TSTP Solution File: SET972+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET972+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n015.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 Aug 31 18:22:54 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  186 (  17 unt;   0 def)
%            Number of atoms       :  548 (  47 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  629 ( 267   ~; 281   |;  46   &)
%                                         (  28 <=>;   5  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   24 (  22 usr;  20 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  263 ( 240   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f394,plain,
    $false,
    inference(avatar_sat_refutation,[],[f100,f196,f197,f226,f228,f247,f249,f250,f267,f271,f281,f283,f285,f294,f296,f312,f323,f334,f336,f350,f355,f359,f364,f368,f378,f382,f392,f393]) ).

fof(f393,plain,
    ( spl9_23
    | ~ spl9_22 ),
    inference(avatar_split_clause,[],[f365,f304,f343]) ).

fof(f343,plain,
    ( spl9_23
  <=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).

fof(f304,plain,
    ( spl9_22
  <=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).

fof(f365,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
    | ~ spl9_22 ),
    inference(resolution,[],[f305,f80]) ).

fof(f80,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ( ( ~ in(sK0(X0,X1,X2),X2)
            | in(sK0(X0,X1,X2),X1)
            | ~ in(sK0(X0,X1,X2),X0) )
          & ( in(sK0(X0,X1,X2),X2)
            | ( ~ in(sK0(X0,X1,X2),X1)
              & in(sK0(X0,X1,X2),X0) ) ) ) )
      & ( ! [X4] :
            ( ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) )
            & ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X2)
            | in(X3,X1)
            | ~ in(X3,X0) )
          & ( in(X3,X2)
            | ( ~ in(X3,X1)
              & in(X3,X0) ) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X2)
          | in(sK0(X0,X1,X2),X1)
          | ~ in(sK0(X0,X1,X2),X0) )
        & ( in(sK0(X0,X1,X2),X2)
          | ( ~ in(sK0(X0,X1,X2),X1)
            & in(sK0(X0,X1,X2),X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) ) ) )
      & ( ! [X4] :
            ( ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) )
            & ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X0,X2,X1] :
      ( ( set_difference(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X1)
              | ( ~ in(X3,X2)
                & in(X3,X0) ) ) ) )
      & ( ! [X3] :
            ( ( ( ~ in(X3,X2)
                & in(X3,X0) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) ) )
        | set_difference(X0,X2) != X1 ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X2,X1] :
      ( ( set_difference(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X1)
              | ( ~ in(X3,X2)
                & in(X3,X0) ) ) ) )
      & ( ! [X3] :
            ( ( ( ~ in(X3,X2)
                & in(X3,X0) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) ) )
        | set_difference(X0,X2) != X1 ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X2,X1] :
      ( set_difference(X0,X2) = X1
    <=> ! [X3] :
          ( ( ~ in(X3,X2)
            & in(X3,X0) )
        <=> in(X3,X1) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X2,X1] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( ( in(X3,X0)
            & ~ in(X3,X1) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f305,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
    | ~ spl9_22 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f392,plain,
    ( spl9_24
    | ~ spl9_26 ),
    inference(avatar_contradiction_clause,[],[f391]) ).

fof(f391,plain,
    ( $false
    | spl9_24
    | ~ spl9_26 ),
    inference(subsumption_resolution,[],[f389,f348]) ).

fof(f348,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | spl9_24 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f347,plain,
    ( spl9_24
  <=> in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).

fof(f389,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | ~ spl9_26 ),
    inference(resolution,[],[f377,f73]) ).

fof(f73,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
      | in(X1,X2) ),
    inference(definition_unfolding,[],[f59,f66]) ).

fof(f66,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f59,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X2)
      | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
        | ~ in(X1,X2)
        | ~ in(X3,X0) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,plain,
    ! [X1,X2,X0,X3] :
      ( ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
        | ~ in(X2,X0)
        | ~ in(X3,X1) )
      & ( ( in(X2,X0)
          & in(X3,X1) )
        | ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X1,X2,X0,X3] :
      ( ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
        | ~ in(X2,X0)
        | ~ in(X3,X1) )
      & ( ( in(X2,X0)
          & in(X3,X1) )
        | ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X2,X0,X3] :
      ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
    <=> ( in(X2,X0)
        & in(X3,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1] :
      ( ( in(X1,X3)
        & in(X0,X2) )
    <=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f377,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
    | ~ spl9_26 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f375,plain,
    ( spl9_26
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).

