(* 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;;


(* set to false to disable paramodulation inside auto_tac *)
let connect_to_auto = true;;


(* profiling statistics... *)
let infer_time = ref 0.;;
let forward_simpl_time = ref 0.;;
let forward_simpl_new_time = ref 0.;;
let backward_simpl_time = ref 0.;;
let passive_maintainance_time = ref 0.;;

(* limited-resource-strategy related globals *)
let processed_clauses = ref 0;; (* number of equalities selected so far... *)
let time_limit = ref 0.;; (* in seconds, settable by the user... *)
let start_time = ref 0.;; (* time at which the execution started *)
let elapsed_time = ref 0.;;
(* let maximal_weight = ref None;; *)
let maximal_retained_equality = ref None;;

(* equality-selection related globals *)
let use_fullred = ref true;;
let weight_age_ratio = ref (* 5 *) 4;; (* settable by the user *)
let weight_age_counter = ref !weight_age_ratio;;
let symbols_ratio = ref (* 0 *) 3;;
let symbols_counter = ref 0;;

(* non-recursive Knuth-Bendix term ordering by default *)
Utils.compare_terms := Utils.nonrec_kbo;; 

(* statistics... *)
let derived_clauses = ref 0;;
let kept_clauses = ref 0;;

(* index of the greatest Cic.Meta created - TODO: find a better way! *)
let maxmeta = ref 0;;

(* varbiables controlling the search-space *)
let maxdepth = ref 3;;
let maxwidth = ref 3;;


type result =
  | ParamodulationFailure
  | ParamodulationSuccess of Inference.proof option * environment
;;

type goal = proof * Cic.metasenv * Cic.term;;

type theorem = Cic.term * Cic.term * Cic.metasenv;;


let symbols_of_equality ((_, _, (_, left, right, _), _, _) as equality) =
  let m1 = symbols_of_term left in
  let m = 
    TermMap.fold
      (fun k v res ->
         try
           let c = TermMap.find k res in
           TermMap.add k (c+v) res
         with Not_found ->
           TermMap.add k v res)
      (symbols_of_term right) m1
  in
  m
;;


module OrderedEquality = struct
  type t = Inference.equality

  let compare eq1 eq2 =
    match meta_convertibility_eq eq1 eq2 with
    | true -> 0
    | false ->
        let w1, _, (ty, left, right, _), _, a = eq1
        and w2, _, (ty', left', right', _), _, a' = eq2 in
        match Pervasives.compare w1 w2 with
        | 0 ->
            let res = (List.length a) - (List.length a') in
            if res <> 0 then res else (
              try
                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
            )
        | res -> res
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
  in
  if !weight_age_ratio > 0 then
    weight_age_counter := !weight_age_counter - 1;
  match !weight_age_counter with
  | 0 -> (
      weight_age_counter := !weight_age_ratio;
      match neg_list, pos_list with
      | hd::tl, pos ->
          (* Negatives aren't indexed, no need to remove them... *)
          (Negative, hd),
          ((tl, EqualitySet.remove hd neg_set), (pos, pos_set), passive_table)
      | [], hd::tl ->
          let passive_table =
            Indexing.remove_index passive_table hd
          in
          (Positive, hd),
          (([], neg_set), (tl, EqualitySet.remove hd pos_set), passive_table)
      | _, _ -> assert false
    )
  | _ when (!symbols_counter > 0) && (EqualitySet.is_empty neg_set) -> (
      symbols_counter := !symbols_counter - 1;
      let cardinality map =
        TermMap.fold (fun k v res -> res + v) map 0
      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 (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;
      let set_selection set = EqualitySet.min_elt set in
      if EqualitySet.is_empty neg_set then
        let current = set_selection pos_set in
        let passive =
          (neg_list, neg_set),
          (remove current pos_list, EqualitySet.remove current pos_set),
          Indexing.remove_index passive_table current
        in
        (Positive, current), passive
      else
        let current = set_selection neg_set in
        let passive =
          (remove current neg_list, EqualitySet.remove current neg_set),
          (pos_list, pos_set),
          passive_table
        in
        (Negative, current), passive
;;


(* 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
  in
  let table =
      List.fold_left (fun tbl e -> Indexing.index tbl e)
        (Indexing.empty_table ()) pos
  in
  (neg, set_of neg),
  (pos, set_of pos),
  table
;;


let make_active () =
  [], Indexing.empty_table () 
;;


(* 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
  in
  let add set equalities =
    List.fold_left (fun s e -> EqualitySet.add e s) set equalities
  in
  (neg @ neg_list, add neg_set neg),
  (pos_list @ pos, add pos_set pos),
  table
;;


let passive_is_empty = function
  | ([], _), ([], _), _ -> true
  | _ -> false
;;


let size_of_passive ((_, ns), (_, ps), _) =
  (EqualitySet.cardinal ns) + (EqualitySet.cardinal ps)
;;


