TSTP Solution File: SET621+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n014.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 18:21:38 EDT 2022

% Result   : Theorem 1.32s 0.53s
% Output   : Refutation 1.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  130 (  14 unt;   0 def)
%            Number of atoms       :  327 (  23 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  345 ( 148   ~; 152   |;  23   &)
%                                         (  20 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   17 (  15 usr;  14 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   96 (  84   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f374,plain,
    $false,
    inference(avatar_sat_refutation,[],[f92,f123,f148,f161,f217,f219,f236,f239,f259,f260,f261,f285,f290,f311,f320,f324,f328,f333,f334,f337,f344,f345,f348,f350,f353,f354,f359,f370,f373]) ).

fof(f373,plain,
    ( spl6_10
    | ~ spl6_11
    | spl6_15 ),
    inference(avatar_split_clause,[],[f371,f189,f145,f141]) ).

fof(f141,plain,
    ( spl6_10
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).

fof(f145,plain,
    ( spl6_11
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).

fof(f189,plain,
    ( spl6_15
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).

fof(f371,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | spl6_15 ),
    inference(resolution,[],[f190,f59]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | ~ member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) )
      & ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X1,X0,X2] :
      ( ( ( ~ member(X1,X0)
          & member(X1,X2) )
        | ~ member(X1,difference(X2,X0)) )
      & ( member(X1,difference(X2,X0))
        | member(X1,X0)
        | ~ member(X1,X2) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0,X2] :
      ( ( ( ~ member(X1,X0)
          & member(X1,X2) )
        | ~ member(X1,difference(X2,X0)) )
      & ( member(X1,difference(X2,X0))
        | member(X1,X0)
        | ~ member(X1,X2) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0,X2] :
      ( ( ~ member(X1,X0)
        & member(X1,X2) )
    <=> member(X1,difference(X2,X0)) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X0] :
      ( member(X2,difference(X0,X1))
    <=> ( member(X2,X0)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

fof(f190,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
    | spl6_15 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f370,plain,
    ( ~ spl6_10
    | spl6_14 ),
    inference(avatar_split_clause,[],[f367,f182,f141]) ).

fof(f182,plain,
    ( spl6_14
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).

fof(f367,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | spl6_14 ),
    inference(resolution,[],[f183,f49]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X2,X0))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f31]) ).

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

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,union(X2,X0))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) )
      & ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X2,X0)) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( member(X1,union(X2,X0))
    <=> ( member(X1,X0)
        | member(X1,X2) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X2,X0] :
      ( ( member(X2,X1)
        | member(X2,X0) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f183,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
    | spl6_14 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f359,plain,
    ( ~ spl6_15
    | spl6_8 ),
    inference(avatar_split_clause,[],[f356,f127,f189]) ).

fof(f127,plain,
    ( spl6_8
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

fof(f356,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
    | spl6_8 ),
    inference(resolution,[],[f129,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X2,X0))
      | ~ member(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f129,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
    | spl6_8 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f354,plain,
    ( ~ spl6_14
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f352,f155,f182]) ).

fof(f155,plain,
    ( spl6_13
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).

fof(f352,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
    | ~ spl6_13 ),
    inference(resolution,[],[f157,f61]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f157,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
    | ~ spl6_13 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f353,plain,
    ( spl6_11
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f351,f155,f145]) ).

fof(f351,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | ~ spl6_13 ),
    inference(resolution,[],[f157,f60]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f350,plain,
    ( spl6_12
    | spl6_13
    | ~ spl6_1 ),
    inference(avatar_split_clause,[],[f349,f85,f155,f151]) ).

fof(f151,plain,
    ( spl6_12
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).

fof(f85,plain,
    ( spl6_1
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f349,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
    | ~ spl6_1 ),
    inference(resolution,[],[f86,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,union(X2,X0))
      | member(X1,X0)
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f86,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f348,plain,
    ( ~ spl6_8
    | spl6_9
    | spl6_2 ),
    inference(avatar_split_clause,[],[f346,f89,f131,f127]) ).

