkImplicit.identity_relocation_list_for_metavariable context in
+    let _, context, ty = CicUtil.lookup_meta goal' metasenv in
+    debug_print
+      (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty)));
+    Cic.Meta (maxm+1, irl),
+    (maxm+1, context, ty)::metasenv,
+    ty
+  in
+  let ugraph = CicUniv.empty_ugraph in
+  let env = (metasenv, context, ugraph) in
+  let goal = Inference.BasicProof new_meta_goal, [], goal in
+  let t1 = Unix.gettimeofday () in
+  let lib_eq_uris, library_equalities, maxm =
+    find_library_equalities dbd context (proof, goal') (maxm+2)
+  in
+  let t2 = Unix.gettimeofday () in
+    maxmeta := maxm+2;
+    let equalities =
+      let equalities = (* equalities @ *) library_equalities in
+	debug_print
+          (lazy
+             (Printf.sprintf "\n\nequalities:\n%s\n"
+		(String.concat "\n"
+                   (List.map 
+		      (fun (u, e) ->
+(* 			 Printf.sprintf "%s: %s" *)
+			   (UriManager.string_of_uri u)
+(* 			   (string_of_equality e) *)
+		      )
+		      equalities))));
+	debug_print (lazy "SIMPLYFYING EQUALITIES...");
+	let rec simpl e others others_simpl =
+	  let (u, e) = e in
+          let active = List.map (fun (u, e) -> (Positive, e))
+	    (others @ others_simpl) in
+          let tbl =
+            List.fold_left
+              (fun t (_, e) -> Indexing.index t e)
+              (Indexing.empty_table ()) active
+          in
+          let res = forward_simplify env (Positive, e) (active, tbl) in
+            match others with
+              | hd::tl -> (
+		  match res with
+		    | None -> simpl hd tl others_simpl
+		    | Some e -> simpl hd tl ((u, (snd e))::others_simpl)
+		)
+              | [] -> (
+		  match res with
+		    | None -> others_simpl
+		    | Some e -> (u, (snd e))::others_simpl
+		)
+	in
+	  match equalities with
+	    | [] -> []
+	    | hd::tl ->
+		let others = tl in (* List.map (fun e -> (Positive, e)) tl in *)
+		let res =
+		  List.rev (simpl (*(Positive,*) hd others [])
+		in
+		  debug_print
+		    (lazy
+		       (Printf.sprintf "\nequalities AFTER:\n%s\n"
+			  (String.concat "\n"
+			     (List.map
+				(fun (u, e) ->
+				   Printf.sprintf "%s: %s"
+				     (UriManager.string_of_uri u)
+				     (string_of_equality e)
+				)
+				res))));
+		  res
+    in
+      debug_print
+	(lazy
+           (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)))
+;;