let size_of_active (active_list, _) =
  List.length 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
  and ratio = float_of_int !weight_age_ratio in
  let round v =
    let t = ceil v in 
    int_of_float (if t -. v < 0.5 then t else v)
  in
  let in_weight = round (howmany *. ratio /. (ratio +. 1.))
  and in_age = round (howmany /. (ratio +. 1.)) in 
  debug_print
    (lazy (Printf.sprintf "in_weight: %d, in_age: %d\n" in_weight in_age));
  let symbols, card =
    match active with
    | (Negative, e)::_ ->
        let symbols = symbols_of_equality e in
        let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
        Some symbols, card
    | _ -> None, 0
  in
  let counter = ref !symbols_ratio in
  let rec pickw w ns ps =
    if w > 0 then
      if not (EqualitySet.is_empty ns) then
        let e = EqualitySet.min_elt ns in
        let ns', ps = pickw (w-1) (EqualitySet.remove e ns) ps in
        EqualitySet.add e ns', ps
      else if !counter > 0 then
        let _ =
          counter := !counter - 1;
          if !counter = 0 then counter := !symbols_ratio
        in
        match symbols with
        | None ->
            let e = EqualitySet.min_elt ps in
            let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
            ns, EqualitySet.add e ps'
        | Some symbols ->
            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 ps in
            let initial =
              let common, others = 
                TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
              in
              (others + (abs (common - card))), e1
            in
            let _, e = EqualitySet.fold f ps initial in
            let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
            ns, EqualitySet.add e ps'
      else
        let e = EqualitySet.min_elt ps in
        let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
        ns, EqualitySet.add e ps'        
    else
      EqualitySet.empty, EqualitySet.empty
  in
  let ns, ps = pickw in_weight ns ps in
  let rec picka w s l =
    if w > 0 then
      match l with
      | [] -> w, s, []
      | hd::tl when not (EqualitySet.mem hd s) ->
          let w, s, l = picka (w-1) s tl in
          w, EqualitySet.add hd s, hd::l
      | hd::tl ->
          let w, s, l = picka w s tl in
          w, s, hd::l
    else
      0, s, l
  in
  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_retained_equality := Some (EqualitySet.max_elt ps); 
  let tbl =
    EqualitySet.fold
      (fun e tbl -> Indexing.index tbl e) ps (Indexing.empty_table ())
  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
    | Negative ->
        let maxm, res = 
          Indexing.superposition_left !maxmeta env active_table current in
        maxmeta := maxm;
        res, [] 
    | Positive ->
        let maxm, res =
          Indexing.superposition_right !maxmeta env active_table current in
        maxmeta := maxm;
        let rec infer_positive table = function
          | [] -> [], []
          | (Negative, equality)::tl ->
              let maxm, res =
                Indexing.superposition_left !maxmeta env table equality in
              maxmeta := maxm;
              let neg, pos = infer_positive table tl in
              res @ neg, pos
          | (Positive, equality)::tl ->
              let maxm, res =
                Indexing.superposition_right !maxmeta env table equality in
              maxmeta := maxm;
              let neg, pos = infer_positive table tl in
              neg, res @ pos
        in
        let curr_table = Indexing.index (Indexing.empty_table ()) current in
        let neg, pos = infer_positive curr_table active_list in
        neg, res @ pos
  in
  derived_clauses := !derived_clauses + (List.length new_neg) +
    (List.length new_pos);
  match !maximal_retained_equality with
  | None -> new_neg, new_pos
  | Some eq ->
      (* if we have a maximal_retained_equality, we can discard all equalities
         "greater" than it, as they will never be reached...  An equality is
         greater than maximal_retained_equality if it is bigger
         wrt. OrderedEquality.compare and it is less similar than
         maximal_retained_equality to the current goal *)
      let symbols, card =
        match active_list with
        | (Negative, e)::_ ->
            let symbols = symbols_of_equality e in
            let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
            Some symbols, card
        | _ -> None, 0
      in
      let new_pos = 
        match symbols with
        | None ->
            List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos
        | Some symbols ->
            let filterfun e =
              if OrderedEquality.compare e eq <= 0 then
                true
              else
                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 initial =
                  let common, others =
                    TermMap.fold foldfun (symbols_of_equality eq) (0, 0) in
                  others + (abs (common - card))
                in
                let common, others =
                  TermMap.fold foldfun (symbols_of_equality e) (0, 0) in
                let c = others + (abs (common - card)) in
                if c < initial then true else false 
            in
            List.filter filterfun new_pos
      in
      new_neg, new_pos
;;


let contains_empty env (negative, positive) =
  let metasenv, context, ugraph = env in
  try
    let found =
      List.find
        (fun (w, proof, (ty, left, right, ordering), m, a) ->
           fst (CicReduction.are_convertible context left right ugraph))
        negative
    in
    true, Some found
  with Not_found ->
    false, None
;;


(** simplifies current using active and passive *)
let forward_simplify env (sign, current) ?passive (active_list, active_table) =
  let pl, passive_table =
    match passive with
    | None -> [], None
    | Some ((pn, _), (pp, _), pt) ->
        let pn = List.map (fun e -> (Negative, e)) pn
        and pp = List.map (fun e -> (Positive, e)) pp in
        pn @ pp, Some pt
  in
  let all = if pl = [] then active_list else active_list @ pl in
  
  let demodulate table current = 
    let newmeta, newcurrent =
      Indexing.demodulation_equality !maxmeta env table sign current in
    maxmeta := newmeta;
    if is_identity env newcurrent then
      if sign = Negative then Some (sign, newcurrent)
      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
  let res =
    let res = demodulate active_table current in
    match res with
    | None -> None
    | Some (sign, newcurrent) ->
        match passive_table with
        | None -> res
        | Some passive_table -> demodulate passive_table newcurrent
  in
  match res with
  | None -> None
  | Some (Negative, c) ->
      let ok = not (
        List.exists
          (fun (s, eq) -> s = Negative && meta_convertibility_eq eq c)
          all)
      in
      if ok then res else None
  | Some (Positive, c) ->
      if Indexing.in_index active_table c then
        None
      else
        match passive_table with
        | 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 
	      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 = {
  mutable build_all: float;
  mutable demodulate: float;
  mutable subsumption: float;
};;