fof(f382,plain,
    ( ~ spl9_21
    | ~ spl9_23
    | spl9_25 ),
    inference(avatar_contradiction_clause,[],[f381]) ).

fof(f381,plain,
    ( $false
    | ~ spl9_21
    | ~ spl9_23
    | spl9_25 ),
    inference(subsumption_resolution,[],[f380,f301]) ).

fof(f301,plain,
    ( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ spl9_21 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f300,plain,
    ( spl9_21
  <=> in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).

fof(f380,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ spl9_23
    | spl9_25 ),
    inference(subsumption_resolution,[],[f379,f344]) ).

fof(f344,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
    | ~ spl9_23 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f379,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
    | ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | spl9_25 ),
    inference(resolution,[],[f373,f72]) ).

fof(f72,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
      | ~ in(X3,X0)
      | ~ in(X1,X2) ),
    inference(definition_unfolding,[],[f60,f66]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X1,X3),cartesian_product2(X2,X0))
      | ~ in(X1,X2)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f373,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
    | spl9_25 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f371,plain,
    ( spl9_25
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).

fof(f378,plain,
    ( ~ spl9_25
    | spl9_26
    | spl9_13 ),
    inference(avatar_split_clause,[],[f369,f171,f375,f371]) ).

fof(f171,plain,
    ( spl9_13
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).

fof(f369,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
    | ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
    | spl9_13 ),
    inference(resolution,[],[f173,f81]) ).

fof(f81,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_difference(X0,X1))
      | in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | in(X4,X1)
      | ~ in(X4,X0)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f173,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
    | spl9_13 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f368,plain,
    ( ~ spl9_24
    | ~ spl9_22 ),
    inference(avatar_split_clause,[],[f366,f304,f347]) ).

fof(f366,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | ~ spl9_22 ),
    inference(resolution,[],[f305,f79]) ).

fof(f79,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f364,plain,
    ( spl9_22
    | ~ spl9_12 ),
    inference(avatar_split_clause,[],[f362,f167,f304]) ).

fof(f167,plain,
    ( spl9_12
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).

fof(f362,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
    | ~ spl9_12 ),
    inference(resolution,[],[f168,f73]) ).

fof(f168,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
    | ~ spl9_12 ),
    inference(avatar_component_clause,[],[f167]) ).

fof(f359,plain,
    ( ~ spl9_24
    | ~ spl9_13
    | ~ spl9_21 ),
    inference(avatar_split_clause,[],[f358,f300,f171,f347]) ).

fof(f358,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | ~ spl9_13
    | ~ spl9_21 ),
    inference(subsumption_resolution,[],[f357,f301]) ).

fof(f357,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | ~ spl9_13 ),
    inference(resolution,[],[f338,f72]) ).

fof(f338,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK5,sK4))
    | ~ spl9_13 ),
    inference(resolution,[],[f172,f79]) ).

fof(f172,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
    | ~ spl9_13 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f355,plain,
    ( spl9_23
    | ~ spl9_13 ),
    inference(avatar_split_clause,[],[f353,f171,f343]) ).

fof(f353,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
    | ~ spl9_13 ),
    inference(resolution,[],[f337,f73]) ).

fof(f337,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
    | ~ spl9_13 ),
    inference(resolution,[],[f172,f80]) ).

fof(f350,plain,
    ( ~ spl9_23
    | spl9_24
    | spl9_22 ),
    inference(avatar_split_clause,[],[f341,f304,f347,f343]) ).

fof(f341,plain,
    ( in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK5)
    | ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK3)
    | spl9_22 ),
    inference(resolution,[],[f306,f81]) ).

fof(f306,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
    | spl9_22 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f336,plain,
    ( ~ spl9_22
    | ~ spl9_21
    | spl9_12 ),
    inference(avatar_split_clause,[],[f335,f167,f300,f304]) ).

