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
;;


(*
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 = 
    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
(*   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
;;


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
(*         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
            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
(*               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

module EqualitySet = Set.Make(OrderedEquality);;


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
(*             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)
      | _, _ -> 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
(*       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 *)
    )
  | _ ->
      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
(*           if !use_fullred then Indexing.remove_index passive_table current *)
(*           else passive_table *)
        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
;;


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
(*     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),
  table
;;


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


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 *)
  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
;;


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 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
      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_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  
;;


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
;;


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 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 =
      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 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 -> 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 *)
;;

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. };;


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 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 =
    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 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 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 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 *)
;;


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 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 ()),
    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
;;


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
      | 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
;;


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.)))
;;

  
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;
    newgoal
  in
  let goal =
    match passive_table with
    | None -> demodulate active_table goal
    | Some passive_table ->
        let goal = demodulate active_table goal in
        demodulate passive_table 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
  goal
;;


let simplify_goals env goals ?passive active =
  List.map
    (fun (d, gl) ->
       let gl = List.map (fun g -> simplify_goal env g ?passive active) gl in
       d, gl)
    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 demodulate table theorem =
    let newmeta, newthm =
      Indexing.demodulation_theorem !maxmeta env table theorem in
    maxmeta := newmeta;
    newthm
  in
  match passive_table with
  | None -> List.map (demodulate active_table) theorems
  | Some passive_table ->
      let theorems = List.map (demodulate active_table) theorems in
      List.map (demodulate passive_table) theorems
;;


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
  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 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 apply_to_goal env theorems 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, %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
        | ProofGoalBlock (_, p) -> get_meta p
        | _ ->
            let n = new_meta () in (* CicMkImplicit.new_meta metasenv [] in *)
            Cic.Meta (n, irl), n
      in
      get_meta proof
    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) *)
  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
(*             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
            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) ->
(*                            SubProof (p, i, sp) *)
                           ProofGoalBlock (sp1, gp sp2)
(*                            gp sp *)
                       | 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)
(*                        | _ -> assert false *)
                     in gp proof
                   in
                   debug_print
                     (lazy
                        (Printf.sprintf "new sub goal: %s, %s"
                           (string_of_proof p') (CicPp.ppterm ty)));
                   (p', menv, ty))
                newgoals
            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)
        with ProofEngineTypes.Fail msg ->
          aux tl
  in
  let r, s, l =
    if Inference.term_is_equality term then
      let rec appleq = 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 tl
        | _::tl -> appleq tl
      in
      let al, _ = active in
      appleq al
    else
      false, [], []
  in
  if r = true then `Ok (s, l) else aux theorems
;;


let apply_to_goal_conj env theorems 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 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
              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
  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)));
    `No (depth, goals)
  ) else
    aux goals
;;


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
(*       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 =
    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 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 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
  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
;;


let rec given_clause 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);
    
(*   let refl_equal = *)
(*     CicUtil.term_of_uri *)
(*       (UriManager.uri_of_string "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)") *)
(*   in *)
  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 = 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 is_passive_empty (* passive_is_empty passive *) with
      | true -> (* ParamodulationFailure *)
          given_clause env goals theorems passive active
      | false ->
          let (sign, current), passive = select env 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 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 (* current *), 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 (* goal *), 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
(*               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 =
                        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
(*                   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 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 (* goal *), env)
              )
  with SearchSpaceOver ->
    ParamodulationFailure
;;


let rec given_clause_fullred 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);

(*   let refl_equal = *)
(*     CicUtil.term_of_uri *)
(*       (UriManager.uri_of_string "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)") *)
(*   in *)
  let goals = simplify_goals env goals ~passive active in
  let theorems = simplify_theorems env theorems ~passive active in
  let is_passive_empty = passive_is_empty passive in
  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 is_passive_empty (* passive_is_empty passive *) with
      | true -> (* ParamodulationFailure *)
          given_clause_fullred env goals theorems passive active        
      | false ->
          let (sign, current), passive = select env 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 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 (* current *), 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
(*                 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 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 (* goal *), env)
              )
  with SearchSpaceOver ->
    ParamodulationFailure
;;


(* let given_clause_ref = ref given_clause;; *)

let main 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 _, 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
  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 ();
    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 theorems = find_library_theorems dbd env (proof, goal') lib_eq_uris in
  let context_hyp = find_context_hypotheses env eq_indexes in
  let theorems = context_hyp @ theorems 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))
                  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
            )
        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 [] (* [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)));
      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 finish = Unix.gettimeofday () in
      let _ =
        match res with
        | ParamodulationFailure ->
            Printf.printf "NO proof found! :-(\n\n"
        | ParamodulationSuccess (Some proof (* goal *), env) ->
(*             let proof = Inference.build_proof_term goal in          *)
            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 _ =
              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"
                  (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 saturate
    dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status = 
  let module C = Cic in
  maxmeta := 0;
  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 lib_eq_uris, library_equalities, maxm =
      find_library_equalities dbd context (proof, goal') (maxm+2)
    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
    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 _ =
      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))
                    theorems))))
    in
    let active = make_active () in
    let passive = make_passive [(* term_equality *)] equalities in
    let start = Unix.gettimeofday () in
    let res = given_clause_fullred env [0, [goal]] theorems passive active in
    let finish = Unix.gettimeofday () in
    (res, finish -. start)
  in
  match res with
  | ParamodulationSuccess (Some proof (* goal *), 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 =
        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
                   "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")
;;

(* 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;
);;