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

  let active_list, active_table = active in
  let pl, passive_table =
    match passive with
    | None -> [], None
    | Some ((pn, _), (pp, _), pt) ->
        let pn = List.map (fun e -> (Negative, e)) pn
        and pp = List.map (fun e -> (Positive, e)) pp in
        pn @ pp, Some pt
  in
  let all = active_list @ pl in
  
  let t2 = Unix.gettimeofday () in
  fs_time_info.build_all <- fs_time_info.build_all +. (t2 -. t1);
  
  let demodulate sign table target =
    let newmeta, newtarget =
      Indexing.demodulation_equality !maxmeta env table sign target in
    maxmeta := newmeta;
    newtarget
  in
  let t1 = Unix.gettimeofday () in

  let new_neg, new_pos =
    let new_neg = List.map (demodulate Negative active_table) new_neg
    and new_pos = List.map (demodulate Positive active_table) new_pos in
    match passive_table with
    | None -> new_neg, new_pos
    | Some passive_table ->
        List.map (demodulate Negative passive_table) new_neg,
        List.map (demodulate Positive passive_table) new_pos
  in

  let t2 = Unix.gettimeofday () in
  fs_time_info.demodulate <- fs_time_info.demodulate +. (t2 -. t1);

  let new_pos_set =
    List.fold_left
      (fun s e ->
         if not (Inference.is_identity env e) then
           if EqualitySet.mem e s then s
           else EqualitySet.add e s
         else s)
      EqualitySet.empty new_pos
  in
  let new_pos = EqualitySet.elements new_pos_set in

  let subs =
    match passive_table with
    | None ->
        (fun e -> not (fst (Indexing.subsumption env active_table e)))
    | Some passive_table ->
        (fun e -> not ((fst (Indexing.subsumption env active_table e)) ||
                         (fst (Indexing.subsumption env passive_table e))))
  in
(*   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 ->
        (fun e -> not (Indexing.in_index active_table e))
    | Some passive_table ->
        (fun e ->
           not ((Indexing.in_index active_table e) ||
                  (Indexing.in_index passive_table e)))
  in
  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 = 
    List.fold_right
      (fun (s, equality) (res, newn) ->
         let ew, _, _, _, _ = equality in
         if ew < min_weight then
           (s, equality)::res, newn
         else
           match forward_simplify env (s, equality) (new_pos, new_table) with
           | None -> res, newn
           | Some (s, e) ->
               if equality = e then
                 (s, e)::res, newn
               else 
                 res, (s, e)::newn)
      active_list ([], [])
  in
  let find eq1 where =
    List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
  in
  let active, newa =
    List.fold_right
      (fun (s, eq) (res, tbl) ->
         if List.mem (s, eq) res then
           res, tbl
         else if (is_identity env eq) || (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 ()),
    List.fold_right
      (fun (s, eq) (n, p) ->
         if (s <> Negative) && (is_identity env eq) then (
           (n, p)
         ) else
           if s = Negative then eq::n, p
           else n, eq::p)
      newa ([], [])
  in
  match newa with
  | [], [] -> active, None
  | _ -> active, Some newa
;;


(** 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
      equality::resl, ress, newn
    else
      match forward_simplify env (sign, equality) (new_pos, new_table) with
      | None -> resl, EqualitySet.remove equality ress, newn
      | Some (s, e) ->
          if equality = e then
            equality::resl, ress, newn
          else
            let ress = EqualitySet.remove equality ress in
            resl, ress, e::newn
  in
  let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
  and pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in
  let passive_table =
    List.fold_left
      (fun tbl e -> Indexing.index tbl e) (Indexing.empty_table ()) pl
  in
  match newn, newp with
  | [], [] -> ((nl, ns), (pl, ps), passive_table), None
  | _, _ -> ((nl, ns), (pl, ps), passive_table), Some (newn, newp)
;;


let backward_simplify env new' ?passive active =
  let new_pos, new_table, min_weight =
    List.fold_left
      (fun (l, t, w) e ->
         let ew, _, _, _, _ = e in
         (Positive, e)::l, Indexing.index t e, min ew w)
      ([], Indexing.empty_table (), 1000000) (snd new')
  in
  let active, newa =
    backward_simplify_active env new_pos new_table min_weight active in
  match passive with
  | None ->
      active, (make_passive [] []), newa, None
  | Some passive ->
      let passive, newp =
        backward_simplify_passive env new_pos new_table min_weight passive in
      active, passive, newa, newp
;;


(* 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)) *)
  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
  active, passive
;;