fof(f335,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ in(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),set_difference(sK3,sK5))
    | spl9_12 ),
    inference(resolution,[],[f169,f72]) ).

fof(f169,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
    | spl9_12 ),
    inference(avatar_component_clause,[],[f167]) ).

fof(f334,plain,
    ( ~ spl9_12
    | spl9_21 ),
    inference(avatar_contradiction_clause,[],[f333]) ).

fof(f333,plain,
    ( $false
    | ~ spl9_12
    | spl9_21 ),
    inference(subsumption_resolution,[],[f329,f302]) ).

fof(f302,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | spl9_21 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f329,plain,
    ( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ spl9_12 ),
    inference(resolution,[],[f168,f74]) ).

fof(f74,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X0))
      | in(X3,X0) ),
    inference(definition_unfolding,[],[f58,f66]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X0)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f323,plain,
    ( ~ spl9_13
    | spl9_21 ),
    inference(avatar_contradiction_clause,[],[f322]) ).

fof(f322,plain,
    ( $false
    | ~ spl9_13
    | spl9_21 ),
    inference(subsumption_resolution,[],[f319,f302]) ).

fof(f319,plain,
    ( in(sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK4)
    | ~ spl9_13 ),
    inference(resolution,[],[f313,f74]) ).

fof(f313,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(sK3,sK4))
    | ~ spl9_13 ),
    inference(resolution,[],[f172,f80]) ).

fof(f312,plain,
    ( ~ spl9_18
    | ~ spl9_9 ),
    inference(avatar_split_clause,[],[f310,f146,f210]) ).

fof(f210,plain,
    ( spl9_18
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).

fof(f146,plain,
    ( spl9_9
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).

fof(f310,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
    | ~ spl9_9 ),
    inference(resolution,[],[f147,f79]) ).

fof(f147,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
    | ~ spl9_9 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f296,plain,
    ( spl9_11
    | spl9_10
    | ~ spl9_12
    | ~ spl9_13
    | spl9_2 ),
    inference(avatar_split_clause,[],[f291,f97,f171,f167,f161,f164]) ).

fof(f164,plain,
    ( spl9_11
  <=> ! [X4,X5] : ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).

fof(f161,plain,
    ( spl9_10
  <=> ! [X6,X7] : ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).

fof(f97,plain,
    ( spl9_2
  <=> sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f291,plain,
    ( ! [X6,X7,X4,X5] :
        ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)))
        | ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
        | ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7))
        | ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5)) )
    | spl9_2 ),
    inference(resolution,[],[f99,f88]) ).

fof(f88,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sQ8_eqProxy(X0,X3)
      | ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
      | ~ subset(X3,cartesian_product2(X5,X2))
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3) ),
    inference(equality_proxy_replacement,[],[f76,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( sQ8_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ8_eqProxy])]) ).

fof(f76,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
      | ~ in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(definition_unfolding,[],[f69,f66,f66]) ).

fof(f69,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
      | ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3)
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( ( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
          | ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) )
        & ( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
          | in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) ) )
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f47,f48]) ).

