TSTP Solution File: SET156+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET156+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n021.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 03:45:27 EDT 2024

% Result   : Theorem 0.70s 0.91s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   92 (   2 unt;   0 def)
%            Number of atoms       :  258 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  266 ( 100   ~; 103   |;  39   &)
%                                         (  17 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   9 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  115 ( 103   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f140,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f79,f85,f90,f104,f114,f120,f124,f130,f139]) ).

fof(f139,plain,
    ( ~ spl4_6
    | ~ spl4_8 ),
    inference(avatar_contradiction_clause,[],[f138]) ).

fof(f138,plain,
    ( $false
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(subsumption_resolution,[],[f136,f127]) ).

fof(f127,plain,
    ( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK0)
    | ~ spl4_8 ),
    inference(resolution,[],[f113,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',difference) ).

fof(f113,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0))
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f111,plain,
    ( spl4_8
  <=> member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f136,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK0)
    | ~ spl4_6 ),
    inference(resolution,[],[f103,f42]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',intersection) ).

fof(f103,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1))
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f101,plain,
    ( spl4_6
  <=> member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f130,plain,
    ( spl4_5
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f126,f111,f97]) ).

fof(f97,plain,
    ( spl4_5
  <=> member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f126,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2)
    | ~ spl4_8 ),
    inference(resolution,[],[f113,f49]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f124,plain,
    ( ~ spl4_6
    | ~ spl4_7 ),
    inference(avatar_contradiction_clause,[],[f123]) ).

fof(f123,plain,
    ( $false
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(subsumption_resolution,[],[f122,f117]) ).

fof(f117,plain,
    ( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK1)
    | ~ spl4_7 ),
    inference(resolution,[],[f109,f50]) ).

fof(f109,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1))
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f107]) ).

fof(f107,plain,
    ( spl4_7
  <=> member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f122,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK1)
    | ~ spl4_6 ),
    inference(resolution,[],[f103,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f120,plain,
    ( spl4_5
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f116,f107,f97]) ).

fof(f116,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2)
    | ~ spl4_7 ),
    inference(resolution,[],[f109,f49]) ).

fof(f114,plain,
    ( spl4_7
    | spl4_8
    | spl4_2 ),
    inference(avatar_split_clause,[],[f105,f60,f111,f107]) ).

fof(f60,plain,
    ( spl4_2
  <=> subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f105,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK0))
    | member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,sK1))
    | spl4_2 ),
    inference(resolution,[],[f92,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',union) ).

fof(f92,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),union(difference(sK2,sK0),difference(sK2,sK1)))
    | spl4_2 ),
    inference(resolution,[],[f62,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',subset) ).

fof(f62,plain,
    ( ~ subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1)))
    | spl4_2 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f104,plain,
    ( ~ spl4_5
    | spl4_6
    | spl4_2 ),
    inference(avatar_split_clause,[],[f95,f60,f101,f97]) ).

fof(f95,plain,
    ( member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),intersection(sK0,sK1))
    | ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),sK2)
    | spl4_2 ),
    inference(resolution,[],[f93,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f93,plain,
    ( ~ member(sK3(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1))),difference(sK2,intersection(sK0,sK1)))
    | spl4_2 ),
    inference(resolution,[],[f62,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f90,plain,
    ( spl4_1
    | spl4_4 ),
    inference(avatar_contradiction_clause,[],[f89]) ).

fof(f89,plain,
    ( $false
    | spl4_1
    | spl4_4 ),
    inference(subsumption_resolution,[],[f88,f66]) ).

fof(f66,plain,
    ( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2)
    | spl4_1 ),
    inference(resolution,[],[f64,f49]) ).

fof(f64,plain,
    ( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,intersection(sK0,sK1)))
    | spl4_1 ),
    inference(resolution,[],[f58,f40]) ).

fof(f58,plain,
    ( ~ subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
    | spl4_1 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl4_1
  <=> subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f88,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2)
    | spl4_1
    | spl4_4 ),
    inference(subsumption_resolution,[],[f87,f78]) ).

fof(f78,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1)
    | spl4_4 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f76,plain,
    ( spl4_4
  <=> member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f87,plain,
    ( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1)
    | ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2)
    | spl4_1 ),
    inference(resolution,[],[f69,f51]) ).

fof(f69,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK1))
    | spl4_1 ),
    inference(resolution,[],[f65,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f65,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),union(difference(sK2,sK0),difference(sK2,sK1)))
    | spl4_1 ),
    inference(resolution,[],[f58,f41]) ).

fof(f85,plain,
    ( spl4_3
    | spl4_1 ),
    inference(avatar_split_clause,[],[f84,f56,f72]) ).

fof(f72,plain,
    ( spl4_3
  <=> member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f84,plain,
    ( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0)
    | spl4_1 ),
    inference(subsumption_resolution,[],[f80,f66]) ).