(** initializes the set of theorems *)
let make_theorems theorems =
  theorems, []
;;


let activate_goal (active, passive) =
  match passive with
  | goal_conj::tl -> true, (goal_conj::active, tl)
  | [] -> false, (active, passive)
;;


let activate_theorem (active, passive) =
  match passive with
  | theorem::tl -> true, (theorem::active, tl)
  | [] -> 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
    | None -> [], None
    | Some ((pn, _), (pp, _), pt) ->
        let pn = List.map (fun e -> (Negative, e)) pn
        and pp = List.map (fun e -> (Positive, e)) pp in
        pn @ pp, Some pt
  in
  let all = if pl = [] then active_list else active_list @ pl in

  let demodulate table goal = 
    let newmeta, newgoal =
      Indexing.demodulation_goal !maxmeta env table goal in
    maxmeta := newmeta;
    goal != newgoal, newgoal
  in
  let changed, goal =
    match passive_table with
    | None -> demodulate active_table goal
    | Some passive_table ->
        let changed, goal = demodulate active_table goal in
        let changed', goal = demodulate passive_table goal in
        (changed || changed'), goal
  in
  changed, goal
;;


let simplify_goals env goals ?passive active =
  let a_goals, p_goals = goals in
  let p_goals = 
    List.map
      (fun (d, gl) ->
         let gl =
           List.map (fun g -> snd (simplify_goal env g ?passive active)) gl in
         d, gl)
      p_goals
  in
  let goals =
    List.fold_left
      (fun (a, p) (d, gl) ->
         let changed = ref false in
         let gl =
           List.map
             (fun g ->
                let c, g = simplify_goal env g ?passive active in
                changed := !changed || c; g) gl in
         if !changed then (a, (d, gl)::p) else ((d, gl)::a, p))
      ([], p_goals) a_goals
  in
  goals
;;


let simplify_theorems env theorems ?passive (active_list, active_table) =
  let pl, passive_table =
    match passive with
    | None -> [], None
    | Some ((pn, _), (pp, _), pt) ->
        let pn = List.map (fun e -> (Negative, e)) pn
        and pp = List.map (fun e -> (Positive, e)) pp in
        pn @ pp, Some pt
  in
  let all = if pl = [] then active_list else active_list @ pl in
  let a_theorems, p_theorems = theorems in
  let demodulate table theorem =
    let newmeta, newthm =
      Indexing.demodulation_theorem !maxmeta env table theorem in
    maxmeta := newmeta;
    theorem != newthm, newthm
  in
  let foldfun table (a, p) theorem =
    let changed, theorem = demodulate table theorem in
    if changed then (a, theorem::p) else (theorem::a, p)
  in
  let mapfun table theorem = snd (demodulate table theorem) in
  match passive_table with
  | None ->
      let p_theorems = List.map (mapfun active_table) p_theorems in
      List.fold_left (foldfun active_table) ([], p_theorems) a_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
;;


(* 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
  let module I = Inference in
  let metasenv, context, ugraph = env in
  let _, proof, (ty, left, right, _), metas, args = equality in
  let eqterm =
    C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right] in
  let gproof, gmetas, gterm = goal in
(*   debug_print *)
(*     (lazy *)
(*        (Printf.sprintf "APPLY EQUALITY TO GOAL: %s, %s" *)
(*           (string_of_equality equality) (CicPp.ppterm gterm))); *)
  try
    let subst, metasenv', _ =
      let menv = metasenv @ metas @ gmetas in
      Inference.unification menv context eqterm gterm ugraph
    in
    let newproof =
      match proof with
      | I.BasicProof t -> I.BasicProof (CicMetaSubst.apply_subst subst t)
      | I.ProofBlock (s, uri, nt, t, pe, p) ->
          I.ProofBlock (subst @ s, uri, nt, t, pe, p)
      | _ -> assert false
    in
    let newgproof =
      let rec repl = function
        | I.ProofGoalBlock (_, gp) -> I.ProofGoalBlock (newproof, gp)
        | I.NoProof -> newproof
        | I.BasicProof p -> newproof
        | I.SubProof (t, i, p) -> I.SubProof (t, i, repl p)
        | _ -> assert false
      in
      repl gproof
    in
    true, subst, newgproof
  with CicUnification.UnificationFailure _ ->
    false, [], I.NoProof
;;