fof(f48,plain,
    ! [X0,X3] :
      ( ? [X6,X7] :
          ( ( ~ in(ordered_pair(X6,X7),X0)
            | ~ in(ordered_pair(X6,X7),X3) )
          & ( in(ordered_pair(X6,X7),X0)
            | in(ordered_pair(X6,X7),X3) ) )
     => ( ( ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
          | ~ in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) )
        & ( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
          | in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ? [X6,X7] :
          ( ( ~ in(ordered_pair(X6,X7),X0)
            | ~ in(ordered_pair(X6,X7),X3) )
          & ( in(ordered_pair(X6,X7),X0)
            | in(ordered_pair(X6,X7),X3) ) )
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ! [X4,X3,X0,X1,X5,X2] :
      ( ? [X7,X6] :
          ( ( ~ in(ordered_pair(X7,X6),X4)
            | ~ in(ordered_pair(X7,X6),X1) )
          & ( in(ordered_pair(X7,X6),X4)
            | in(ordered_pair(X7,X6),X1) ) )
      | X1 = X4
      | ~ subset(X4,cartesian_product2(X3,X5))
      | ~ subset(X1,cartesian_product2(X2,X0)) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X4,X3,X0,X1,X5,X2] :
      ( ? [X7,X6] :
          ( in(ordered_pair(X7,X6),X1)
        <~> in(ordered_pair(X7,X6),X4) )
      | X1 = X4
      | ~ subset(X4,cartesian_product2(X3,X5))
      | ~ subset(X1,cartesian_product2(X2,X0)) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X2,X5,X1,X3,X0,X4] :
      ( X1 = X4
      | ~ subset(X1,cartesian_product2(X2,X0))
      | ? [X7,X6] :
          ( in(ordered_pair(X7,X6),X1)
        <~> in(ordered_pair(X7,X6),X4) )
      | ~ subset(X4,cartesian_product2(X3,X5)) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X2,X5,X1,X3,X0,X4] :
      ( ( subset(X1,cartesian_product2(X2,X0))
        & ! [X6,X7] :
            ( in(ordered_pair(X7,X6),X4)
          <=> in(ordered_pair(X7,X6),X1) )
        & subset(X4,cartesian_product2(X3,X5)) )
     => X1 = X4 ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X2,X0,X1,X4,X3,X5] :
      ( ( subset(X3,cartesian_product2(X4,X5))
        & subset(X0,cartesian_product2(X1,X2))
        & ! [X7,X6] :
            ( in(ordered_pair(X6,X7),X0)
          <=> in(ordered_pair(X6,X7),X3) ) )
     => X0 = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).

fof(f99,plain,
    ( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))
    | spl9_2 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f294,plain,
    ( spl9_13
    | spl9_11
    | spl9_12
    | spl9_10
    | spl9_2 ),
    inference(avatar_split_clause,[],[f290,f97,f161,f167,f164,f171]) ).

fof(f290,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X2,X3))
        | in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),cartesian_product2(set_difference(sK3,sK5),sK4))
        | ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X0,X1))
        | in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)),sK7(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))),singleton(sK6(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4)))),set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4))) )
    | spl9_2 ),
    inference(resolution,[],[f99,f89]) ).

fof(f89,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sQ8_eqProxy(X0,X3)
      | in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
      | in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
      | ~ subset(X3,cartesian_product2(X5,X2))
      | ~ subset(X0,cartesian_product2(X1,X4)) ),
    inference(equality_proxy_replacement,[],[f77,f82]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X0)
      | in(unordered_pair(unordered_pair(sK6(X0,X3),sK7(X0,X3)),singleton(sK6(X0,X3))),X3)
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(definition_unfolding,[],[f68,f66,f66]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X0)
      | in(ordered_pair(sK6(X0,X3),sK7(X0,X3)),X3)
      | X0 = X3
      | ~ subset(X0,cartesian_product2(X1,X4))
      | ~ subset(X3,cartesian_product2(X5,X2)) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f285,plain,
    ~ spl9_10,
    inference(avatar_contradiction_clause,[],[f284]) ).

fof(f284,plain,
    ( $false
    | ~ spl9_10 ),
    inference(resolution,[],[f162,f64]) ).

fof(f64,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0] : subset(set_difference(X1,X0),X1),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X1,X0] : subset(set_difference(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).

fof(f162,plain,
    ( ! [X6,X7] : ~ subset(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(X6,X7))
    | ~ spl9_10 ),
    inference(avatar_component_clause,[],[f161]) ).

fof(f283,plain,
    ~ spl9_11,
    inference(avatar_contradiction_clause,[],[f282]) ).

fof(f282,plain,
    ( $false
    | ~ spl9_11 ),
    inference(resolution,[],[f165,f71]) ).

fof(f71,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1] : subset(X1,X1),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f165,plain,
    ( ! [X4,X5] : ~ subset(cartesian_product2(set_difference(sK3,sK5),sK4),cartesian_product2(X4,X5))
    | ~ spl9_11 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f281,plain,
    ( ~ spl9_18
    | spl9_19 ),
    inference(avatar_contradiction_clause,[],[f280]) ).

