TSTP Solution File: SCT105+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May  1 03:42:54 EDT 2024

% Result   : Theorem 0.60s 0.85s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   72 (   1 unt;   0 def)
%            Number of atoms       :  321 (  42 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  389 ( 140   ~; 148   |;  72   &)
%                                         (  16 <=>;  10  =>;   0  <=;   3 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   17 (  15 usr;  14 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-4 aty)
%            Number of variables   :   96 (  72   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f758,plain,
    $false,
    inference(avatar_sat_refutation,[],[f647,f652,f657,f661,f665,f666,f675,f680,f685,f686,f687,f688,f741,f743,f755,f757]) ).

fof(f757,plain,
    ( ~ spl13_8
    | ~ spl13_9 ),
    inference(avatar_contradiction_clause,[],[f756]) ).

fof(f756,plain,
    ( $false
    | ~ spl13_8
    | ~ spl13_9 ),
    inference(subsumption_resolution,[],[f670,f664]) ).

fof(f664,plain,
    ( ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
    | ~ spl13_8 ),
    inference(avatar_component_clause,[],[f663]) ).

fof(f663,plain,
    ( spl13_8
  <=> ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f670,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L)
    | ~ spl13_9 ),
    inference(avatar_component_clause,[],[f668]) ).

fof(f668,plain,
    ( spl13_9
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f755,plain,
    ( spl13_11
    | ~ spl13_7
    | spl13_10
    | spl13_12 ),
    inference(avatar_split_clause,[],[f749,f682,f672,f659,f677]) ).

fof(f677,plain,
    ( spl13_11
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK5),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).

fof(f659,plain,
    ( spl13_7
  <=> ! [X4,X3] :
        ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
        | X3 = X4
        | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f672,plain,
    ( spl13_10
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK4),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f682,plain,
    ( spl13_12
  <=> sK4 = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f749,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK5),v_L)
    | ~ spl13_7
    | spl13_10
    | spl13_12 ),
    inference(unit_resulting_resolution,[],[f684,f674,f660]) ).

fof(f660,plain,
    ( ! [X3,X4] :
        ( X3 = X4
        | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
        | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L) )
    | ~ spl13_7 ),
    inference(avatar_component_clause,[],[f659]) ).

fof(f674,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK4),v_L)
    | spl13_10 ),
    inference(avatar_component_clause,[],[f672]) ).

fof(f684,plain,
    ( sK4 != sK5
    | spl13_12 ),
    inference(avatar_component_clause,[],[f682]) ).

fof(f743,plain,
    ( ~ spl13_2
    | ~ spl13_8 ),
    inference(avatar_contradiction_clause,[],[f742]) ).

fof(f742,plain,
    ( $false
    | ~ spl13_2
    | ~ spl13_8 ),
    inference(subsumption_resolution,[],[f638,f664]) ).

fof(f638,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L)
    | ~ spl13_2 ),
    inference(avatar_component_clause,[],[f636]) ).

fof(f636,plain,
    ( spl13_2
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f741,plain,
    ( spl13_5
    | spl13_3
    | spl13_6
    | ~ spl13_7 ),
    inference(avatar_split_clause,[],[f719,f659,f654,f640,f649]) ).

fof(f649,plain,
    ( spl13_5
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK1),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f640,plain,
    ( spl13_3
  <=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK1,sK2),v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f654,plain,
    ( spl13_6
  <=> sK1 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f719,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK1),v_L)
    | spl13_3
    | spl13_6
    | ~ spl13_7 ),
    inference(unit_resulting_resolution,[],[f656,f642,f660]) ).

fof(f642,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK1,sK2),v_L)
    | spl13_3 ),
    inference(avatar_component_clause,[],[f640]) ).

fof(f656,plain,
    ( sK1 != sK2
    | spl13_6 ),
    inference(avatar_component_clause,[],[f654]) ).

fof(f688,plain,
    ( spl13_4
    | spl13_1 ),
    inference(avatar_split_clause,[],[f587,f632,f644]) ).

fof(f644,plain,
    ( spl13_4
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f632,plain,
    ( spl13_1
  <=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f587,plain,
    ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
    | sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f568,plain,
    ( ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK4),v_L)
        & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK5),v_L)
        & sK4 != sK5 )
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
      | ~ sP0 )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f565,f567,f566]) ).