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))); *)
  let status =
    let irl =
      CicMkImplicit.identity_relocation_list_for_metavariable context in
    let proof', newmeta =
      let rec get_meta = function
        | 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
        | _ -> Cic.Implicit None, -1
      in
      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 metasenv = (newmeta, context, term)::metasenv @ metas in
    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
    | (theorem, thmty, _)::tl ->
        try
          let subst, (newproof, newgoals) =
            PrimitiveTactics.apply_tac_verbose_with_subst ~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
            let _, m = status in
            let subst = List.filter (fun (i, _) -> i = m) subst in
            `Ok (subst, [newp, metas, term])
          else
            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 p' =
                     let rec gp = function
                       | SubProof (t, i, p) ->
                           SubProof (t, i, gp p)
                       | ProofGoalBlock (sp1, sp2) ->
                           ProofGoalBlock (sp1, gp sp2)
                       | BasicProof _
                       | NoProof ->
                           SubProof (p, i, BasicProof (Cic.Meta (i, irl)))
                       | ProofSymBlock (s, sp) ->
                           ProofSymBlock (s, gp sp)
                       | ProofBlock (s, u, nt, t, pe, sp) ->
                           ProofBlock (s, u, nt, t, pe, gp sp)
                     in gp proof
                   in
                   (p', menv, ty))
                newgoals
            in
            let goals =
              let weight t =
                let w, m = weight_of_term t in
                w + 2 * (List.length m)
              in
              List.sort
                (fun (_, _, t1) (_, _, t2) ->
                   Pervasives.compare (weight t1) (weight t2))
                goals
            in
            let best = aux tl in
            match best with
            | `Ok (_, _) -> best
            | `No -> `GoOn ([subst, goals])
            | `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 rec appleq_a = function
        | [] -> false, [], []
        | (Positive, equality)::tl ->
            let ok, s, newproof = apply_equality_to_goal env equality goal in
            if ok then true, s, [newproof, metas, term] else appleq_a tl
        | _::tl -> appleq_a tl
      in
      let rec appleq_p = function
        | [] -> false, [], []
        | equality::tl ->
            let ok, s, newproof = apply_equality_to_goal env equality goal in
            if ok then true, s, [newproof, metas, term] else appleq_p tl
      in
      let al, _ = active in
      match passive with
      | None -> appleq_a al
      | Some (_, (pl, _), _) ->
          let r, s, l = appleq_a al in if r then r, s, l else appleq_p pl
    else
      false, [], []
  in
  if r = true then `Ok (s, l) else aux theorems
;;


(* 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
              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
  if depth > !maxdepth || (List.length goals) > !maxwidth then 
    `No (depth, 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

  let compare g1 g2 =
    let d1, l1 = g1
    and d2, l2 = g2 in
    let r = d2 - d1 in
    if r <> 0 then r
    else let r = (List.length l1) - (List.length l2) in
    if r <> 0 then r
    else
      let res = ref 0 in
      let _ = 
        List.exists2
          (fun (_, _, t1) (_, _, t2) ->
             let r = Pervasives.compare t1 t2 in
             if r <> 0 then (
               res := r;
               true
             ) else
               false) l1 l2
      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 =
    List.fold_left (fun s g -> GoalsSet.add g s) set goals 
  in
  let rec aux set = function
    | [] ->
        debug_print (lazy "HERE!!!");
        if is_passive_empty then raise SearchSpaceOver else false, set
    | goals::tl ->
        let res = apply_to_goal_conj env theorems active goals in
        match res with
        | `Ok newgoals ->
            let _ =
              let d, p, t =
                match newgoals with
                | (d, (p, _, t)::_) -> d, p, t
                | _ -> assert false
              in
              debug_print
                (lazy
                   (Printf.sprintf "\nOK!!!!\ndepth: %d\nProof: %s\ngoal: %s\n"
                      d (string_of_proof p) (CicPp.ppterm t)))
            in
            true, GoalsSet.singleton newgoals
        | `GoOn newgoals ->
            let set' = add_to set (goals::tl) in
            let set' = add_to set' newgoals in
            false, set'
        | `No newgoals ->
            aux set tl
  in
  let n = List.length goals in
  let res, goals = aux (add_to GoalsSet.empty goals) goals in
  let goals = GoalsSet.elements goals in
  debug_print (lazy "\n\tapply_to_goals end\n");
  let m = List.length goals in
  if m = n && is_passive_empty then
    raise SearchSpaceOver
  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 a_goals, p_goals = goals in
  let goal = List.hd a_goals in
  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
              false)
         a_goals)
  in
  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 theorems
;;


let apply_theorem_to_goals env theorems active goals =
  let a_goals, p_goals = goals in
  let theorem = List.hd (fst theorems) in
  let theorems = [theorem] in
  let rec aux p = function
    | [] -> false, ([], p)
    | goal::tl ->
        let res = apply_to_goal_conj env theorems active goal in
        match res with
        | `Ok newgoals -> true, ([newgoals], [])
        | `No _ -> aux p tl
        | `GoOn newgoals -> aux (newgoals @ p) tl
  in
  let ok, (a, p) = aux p_goals a_goals in
  if ok then
    ok, (a, p)
  else
    let p_goals =
      List.stable_sort
        (fun (d1, l1) (d2, l2) ->
           let r = d2 - d1 in
           if r <> 0 then r
           else let r = (List.length l1) - (List.length l2) in
           if r <> 0 then r
           else
             let res = ref 0 in
             let _ = 
               List.exists2
                 (fun (_, _, t1) (_, _, t2) ->
                    let r = Pervasives.compare t1 t2 in
                    if r <> 0 then (res := r; true) else false) l1 l2
             in !res)
        p
    in
    ok, (a_goals, p_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 *)
  if ok then
    let ok, goals = apply_goal_to_theorems dbd env theorems active goals in
    if ok then
      let proof =
        match (fst goals) with
        | (_, [proof, _, _])::_ -> Some proof
        | _ -> assert false
      in
      ParamodulationSuccess (proof, env)
    else
      given_clause_aux dbd env goals theorems passive active
  else
(*     let ok', theorems = activate_theorem theorems in *)
    let ok', theorems = false, theorems in
    if ok' then
      let ok, goals = apply_theorem_to_goals env theorems active goals in
      if ok then
        let proof =
          match (fst goals) with
          | (_, [proof, _, _])::_ -> Some proof
          | _ -> assert false
        in
        ParamodulationSuccess (proof, env)
      else
        given_clause_aux dbd env goals theorems passive active
    else
      if (passive_is_empty passive) then ParamodulationFailure
      else given_clause_aux dbd env goals theorems passive active