fof(f280,plain,
    ( $false
    | ~ spl9_18
    | spl9_19 ),
    inference(subsumption_resolution,[],[f277,f254]) ).

fof(f254,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | spl9_19 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f252,plain,
    ( spl9_19
  <=> in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).

fof(f277,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | ~ spl9_18 ),
    inference(resolution,[],[f212,f74]) ).

fof(f212,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
    | ~ spl9_18 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f271,plain,
    ( ~ spl9_19
    | ~ spl9_6 ),
    inference(avatar_split_clause,[],[f269,f136,f252]) ).

fof(f136,plain,
    ( spl9_6
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

fof(f269,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | ~ spl9_6 ),
    inference(resolution,[],[f261,f79]) ).

fof(f261,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
    | ~ spl9_6 ),
    inference(resolution,[],[f137,f74]) ).

fof(f137,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
    | ~ spl9_6 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f267,plain,
    ( spl9_18
    | ~ spl9_17
    | spl9_9 ),
    inference(avatar_split_clause,[],[f266,f146,f206,f210]) ).

fof(f206,plain,
    ( spl9_17
  <=> in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).

fof(f266,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
    | in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
    | spl9_9 ),
    inference(resolution,[],[f148,f81]) ).

fof(f148,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
    | spl9_9 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f250,plain,
    ( spl9_17
    | ~ spl9_9 ),
    inference(avatar_split_clause,[],[f237,f146,f206]) ).

fof(f237,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
    | ~ spl9_9 ),
    inference(resolution,[],[f147,f80]) ).

fof(f249,plain,
    ~ spl9_7,
    inference(avatar_contradiction_clause,[],[f248]) ).

fof(f248,plain,
    ( $false
    | ~ spl9_7 ),
    inference(resolution,[],[f141,f64]) ).

fof(f141,plain,
    ( ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3))
    | ~ spl9_7 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f140,plain,
    ( spl9_7
  <=> ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

fof(f247,plain,
    ( spl9_6
    | ~ spl9_17
    | spl9_18 ),
    inference(avatar_contradiction_clause,[],[f246]) ).

fof(f246,plain,
    ( $false
    | spl9_6
    | ~ spl9_17
    | spl9_18 ),
    inference(subsumption_resolution,[],[f245,f242]) ).

fof(f242,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | spl9_6
    | ~ spl9_17 ),
    inference(subsumption_resolution,[],[f241,f230]) ).

fof(f230,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
    | ~ spl9_17 ),
    inference(resolution,[],[f207,f74]) ).

fof(f207,plain,
    ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
    | ~ spl9_17 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f241,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
    | in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | spl9_6
    | ~ spl9_17 ),
    inference(resolution,[],[f236,f81]) ).

fof(f236,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
    | spl9_6
    | ~ spl9_17 ),
    inference(subsumption_resolution,[],[f235,f231]) ).

fof(f231,plain,
    ( in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
    | ~ spl9_17 ),
    inference(resolution,[],[f207,f73]) ).

fof(f235,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
    | ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
    | spl9_6 ),
    inference(resolution,[],[f138,f72]) ).

fof(f138,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
    | spl9_6 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f245,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | ~ spl9_17
    | spl9_18 ),
    inference(subsumption_resolution,[],[f244,f231]) ).

fof(f244,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
    | ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK5)
    | spl9_18 ),
    inference(resolution,[],[f211,f72]) ).

fof(f211,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK5))
    | spl9_18 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f228,plain,
    ~ spl9_8,
    inference(avatar_contradiction_clause,[],[f227]) ).

fof(f227,plain,
    ( $false
    | ~ spl9_8 ),
    inference(resolution,[],[f144,f71]) ).

fof(f144,plain,
    ( ! [X0,X1] : ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1))
    | ~ spl9_8 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl9_8
  <=> ! [X0,X1] : ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).

fof(f226,plain,
    ( ~ spl9_6
    | spl9_17 ),
    inference(avatar_contradiction_clause,[],[f225]) ).

fof(f225,plain,
    ( $false
    | ~ spl9_6
    | spl9_17 ),
    inference(subsumption_resolution,[],[f219,f215]) ).