fof(f131,plain,
    ( spl6_9
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

fof(f89,plain,
    ( spl6_2
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f346,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
    | spl6_2 ),
    inference(resolution,[],[f91,f59]) ).

fof(f91,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
    | spl6_2 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f345,plain,
    ( spl6_10
    | ~ spl6_16 ),
    inference(avatar_split_clause,[],[f338,f193,f141]) ).

fof(f193,plain,
    ( spl6_16
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).

fof(f338,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | ~ spl6_16 ),
    inference(resolution,[],[f195,f60]) ).

fof(f195,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
    | ~ spl6_16 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f344,plain,
    ( spl6_9
    | spl6_11
    | ~ spl6_18 ),
    inference(avatar_split_clause,[],[f343,f294,f145,f131]) ).

fof(f294,plain,
    ( spl6_18
  <=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).

fof(f343,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | ~ spl6_18 ),
    inference(resolution,[],[f296,f48]) ).

fof(f296,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
    | ~ spl6_18 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f337,plain,
    ( spl6_18
    | ~ spl6_10
    | spl6_12 ),
    inference(avatar_split_clause,[],[f335,f151,f141,f294]) ).

fof(f335,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
    | spl6_12 ),
    inference(resolution,[],[f152,f59]) ).

fof(f152,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
    | spl6_12 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f334,plain,
    ( ~ spl6_13
    | spl6_1 ),
    inference(avatar_split_clause,[],[f331,f85,f155]) ).

fof(f331,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
    | spl6_1 ),
    inference(resolution,[],[f87,f50]) ).

fof(f87,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
    | spl6_1 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f333,plain,
    ( ~ spl6_12
    | spl6_1 ),
    inference(avatar_split_clause,[],[f330,f85,f151]) ).

fof(f330,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
    | spl6_1 ),
    inference(resolution,[],[f87,f49]) ).

fof(f328,plain,
    ( spl6_8
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f326,f89,f127]) ).

fof(f326,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
    | ~ spl6_2 ),
    inference(resolution,[],[f90,f60]) ).

fof(f90,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f324,plain,
    ( ~ spl6_11
    | spl6_18 ),
    inference(avatar_split_clause,[],[f321,f294,f145]) ).

fof(f321,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | spl6_18 ),
    inference(resolution,[],[f295,f49]) ).

fof(f295,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
    | spl6_18 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f320,plain,
    ( ~ spl6_18
    | ~ spl6_12 ),
    inference(avatar_split_clause,[],[f319,f151,f294]) ).

fof(f319,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
    | ~ spl6_12 ),
    inference(resolution,[],[f153,f61]) ).

fof(f153,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
    | ~ spl6_12 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f311,plain,
    ( ~ spl6_9
    | spl6_14 ),
    inference(avatar_split_clause,[],[f308,f182,f131]) ).

fof(f308,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | spl6_14 ),
    inference(resolution,[],[f183,f50]) ).

fof(f290,plain,
    ( ~ spl6_9
    | ~ spl6_12 ),
    inference(avatar_split_clause,[],[f288,f151,f131]) ).

fof(f288,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | ~ spl6_12 ),
    inference(resolution,[],[f267,f50]) ).

fof(f267,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
    | ~ spl6_12 ),
    inference(resolution,[],[f153,f61]) ).

fof(f285,plain,
    ( ~ spl6_11
    | ~ spl6_16 ),
    inference(avatar_split_clause,[],[f284,f193,f145]) ).

fof(f284,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | ~ spl6_16 ),
    inference(resolution,[],[f195,f61]) ).

fof(f261,plain,
    ( spl6_15
    | spl6_16
    | ~ spl6_8 ),
    inference(avatar_split_clause,[],[f241,f127,f193,f189]) ).

fof(f241,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
    | ~ spl6_8 ),
    inference(resolution,[],[f128,f48]) ).

fof(f128,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f260,plain,
    ( ~ spl6_10
    | ~ spl6_15 ),
    inference(avatar_split_clause,[],[f235,f189,f141]) ).