fof(f566,plain,
    ( ? [X0,X1] :
        ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
        & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
        & X0 != X1 )
   => ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK4),v_L)
      & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK5),v_L)
      & sK4 != sK5 ) ),
    introduced(choice_axiom,[]) ).

fof(f567,plain,
    ( ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
   => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L) ),
    introduced(choice_axiom,[]) ).

fof(f565,plain,
    ( ( ? [X0,X1] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          & X0 != X1 )
      | ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
      | ~ sP0 )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | sP0 ) ),
    inference(rectify,[],[f564]) ).

fof(f564,plain,
    ( ( ? [X3,X4] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
          & X3 != X4 )
      | ? [X5] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
      | ~ sP0 )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | sP0 ) ),
    inference(flattening,[],[f563]) ).

fof(f563,plain,
    ( ( ? [X3,X4] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
          & X3 != X4 )
      | ? [X5] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
      | ~ sP0 )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | sP0 ) ),
    inference(nnf_transformation,[],[f556]) ).

fof(f556,plain,
    ( sP0
  <~> ( ! [X3,X4] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
          | X3 = X4 )
      & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    inference(definition_folding,[],[f541,f555]) ).

fof(f555,plain,
    ( sP0
  <=> ( ! [X0,X1] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          | X0 = X1 )
      & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f541,plain,
    ( ( ! [X0,X1] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          | X0 = X1 )
      & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
  <~> ( ! [X3,X4] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
          | X3 = X4 )
      & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    inference(flattening,[],[f540]) ).

fof(f540,plain,
    ( ( ! [X0,X1] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          | X0 = X1 )
      & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
  <~> ( ! [X3,X4] :
          ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
          | X3 = X4 )
      & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    inference(ennf_transformation,[],[f525]) ).

fof(f525,plain,
    ~ ( ( ! [X0,X1] :
            ( X0 != X1
           => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
              | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) ) )
        & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    <=> ( ! [X3,X4] :
            ( X3 != X4
           => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
              | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    inference(rectify,[],[f524]) ).

fof(f524,negated_conjecture,
    ~ ( ( ! [X2,X5] :
            ( X2 != X5
           => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
              | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L) ) )
        & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    <=> ( ! [X2,X5] :
            ( X2 != X5
           => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L)
              | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L) ) )
        & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    inference(negated_conjecture,[],[f523]) ).

fof(f523,conjecture,
    ( ( ! [X2,X5] :
          ( X2 != X5
         => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L) ) )
      & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
  <=> ( ! [X2,X5] :
          ( X2 != X5
         => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X2),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L) ) )
      & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ) ),
    file('/export/starexec/sandbox/tmp/tmp.OD7g3LOmEm/Vampire---4.8_3445',conj_0) ).

fof(f687,plain,
    ( spl13_4
    | spl13_8 ),
    inference(avatar_split_clause,[],[f588,f663,f644]) ).

fof(f588,plain,
    ! [X5] :
      ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      | sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f686,plain,
    ( spl13_4
    | spl13_7 ),
    inference(avatar_split_clause,[],[f589,f659,f644]) ).

fof(f589,plain,
    ! [X3,X4] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
      | X3 = X4
      | sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f685,plain,
    ( ~ spl13_4
    | ~ spl13_1
    | spl13_9
    | ~ spl13_12 ),
    inference(avatar_split_clause,[],[f590,f682,f668,f632,f644]) ).

fof(f590,plain,
    ( sK4 != sK5
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f680,plain,
    ( ~ spl13_4
    | ~ spl13_1
    | spl13_9
    | ~ spl13_11 ),
    inference(avatar_split_clause,[],[f591,f677,f668,f632,f644]) ).

fof(f591,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK4,sK5),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f675,plain,
    ( ~ spl13_4
    | ~ spl13_1
    | spl13_9
    | ~ spl13_10 ),
    inference(avatar_split_clause,[],[f592,f672,f668,f632,f644]) ).

fof(f592,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK5,sK4),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK6,sK6),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f568]) ).

fof(f666,plain,
    ( ~ spl13_4
    | spl13_1 ),
    inference(avatar_split_clause,[],[f581,f632,f644]) ).

fof(f581,plain,
    ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f562]) ).

fof(f562,plain,
    ( ( sP0
      | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK1,sK2),v_L)
        & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK1),v_L)
        & sK1 != sK2 )
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | ~ sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f559,f561,f560]) ).