and given_clause_aux dbd env goals theorems passive active = 
  let time1 = Unix.gettimeofday () in

  let selection_estimate = get_selection_estimate () in
  let kept = size_of_passive passive in
  let passive =
    if !time_limit = 0. || !processed_clauses = 0 then
      passive
    else if !elapsed_time > !time_limit then (
      debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
                           !time_limit !elapsed_time));
      make_passive [] []
    ) else if kept > selection_estimate then (
      debug_print
        (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
                                 "(kept: %d, selection_estimate: %d)\n")
                 kept selection_estimate));
      prune_passive selection_estimate active passive
    ) else
      passive
  in

  let time2 = Unix.gettimeofday () in
  passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);

  kept_clauses := (size_of_passive passive) + (size_of_active active);
  match passive_is_empty passive with
  | true -> (* ParamodulationFailure *)
      given_clause dbd env goals theorems passive active
  | false ->
      let (sign, current), passive = select env (fst goals) passive active in
      let time1 = Unix.gettimeofday () in
      let res = forward_simplify env (sign, current) ~passive active in
      let time2 = Unix.gettimeofday () in
      forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
      match res with
      | None ->
          given_clause dbd env goals theorems passive active
      | Some (sign, current) ->
          if (sign = Negative) && (is_identity env current) then (
            debug_print
              (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                       (string_of_equality ~env current)));
            let _, proof, _, _, _  = current in
            ParamodulationSuccess (Some proof, env)
          ) else (            
            debug_print
              (lazy "\n================================================");
            debug_print (lazy (Printf.sprintf "selected: %s %s"
                                 (string_of_sign sign)
                                 (string_of_equality ~env current)));

            let t1 = Unix.gettimeofday () in
            let new' = infer env sign current active in
            let t2 = Unix.gettimeofday () in
            infer_time := !infer_time +. (t2 -. t1);
            
            let res, goal' = contains_empty env new' in
            if res then
              let proof =
                match goal' with
                | Some goal -> let _, proof, _, _, _ = goal in Some proof
                | None -> None
              in
              ParamodulationSuccess (proof, env)
            else 
              let t1 = Unix.gettimeofday () in
              let new' = forward_simplify_new env new' active in
              let t2 = Unix.gettimeofday () in
              let _ =
                forward_simpl_new_time :=
                  !forward_simpl_new_time +. (t2 -. t1)
              in
              let active =
                match sign with
                | Negative -> active
                | Positive ->
                    let t1 = Unix.gettimeofday () in
                    let active, _, newa, _ =
                      backward_simplify env ([], [current]) active
                    in
                    let t2 = Unix.gettimeofday () in
                    backward_simpl_time :=
                      !backward_simpl_time +. (t2 -. t1);
                    match newa with
                    | None -> active
                    | Some (n, p) ->
                        let al, tbl = active in
                        let nn = List.map (fun e -> Negative, e) n in
                        let pp, tbl =
                          List.fold_right
                            (fun e (l, t) ->
                               (Positive, e)::l,
                               Indexing.index tbl e)
                            p ([], tbl)
                        in
                        nn @ al @ pp, tbl
              in
              match contains_empty env new' with
              | false, _ -> 
                  let active =
                    let al, tbl = active in
                    match sign with
                    | Negative -> (sign, current)::al, tbl
                    | Positive ->
                        al @ [(sign, current)], Indexing.index tbl current
                  in
                  let passive = add_to_passive passive new' in
                  let (_, ns), (_, ps), _ = passive in
                  given_clause dbd env goals theorems passive active
              | true, goal ->
                  let proof =
                    match goal with
                    | Some goal ->
                        let _, proof, _, _, _ = goal in Some proof
                    | None -> None
                  in
                  ParamodulationSuccess (proof, env)
          )
;;


(** 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 _ = *)
(*       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
    if ok then
      let proof =
        match (fst goals) with
        | (_, [proof, _, _])::_ -> Some proof
        | _ -> assert false
      in
      ParamodulationSuccess (proof, env)
    else
      given_clause_fullred_aux dbd env goals theorems passive active
  else
(*     let ok', theorems = activate_theorem theorems in *)
(*     if ok' then *)
(*       let ok, goals = apply_theorem_to_goals env theorems active goals in *)
(*       if ok then *)
(*         let proof = *)
(*           match (fst goals) with *)
(*           | (_, [proof, _, _])::_ -> Some proof *)
(*           | _ -> assert false *)
(*         in *)
(*         ParamodulationSuccess (proof, env) *)
(*       else *)
(*         given_clause_fullred_aux env goals theorems passive active *)
(*     else *)
      if (passive_is_empty passive) then ParamodulationFailure
      else given_clause_fullred_aux dbd env goals theorems passive active
    
and given_clause_fullred_aux dbd env goals theorems passive active =
  let time1 = Unix.gettimeofday () in
  