fof(f235,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | ~ spl6_15 ),
    inference(resolution,[],[f191,f61]) ).

fof(f191,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
    | ~ spl6_15 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f259,plain,
    ( spl6_9
    | spl6_10
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f258,f182,f141,f131]) ).

fof(f258,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | ~ spl6_14 ),
    inference(resolution,[],[f184,f48]) ).

fof(f184,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
    | ~ spl6_14 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f239,plain,
    ( ~ spl6_11
    | spl6_14
    | spl6_13 ),
    inference(avatar_split_clause,[],[f237,f155,f182,f145]) ).

fof(f237,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
    | ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | spl6_13 ),
    inference(resolution,[],[f156,f59]) ).

fof(f156,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
    | spl6_13 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f236,plain,
    ( spl6_11
    | ~ spl6_15 ),
    inference(avatar_split_clause,[],[f234,f189,f145]) ).

fof(f234,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | ~ spl6_15 ),
    inference(resolution,[],[f191,f60]) ).

fof(f219,plain,
    ~ spl6_7,
    inference(avatar_contradiction_clause,[],[f218]) ).

fof(f218,plain,
    ( $false
    | ~ spl6_7 ),
    inference(resolution,[],[f122,f72]) ).

fof(f72,plain,
    ~ sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),
    inference(equality_proxy_replacement,[],[f64,f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).

fof(f64,plain,
    difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
    inference(definition_unfolding,[],[f47,f51]) ).

fof(f51,plain,
    ! [X0,X1] : symmetric_difference(X1,X0) = union(difference(X1,X0),difference(X0,X1)),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] : symmetric_difference(X1,X0) = union(difference(X1,X0),difference(X0,X1)),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f47,plain,
    difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f27,f28]) ).

fof(f28,plain,
    ( ? [X0,X1,X2] : union(difference(X0,union(X2,X1)),difference(X2,union(X0,X1))) != difference(symmetric_difference(X0,X2),X1)
   => difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ? [X0,X1,X2] : union(difference(X0,union(X2,X1)),difference(X2,union(X0,X1))) != difference(symmetric_difference(X0,X2),X1),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ? [X1,X0,X2] : difference(symmetric_difference(X1,X2),X0) != union(difference(X1,union(X2,X0)),difference(X2,union(X1,X0))),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1,X2] : difference(symmetric_difference(X1,X2),X0) = union(difference(X1,union(X2,X0)),difference(X2,union(X1,X0))),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X2,X0,X1] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X2,X0,X1] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th97) ).

fof(f122,plain,
    ( sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f120]) ).

fof(f120,plain,
    ( spl6_7
  <=> sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

fof(f217,plain,
    ( spl6_10
    | ~ spl6_12 ),
    inference(avatar_split_clause,[],[f215,f151,f141]) ).

fof(f215,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | ~ spl6_12 ),
    inference(resolution,[],[f153,f60]) ).

fof(f161,plain,
    ( ~ spl6_9
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f160,f89,f131]) ).

fof(f160,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
    | ~ spl6_2 ),
    inference(resolution,[],[f90,f61]) ).

fof(f148,plain,
    ( ~ spl6_10
    | spl6_11
    | spl6_8 ),
    inference(avatar_split_clause,[],[f138,f127,f145,f141]) ).

fof(f138,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
    | ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
    | spl6_8 ),
    inference(resolution,[],[f135,f59]) ).

fof(f135,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
    | spl6_8 ),
    inference(resolution,[],[f129,f49]) ).

fof(f123,plain,
    ( spl6_7
    | spl6_2
    | spl6_1 ),
    inference(avatar_split_clause,[],[f115,f85,f89,f120]) ).

fof(f115,plain,
    ( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
    | sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
    | spl6_1 ),
    inference(resolution,[],[f87,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X1)
      | sQ5_eqProxy(X0,X1)
      | member(sK4(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f55,f70]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK4(X0,X1),X0)
      | member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK4(X0,X1),X0)
            | ~ member(sK4(X0,X1),X1) )
          & ( member(sK4(X0,X1),X0)
            | member(sK4(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f34,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK4(X0,X1),X0)
          | ~ member(sK4(X0,X1),X1) )
        & ( member(sK4(X0,X1),X0)
          | member(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f92,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f83,f89,f85]) ).