fof(f215,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
    | ~ spl9_6 ),
    inference(resolution,[],[f200,f80]) ).

fof(f200,plain,
    ( in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),set_difference(sK3,sK5))
    | ~ spl9_6 ),
    inference(resolution,[],[f137,f74]) ).

fof(f219,plain,
    ( ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
    | ~ spl9_6
    | spl9_17 ),
    inference(subsumption_resolution,[],[f218,f201]) ).

fof(f201,plain,
    ( in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
    | ~ spl9_6 ),
    inference(resolution,[],[f137,f73]) ).

fof(f218,plain,
    ( ~ in(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK4)
    | ~ in(sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK3)
    | spl9_17 ),
    inference(resolution,[],[f208,f72]) ).

fof(f208,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,sK3))
    | spl9_17 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f197,plain,
    ( ~ spl9_9
    | ~ spl9_6
    | spl9_8
    | spl9_7
    | spl9_1 ),
    inference(avatar_split_clause,[],[f195,f93,f140,f143,f136,f146]) ).

fof(f93,plain,
    ( spl9_1
  <=> sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f195,plain,
    ( ! [X6,X7,X4,X5] :
        ( ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X6,X7))
        | ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X4,X5))
        | ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
        | ~ in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5))) )
    | spl9_1 ),
    inference(resolution,[],[f95,f88]) ).

fof(f95,plain,
    ( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))
    | spl9_1 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f196,plain,
    ( spl9_8
    | spl9_7
    | spl9_6
    | spl9_9
    | spl9_1 ),
    inference(avatar_split_clause,[],[f194,f93,f146,f136,f140,f143]) ).

fof(f194,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)))
        | in(unordered_pair(unordered_pair(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))),sK7(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5)))),singleton(sK6(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))))),cartesian_product2(sK4,set_difference(sK3,sK5)))
        | ~ subset(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(X2,X3))
        | ~ subset(cartesian_product2(sK4,set_difference(sK3,sK5)),cartesian_product2(X0,X1)) )
    | spl9_1 ),
    inference(resolution,[],[f95,f89]) ).

fof(f100,plain,
    ( ~ spl9_1
    | ~ spl9_2 ),
    inference(avatar_split_clause,[],[f87,f97,f93]) ).

fof(f87,plain,
    ( ~ sQ8_eqProxy(set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)),cartesian_product2(set_difference(sK3,sK5),sK4))
    | ~ sQ8_eqProxy(set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,set_difference(sK3,sK5))) ),
    inference(equality_proxy_replacement,[],[f63,f82,f82]) ).

fof(f63,plain,
    ( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
    | set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
    | set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f40,f41]) ).