  let selection_estimate = get_selection_estimate () in
  let kept = size_of_passive passive in
  let passive =
    if !time_limit = 0. || !processed_clauses = 0 then
      passive
    else if !elapsed_time > !time_limit then (
      debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
                           !time_limit !elapsed_time));
      make_passive [] []
    ) else if kept > selection_estimate then (
      debug_print
        (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
                                 "(kept: %d, selection_estimate: %d)\n")
                 kept selection_estimate));
      prune_passive selection_estimate active passive
    ) else
      passive
  in

  let time2 = Unix.gettimeofday () in
  passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
  
  kept_clauses := (size_of_passive passive) + (size_of_active active);
  match passive_is_empty passive with
  | true -> (* ParamodulationFailure *)
      given_clause_fullred dbd env goals theorems passive active        
  | false ->
      let (sign, current), passive = select env (fst goals) passive active in
      let time1 = Unix.gettimeofday () in
      let res = forward_simplify env (sign, current) ~passive active in
      let time2 = Unix.gettimeofday () in
      forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
      match res with
      | None ->
          given_clause_fullred dbd env goals theorems passive active
      | Some (sign, current) ->
          if (sign = Negative) && (is_identity env current) then (
            debug_print
              (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                       (string_of_equality ~env current)));
            let _, proof, _, _, _ = current in 
            ParamodulationSuccess (Some proof, env)
          ) else (
            debug_print
              (lazy "\n================================================");
            debug_print (lazy (Printf.sprintf "selected: %s %s"
                                 (string_of_sign sign)
                                 (string_of_equality ~env current)));

            let t1 = Unix.gettimeofday () in
            let new' = infer env sign current active in
            let t2 = Unix.gettimeofday () in
            infer_time := !infer_time +. (t2 -. t1);

            let active =
              if is_identity env current then active
              else
                let al, tbl = active in
                match sign with
                | Negative -> (sign, current)::al, tbl
                | Positive ->
                    al @ [(sign, current)], Indexing.index tbl current
            in
            let rec simplify new' active passive =
              let t1 = Unix.gettimeofday () in
              let new' = forward_simplify_new env new' ~passive active in
              let t2 = Unix.gettimeofday () in
              forward_simpl_new_time :=
                !forward_simpl_new_time +. (t2 -. t1);
              let t1 = Unix.gettimeofday () in
              let active, passive, newa, retained =
                backward_simplify env new' ~passive active in
              let t2 = Unix.gettimeofday () in
              backward_simpl_time := !backward_simpl_time +. (t2 -. t1);
              match newa, retained with
              | None, None -> active, passive, new'
              | Some (n, p), None
              | None, Some (n, p) ->
                  let nn, np = new' in
                  simplify (nn @ n, np @ p) active passive
              | Some (n, p), Some (rn, rp) ->
                  let nn, np = new' in
                  simplify (nn @ n @ rn, np @ p @ rp) active passive
            in
            let active, passive, new' = simplify new' active passive in

            let k = size_of_passive passive in
            if k < (kept - 1) then
              processed_clauses := !processed_clauses + (kept - 1 - k);
            
            let _ =
              debug_print
                (lazy
                   (Printf.sprintf "active:\n%s\n"
                      (String.concat "\n"
                         ((List.map
                             (fun (s, e) -> (string_of_sign s) ^ " " ^
                                (string_of_equality ~env e))
                             (fst active))))))
            in
            let _ =
              match new' with
              | neg, pos ->
                  debug_print
                    (lazy
                       (Printf.sprintf "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)))))
            in
            match contains_empty env new' with
            | false, _ -> 
                let passive = add_to_passive passive new' in
                given_clause_fullred dbd env goals theorems passive active
            | true, goal ->
                let proof =
                  match goal with
                  | Some goal -> let _, proof, _, _, _ = goal in Some proof
                  | None -> None
                in
                ParamodulationSuccess (proof, env)
          )
;;



let main dbd full 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 _, metasenv, meta_proof, _ = proof in
  let _, context, goal = CicUtil.lookup_meta goal' metasenv in
  let eq_indexes, equalities, maxm = find_equalities context proof 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
  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
    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 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, []
    else
      let refl_equal =
        let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
        UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
      in
      let t = CicUtil.term_of_uri refl_equal in
      let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
      [(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
         (Printf.sprintf
            "Theorems:\n-------------------------------------\n%s\n"
            (String.concat "\n"
               (List.map
                  (fun (t, ty, _) ->
                     Printf.sprintf
                       "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty))
                  (fst theorems)))))
  in
  try
    let goal = Inference.BasicProof new_meta_goal, [], goal in
    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
          )
      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
    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 =
        let goals = make_goals goal in
        (if !use_fullred then given_clause_fullred else given_clause)
          dbd env goals theorems passive active
      in
      let finish = Unix.gettimeofday () in
      let _ =
        match res with
        | ParamodulationFailure ->
            Printf.printf "NO proof found! :-(\n\n"
        | 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
               apply  the "apply" tactic to proof and status 
            *)
            let names = names_of_context context in
            print_endline (PP.pp proof names);
            let newmetasenv =
              List.fold_left
                (fun m (_, _, _, menv, _) -> m @ menv) metasenv equalities
            in
            let _ =
              try
                let ty, ug =
                  CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
                in
                print_endline (string_of_float (finish -. start));
                Printf.printf
                  "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n\n"
                  (CicPp.pp type_of_goal names) (CicPp.pp ty names)
                  (string_of_bool
                     (fst (CicReduction.are_convertible
                             context type_of_goal ty ug)));
              with e ->
                Printf.printf "\nEXCEPTION!!! %s\n" (Printexc.to_string e);
                Printf.printf "MAXMETA USED: %d\n" !maxmeta;
                print_endline (string_of_float (finish -. start));
            in
            ()
              