fof(f83,plain,
    ( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
    | ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
    inference(resolution,[],[f72,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
      | ~ member(sK4(X0,X1),X0)
      | ~ member(sK4(X0,X1),X1) ),
    inference(equality_proxy_replacement,[],[f56,f70]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK4(X0,X1),X0)
      | ~ member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:05:48 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.47  % (32206)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)
% 0.21/0.49  % (32206)Instruction limit reached!
% 0.21/0.49  % (32206)------------------------------
% 0.21/0.49  % (32206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (32198)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)
% 0.21/0.49  % (32206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (32206)Termination reason: Unknown
% 0.21/0.49  % (32206)Termination phase: Saturation
% 0.21/0.49  
% 0.21/0.49  % (32206)Memory used [KB]: 5884
% 0.21/0.49  % (32206)Time elapsed: 0.004 s
% 0.21/0.49  % (32206)Instructions burned: 3 (million)
% 0.21/0.49  % (32206)------------------------------
% 0.21/0.49  % (32206)------------------------------
% 0.21/0.50  % (32215)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.50  % (32195)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  % (32220)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.21/0.52  % (32203)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.52  % (32212)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.21/0.52  % (32195)Refutation not found, incomplete strategy% (32195)------------------------------
% 0.21/0.52  % (32195)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (32195)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (32195)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52  
% 0.21/0.52  % (32195)Memory used [KB]: 5884
% 0.21/0.52  % (32195)Time elapsed: 0.105 s
% 0.21/0.52  % (32195)Instructions burned: 3 (million)
% 0.21/0.52  % (32195)------------------------------
% 0.21/0.52  % (32195)------------------------------
% 0.21/0.52  % (32214)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.53  % (32220)Instruction limit reached!
% 0.21/0.53  % (32220)------------------------------
% 0.21/0.53  % (32220)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (32205)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (32203)Instruction limit reached!
% 0.21/0.53  % (32203)------------------------------
% 0.21/0.53  % (32203)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (32203)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (32203)Termination reason: Unknown
% 0.21/0.53  % (32203)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (32203)Memory used [KB]: 6012
% 0.21/0.53  % (32203)Time elapsed: 0.122 s
% 0.21/0.53  % (32203)Instructions burned: 7 (million)
% 0.21/0.53  % (32198)Instruction limit reached!
% 0.21/0.53  % (32198)------------------------------
% 0.21/0.53  % (32198)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (32198)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (32198)Termination reason: Unknown
% 0.21/0.53  % (32198)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (32198)Memory used [KB]: 6396
% 0.21/0.53  % (32198)Time elapsed: 0.113 s
% 0.21/0.53  % (32198)Instructions burned: 39 (million)
% 0.21/0.53  % (32198)------------------------------
% 0.21/0.53  % (32198)------------------------------
% 0.21/0.53  % (32203)------------------------------
% 0.21/0.53  % (32203)------------------------------
% 0.21/0.53  % (32212)First to succeed.
% 1.32/0.53  % (32212)Refutation found. Thanks to Tanya!
% 1.32/0.53  % SZS status Theorem for theBenchmark
% 1.32/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.32/0.54  % (32212)------------------------------
% 1.32/0.54  % (32212)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.32/0.54  % (32212)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.32/0.54  % (32212)Termination reason: Refutation
% 1.32/0.54  
% 1.32/0.54  % (32212)Memory used [KB]: 6012
% 1.32/0.54  % (32212)Time elapsed: 0.120 s
% 1.32/0.54  % (32212)Instructions burned: 8 (million)
% 1.32/0.54  % (32212)------------------------------
% 1.32/0.54  % (32212)------------------------------
% 1.32/0.54  % (32191)Success in time 0.171 s
%------------------------------------------------------------------------------