fof(f560,plain,
    ( ? [X0,X1] :
        ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
        & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
        & X0 != X1 )
   => ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK1,sK2),v_L)
      & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK1),v_L)
      & sK1 != sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f561,plain,
    ( ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
   => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L) ),
    introduced(choice_axiom,[]) ).

fof(f559,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          & X0 != X1 )
      | ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    & ( ( ! [X3,X4] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
            | X3 = X4 )
        & ! [X5] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | ~ sP0 ) ),
    inference(rectify,[],[f558]) ).

fof(f558,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          & X0 != X1 )
      | ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    & ( ( ! [X0,X1] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
            | X0 = X1 )
        & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | ~ sP0 ) ),
    inference(flattening,[],[f557]) ).

fof(f557,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
          & ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          & X0 != X1 )
      | ? [X2] : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
      | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
    & ( ( ! [X0,X1] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
            | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
            | X0 = X1 )
        & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
        & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) )
      | ~ sP0 ) ),
    inference(nnf_transformation,[],[f555]) ).

fof(f665,plain,
    ( ~ spl13_4
    | spl13_8 ),
    inference(avatar_split_clause,[],[f582,f663,f644]) ).

fof(f582,plain,
    ! [X5] :
      ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X5),v_L)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f562]) ).

fof(f661,plain,
    ( ~ spl13_4
    | spl13_7 ),
    inference(avatar_split_clause,[],[f583,f659,f644]) ).

fof(f583,plain,
    ! [X3,X4] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X3),v_L)
      | X3 = X4
      | ~ sP0 ),
    inference(cnf_transformation,[],[f562]) ).

fof(f657,plain,
    ( ~ spl13_1
    | spl13_2
    | ~ spl13_6
    | spl13_4 ),
    inference(avatar_split_clause,[],[f584,f644,f654,f636,f632]) ).

fof(f584,plain,
    ( sP0
    | sK1 != sK2
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
    inference(cnf_transformation,[],[f562]) ).

fof(f652,plain,
    ( ~ spl13_1
    | spl13_2
    | ~ spl13_5
    | spl13_4 ),
    inference(avatar_split_clause,[],[f585,f644,f649,f636,f632]) ).

fof(f585,plain,
    ( sP0
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK2,sK1),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
    inference(cnf_transformation,[],[f562]) ).

fof(f647,plain,
    ( ~ spl13_1
    | spl13_2
    | ~ spl13_3
    | spl13_4 ),
    inference(avatar_split_clause,[],[f586,f644,f640,f636,f632]) ).

fof(f586,plain,
    ( sP0
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK1,sK2),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK3,sK3),v_L)
    | ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
    inference(cnf_transformation,[],[f562]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Apr 30 16:26:18 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.33  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.OD7g3LOmEm/Vampire---4.8_3445
% 0.60/0.84  % (3561)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2994ds/45Mi)
% 0.60/0.84  % (3559)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2994ds/33Mi)
% 0.60/0.84  % (3560)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2994ds/34Mi)
% 0.60/0.84  % (3558)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2994ds/78Mi)
% 0.60/0.84  % (3556)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2994ds/34Mi)
% 0.60/0.84  % (3562)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2994ds/83Mi)
% 0.60/0.84  % (3557)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2994ds/51Mi)
% 0.60/0.84  % (3563)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2994ds/56Mi)
% 0.60/0.85  % (3559)First to succeed.
% 0.60/0.85  % (3556)Also succeeded, but the first one will report.
% 0.60/0.85  % (3563)Also succeeded, but the first one will report.
% 0.60/0.85  % (3559)Refutation found. Thanks to Tanya!
% 0.60/0.85  % SZS status Theorem for Vampire---4
% 0.60/0.85  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.85  % (3559)------------------------------
% 0.60/0.85  % (3559)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.85  % (3559)Termination reason: Refutation
% 0.60/0.85  
% 0.60/0.85  % (3559)Memory used [KB]: 1541
% 0.60/0.85  % (3559)Time elapsed: 0.010 s
% 0.60/0.85  % (3559)Instructions burned: 15 (million)
% 0.60/0.85  % (3559)------------------------------
% 0.60/0.85  % (3559)------------------------------
% 0.60/0.85  % (3554)Success in time 0.515 s
% 0.60/0.85  % Vampire---4.8 exiting
%------------------------------------------------------------------------------