        | ParamodulationSuccess (None, env) ->
            Printf.printf "Success, but no proof?!?\n\n"
      in
      Printf.printf ("infer_time: %.9f\nforward_simpl_time: %.9f\n" ^^
                       "forward_simpl_new_time: %.9f\n" ^^
                       "backward_simpl_time: %.9f\n")
        !infer_time !forward_simpl_time !forward_simpl_new_time
        !backward_simpl_time;
      Printf.printf "passive_maintainance_time: %.9f\n"
        !passive_maintainance_time;
      Printf.printf "    successful unification/matching time: %.9f\n"
        !Indexing.match_unif_time_ok;
      Printf.printf "    failed unification/matching time: %.9f\n"
        !Indexing.match_unif_time_no;
      Printf.printf "    indexing retrieval time: %.9f\n"
        !Indexing.indexing_retrieval_time;
      Printf.printf "    demodulate_term.build_newtarget_time: %.9f\n"
        !Indexing.build_newtarget_time;
      Printf.printf "derived %d clauses, kept %d clauses.\n"
        !derived_clauses !kept_clauses;
  with exc ->
    print_endline ("EXCEPTION: " ^ (Printexc.to_string exc));
    raise exc
;;


let default_depth = !maxdepth
and default_width = !maxwidth;;

let reset_refs () =
  maxmeta := 0;
  symbols_counter := 0;
  weight_age_counter := !weight_age_ratio;
  processed_clauses := 0;
  start_time := 0.;
  elapsed_time := 0.;
  maximal_retained_equality := None;
  infer_time := 0.;
  forward_simpl_time := 0.;
  forward_simpl_new_time := 0.;
  backward_simpl_time := 0.;
  passive_maintainance_time := 0.;
  derived_clauses := 0;
  kept_clauses := 0;
;;

let saturate
    dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status = 
  let module C = Cic in
  reset_refs ();
  Indexing.init_index ();
  maxdepth := depth;
  maxwidth := width;
  let proof, goal = status in
  let goal' = goal 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 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
      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
          )
      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
    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 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, []
      else
        let refl_equal =
          let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
          UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
        in
        let t = CicUtil.term_of_uri refl_equal in
        let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
        [(t, ty, [])], []
    in
    let t2 = Unix.gettimeofday () in
    let _ =
      debug_print
        (lazy
           (Printf.sprintf
              "Theorems:\n-------------------------------------\n%s\n"
              (String.concat "\n"
                 (List.map
                    (fun (t, ty, _) ->
                       Printf.sprintf
                         "Term: %s, type: %s"
                         (CicPp.ppterm t) (CicPp.ppterm ty))
                    (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 [] equalities in
    let start = Unix.gettimeofday () in
    let res =
      let goals = make_goals goal in
      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, env) ->
      debug_print (lazy "OK, found a proof!");
      let proof = Inference.build_proof_term proof in
      let names = names_of_context context in
      let newmetasenv =
        let i1 =
          match new_meta_goal with
          | C.Meta (i, _) -> i | _ -> assert false
        in
        List.filter (fun (i, _, _) -> i <> i1 && i <> goal') metasenv
      in
      let newstatus =
        try
          let ty, ug =
            CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
          in
          debug_print (lazy (CicPp.pp proof [](* names *)));
          debug_print
            (lazy
               (Printf.sprintf
                  "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n"
                  (CicPp.pp type_of_goal names) (CicPp.pp ty names)
                  (string_of_bool
                     (fst (CicReduction.are_convertible
                             context type_of_goal ty ug)))));
          let equality_for_replace i t1 =
            match t1 with
            | C.Meta (n, _) -> n = i
            | _ -> false
          in
          let real_proof =
            ProofEngineReduction.replace
              ~equality:equality_for_replace
              ~what:[goal'] ~with_what:[proof]
              ~where:meta_proof
          in
          debug_print
            (lazy
               (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n"
                  (match uri with Some uri -> UriManager.string_of_uri uri
                   | None -> "")
                  (print_metasenv newmetasenv)
                  (CicPp.pp real_proof [](* names *))
                  (CicPp.pp term_to_prove names)));
          ((uri, newmetasenv, real_proof, term_to_prove), [])
        with CicTypeChecker.TypeCheckerFailure _ ->
          debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
          debug_print (lazy (CicPp.pp proof names));
          raise (ProofEngineTypes.Fail
                  (lazy "Found a proof, but it doesn't typecheck"))
      in
      debug_print (lazy (Printf.sprintf "\nTIME NEEDED: %.9f" time));
      newstatus          
  | _ ->
      raise (ProofEngineTypes.Fail (lazy "NO proof found"))
;;

(* dummy function called within matita to trigger linkage *)
let init () = ();;


(* UGLY SIDE EFFECT... *)
if connect_to_auto then ( 
  AutoTactic.paramodulation_tactic := saturate;
  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)))
;;