fof(f41,plain,
    ( ? [X0,X1,X2] :
        ( set_difference(cartesian_product2(X1,X0),cartesian_product2(X1,X2)) != cartesian_product2(X1,set_difference(X0,X2))
        | cartesian_product2(set_difference(X0,X2),X1) != set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) )
   => ( set_difference(cartesian_product2(sK4,sK3),cartesian_product2(sK4,sK5)) != cartesian_product2(sK4,set_difference(sK3,sK5))
      | set_difference(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK4)) != cartesian_product2(set_difference(sK3,sK5),sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ? [X0,X1,X2] :
      ( set_difference(cartesian_product2(X1,X0),cartesian_product2(X1,X2)) != cartesian_product2(X1,set_difference(X0,X2))
      | cartesian_product2(set_difference(X0,X2),X1) != set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ? [X2,X1,X0] :
      ( cartesian_product2(X1,set_difference(X2,X0)) != set_difference(cartesian_product2(X1,X2),cartesian_product2(X1,X0))
      | cartesian_product2(set_difference(X2,X0),X1) != set_difference(cartesian_product2(X2,X1),cartesian_product2(X0,X1)) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X2,X1] :
        ( cartesian_product2(set_difference(X2,X0),X1) = set_difference(cartesian_product2(X2,X1),cartesian_product2(X0,X1))
        & cartesian_product2(X1,set_difference(X2,X0)) = set_difference(cartesian_product2(X1,X2),cartesian_product2(X1,X0)) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
        & cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X2,X0] :
      ( cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
      & cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET972+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:44:21 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.46  % (31715)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.47  % (31725)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.48  % (31712)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.48  % (31712)Refutation not found, incomplete strategy% (31712)------------------------------
% 0.21/0.48  % (31712)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.48  % (31712)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.48  % (31712)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48  
% 0.21/0.48  % (31712)Memory used [KB]: 1407
% 0.21/0.48  % (31712)Time elapsed: 0.091 s
% 0.21/0.48  % (31712)Instructions burned: 2 (million)
% 0.21/0.48  % (31712)------------------------------
% 0.21/0.48  % (31712)------------------------------
% 0.21/0.48  % (31715)Refutation not found, incomplete strategy% (31715)------------------------------
% 0.21/0.48  % (31715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.48  % (31715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.48  % (31715)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48  
% 0.21/0.48  % (31715)Memory used [KB]: 5884
% 0.21/0.48  % (31715)Time elapsed: 0.092 s
% 0.21/0.48  % (31715)Instructions burned: 3 (million)
% 0.21/0.48  % (31715)------------------------------
% 0.21/0.48  % (31715)------------------------------
% 0.21/0.49  % (31725)Instruction limit reached!
% 0.21/0.49  % (31725)------------------------------
% 0.21/0.49  % (31725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (31717)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.21/0.49  % (31725)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (31725)Termination reason: Unknown
% 0.21/0.49  % (31725)Termination phase: Saturation
% 0.21/0.49  
% 0.21/0.49  % (31725)Memory used [KB]: 1407
% 0.21/0.49  % (31725)Time elapsed: 0.006 s
% 0.21/0.49  % (31725)Instructions burned: 2 (million)
% 0.21/0.49  % (31725)------------------------------
% 0.21/0.49  % (31725)------------------------------
% 0.21/0.49  % (31723)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.49  % (31723)Refutation not found, incomplete strategy% (31723)------------------------------
% 0.21/0.49  % (31723)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (31723)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (31723)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49  
% 0.21/0.49  % (31723)Memory used [KB]: 6012
% 0.21/0.49  % (31723)Time elapsed: 0.099 s
% 0.21/0.49  % (31723)Instructions burned: 3 (million)
% 0.21/0.49  % (31723)------------------------------
% 0.21/0.49  % (31723)------------------------------
% 0.21/0.49  % (31731)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.50  % (31731)First to succeed.
% 0.21/0.51  % (31717)Instruction limit reached!
% 0.21/0.51  % (31717)------------------------------
% 0.21/0.51  % (31717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (31717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (31717)Termination reason: Unknown
% 0.21/0.51  % (31717)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (31717)Memory used [KB]: 6140
% 0.21/0.51  % (31717)Time elapsed: 0.082 s
% 0.21/0.51  % (31717)Instructions burned: 12 (million)
% 0.21/0.51  % (31717)------------------------------
% 0.21/0.51  % (31717)------------------------------
% 0.21/0.51  % (31711)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.51  % (31721)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.51  % (31710)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (31721)Instruction limit reached!
% 0.21/0.51  % (31721)------------------------------
% 0.21/0.51  % (31721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (31721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (31721)Termination reason: Unknown
% 0.21/0.51  % (31721)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (31721)Memory used [KB]: 5884
% 0.21/0.51  % (31721)Time elapsed: 0.002 s
% 0.21/0.51  % (31721)Instructions burned: 3 (million)
% 0.21/0.51  % (31721)------------------------------
% 0.21/0.51  % (31721)------------------------------
% 0.21/0.52  % (31713)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.53  % (31731)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (31731)------------------------------
% 0.21/0.53  % (31731)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (31731)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (31731)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (31731)Memory used [KB]: 6140
% 0.21/0.53  % (31731)Time elapsed: 0.108 s
% 0.21/0.53  % (31731)Instructions burned: 12 (million)
% 0.21/0.53  % (31731)------------------------------
% 0.21/0.53  % (31731)------------------------------
% 0.21/0.53  % (31706)Success in time 0.17 s
%------------------------------------------------------------------------------