fof(f80,plain,
    ( member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0)
    | ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK2)
    | spl4_1 ),
    inference(resolution,[],[f68,f51]) ).

fof(f68,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),difference(sK2,sK0))
    | spl4_1 ),
    inference(resolution,[],[f65,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f79,plain,
    ( ~ spl4_3
    | ~ spl4_4
    | spl4_1 ),
    inference(avatar_split_clause,[],[f70,f56,f76,f72]) ).

fof(f70,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK1)
    | ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),sK0)
    | spl4_1 ),
    inference(resolution,[],[f67,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f67,plain,
    ( ~ member(sK3(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),intersection(sK0,sK1))
    | spl4_1 ),
    inference(resolution,[],[f64,f50]) ).

fof(f63,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f54,f60,f56]) ).

fof(f54,plain,
    ( ~ subset(union(difference(sK2,sK0),difference(sK2,sK1)),difference(sK2,intersection(sK0,sK1)))
    | ~ subset(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))) ),
    inference(resolution,[],[f38,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',equal_set) ).

fof(f38,plain,
    ~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1))),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
    & subset(sK1,sK2)
    & subset(sK0,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f24]) ).

fof(f24,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1)))
        & subset(X1,X2)
        & subset(X0,X2) )
   => ( ~ equal_set(difference(sK2,intersection(sK0,sK1)),union(difference(sK2,sK0),difference(sK2,sK1)))
      & subset(sK1,sK2)
      & subset(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1)))
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1)))
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1,X2] :
        ( ( subset(X1,X2)
          & subset(X0,X2) )
       => equal_set(difference(X2,intersection(X0,X1)),union(difference(X2,X0),difference(X2,X1))) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X3] :
        ( ( subset(X1,X3)
          & subset(X0,X3) )
       => equal_set(difference(X3,intersection(X0,X1)),union(difference(X3,X0),difference(X3,X1))) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X1,X3] :
      ( ( subset(X1,X3)
        & subset(X0,X3) )
     => equal_set(difference(X3,intersection(X0,X1)),union(difference(X3,X0),difference(X3,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906',thI25) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET156+4 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n021.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Tue Apr 30 17:16:56 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.nV9pvhydKu/Vampire---4.8_31906
% 0.70/0.91  % (32139)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)
% 0.70/0.91  % (32134)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2994ds/78Mi)
% 0.70/0.91  % (32135)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)
% 0.70/0.91  % (32136)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)
% 0.70/0.91  % (32132)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)
% 0.70/0.91  % (32133)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)
% 0.70/0.91  % (32137)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)
% 0.70/0.91  % (32138)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)
% 0.70/0.91  % (32137)Refutation not found, incomplete strategy% (32137)------------------------------
% 0.70/0.91  % (32137)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.70/0.91  % (32137)Termination reason: Refutation not found, incomplete strategy
% 0.70/0.91  
% 0.70/0.91  % (32137)Memory used [KB]: 967
% 0.70/0.91  % (32137)Time elapsed: 0.003 s
% 0.70/0.91  % (32137)Instructions burned: 2 (million)
% 0.70/0.91  % (32137)------------------------------
% 0.70/0.91  % (32137)------------------------------
% 0.70/0.91  % (32136)Refutation not found, incomplete strategy% (32136)------------------------------
% 0.70/0.91  % (32136)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.70/0.91  % (32136)Termination reason: Refutation not found, incomplete strategy
% 0.70/0.91  
% 0.70/0.91  % (32136)Memory used [KB]: 1039
% 0.70/0.91  % (32136)Time elapsed: 0.003 s
% 0.70/0.91  % (32136)Instructions burned: 3 (million)
% 0.70/0.91  % (32136)------------------------------
% 0.70/0.91  % (32136)------------------------------
% 0.70/0.91  % (32139)First to succeed.
% 0.70/0.91  % (32139)Refutation found. Thanks to Tanya!
% 0.70/0.91  % SZS status Theorem for Vampire---4
% 0.70/0.91  % SZS output start Proof for Vampire---4
% See solution above
% 0.70/0.91  % (32139)------------------------------
% 0.70/0.91  % (32139)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.70/0.91  % (32139)Termination reason: Refutation
% 0.70/0.91  
% 0.70/0.91  % (32139)Memory used [KB]: 1075
% 0.70/0.91  % (32139)Time elapsed: 0.006 s
% 0.70/0.91  % (32139)Instructions burned: 7 (million)
% 0.70/0.91  % (32139)------------------------------
% 0.70/0.91  % (32139)------------------------------
% 0.70/0.91  % (32077)Success in time 0.534 s
% 0.70/0.91  % Vampire---4.8 exiting
%------------------------------------------------------------------------------