TSTP Solution File: SET612^3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET612^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n019.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 : Tue May 21 03:12:25 EDT 2024

% Result   : Theorem 0.16s 0.40s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   95 (  29 unt;  18 typ;   0 def)
%            Number of atoms       :  649 ( 123 equ;   0 cnn)
%            Maximal formula atoms :    6 (   8 avg)
%            Number of connectives :  531 (  88   ~;  96   |;  54   &; 287   @)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  103 ( 103   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;   8 con; 0-3 aty)
%            Number of variables   :   71 (  55   ^   9   !;   6   ?;  71   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_0,type,
    in: $i > ( $i > $o ) > $o ).

thf(func_def_2,type,
    is_a: $i > ( $i > $o ) > $o ).

thf(func_def_3,type,
    emptyset: $i > $o ).

thf(func_def_4,type,
    unord_pair: $i > $i > $i > $o ).

thf(func_def_5,type,
    singleton: $i > $i > $o ).

thf(func_def_6,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_7,type,
    excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_8,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_9,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_10,type,
    complement: ( $i > $o ) > $i > $o ).

thf(func_def_11,type,
    disjoint: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_12,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_13,type,
    meets: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_14,type,
    misses: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_28,type,
    sK0: $i > $o ).

thf(func_def_29,type,
    sK1: $i > $o ).

thf(func_def_30,type,
    sK2: $i > $o ).

thf(func_def_32,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f159,plain,
    $false,
    inference(avatar_sat_refutation,[],[f124,f125,f139,f145,f152,f158]) ).

thf(f158,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f157]) ).

thf(f157,plain,
    ( $false
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f153]) ).

thf(f153,plain,
    ( ( $true = $false )
    | ~ spl3_3 ),
    inference(superposition,[],[f130,f114]) ).

thf(f114,plain,
    ( ( sK2 @ sK5 )
    = $true ),
    inference(duplicate_literal_removal,[],[f111]) ).

thf(f111,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f105]) ).

thf(f105,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f81]) ).

thf(f81,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f67]) ).

thf(f67,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( ~ ( ( sK1 @ sK5 )
          | ( sK0 @ sK5 ) )
      & ( sK2 @ sK5 ) )
   != ( ~ ( sK0 @ sK5 )
      & ( sK2 @ sK5 )
      & ~ ( sK1 @ sK5 )
      & ( sK2 @ sK5 ) ) ),
    inference(beta_eta_normalization,[],[f65]) ).

thf(f65,plain,
    ( ( ^ [Y0: $i] :
          ( ~ ( ( sK1 @ Y0 )
              | ( sK0 @ Y0 ) )
          & ( sK2 @ Y0 ) )
      @ sK5 )
   != ( ^ [Y0: $i] :
          ( ~ ( sK0 @ Y0 )
          & ( sK2 @ Y0 )
          & ~ ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f64]) ).

thf(f64,plain,
    ( ( ^ [Y0: $i] :
          ( ~ ( ( sK1 @ Y0 )
              | ( sK0 @ Y0 ) )
          & ( sK2 @ Y0 ) ) )
   != ( ^ [Y0: $i] :
          ( ~ ( sK0 @ Y0 )
          & ( sK2 @ Y0 )
          & ~ ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) ) ) ),
    inference(beta_eta_normalization,[],[f63]) ).

thf(f63,plain,
    ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) )
      @ sK2
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ( Y1 @ Y2 )
            | ( Y0 @ Y2 ) )
        @ sK0
        @ sK1 ) )
   != ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y0 @ Y2 )
          & ( Y1 @ Y2 ) )
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ~ ( Y1 @ Y2 )
            & ( Y0 @ Y2 ) )
        @ sK2
        @ sK0 )
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ~ ( Y1 @ Y2 )
            & ( Y0 @ Y2 ) )
        @ sK2
        @ sK1 ) ) ),
    inference(definition_unfolding,[],[f52,f47,f53,f53,f53,f49]) ).

thf(f49,plain,
    ( union
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          | ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f23]) ).

thf(f23,plain,
    ( union
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          | ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f22]) ).

thf(f22,plain,
    ( union
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X0 @ X2 )
          | ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ( union
    = ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X0 @ X3 )
          | ( X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

thf(f53,plain,
    ( setminus
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f35]) ).

thf(f35,plain,
    ( setminus
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f34]) ).

thf(f34,plain,
    ( setminus
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X0 @ X2 )
          & ~ ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ( setminus
    = ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X0 @ X3 )
          & ~ ( X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminus) ).

thf(f47,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y0 @ Y2 )
          & ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y0 @ Y2 )
          & ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f18]) ).

thf(f18,plain,
    ( intersection
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X1 @ X2 )
          & ( X0 @ X2 ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ( intersection
    = ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X2 @ X3 )
          & ( X0 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

thf(f52,plain,
    ( ( intersection @ ( setminus @ sK2 @ sK0 ) @ ( setminus @ sK2 @ sK1 ) )
   != ( setminus @ sK2 @ ( union @ sK0 @ sK1 ) ) ),
    inference(cnf_transformation,[],[f46]) ).

thf(f46,plain,
    ( ( intersection @ ( setminus @ sK2 @ sK0 ) @ ( setminus @ sK2 @ sK1 ) )
   != ( setminus @ sK2 @ ( union @ sK0 @ sK1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f44,f45]) ).

thf(f45,plain,
    ( ? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
        ( ( setminus @ X2 @ ( union @ X0 @ X1 ) )
       != ( intersection @ ( setminus @ X2 @ X0 ) @ ( setminus @ X2 @ X1 ) ) )
   => ( ( intersection @ ( setminus @ sK2 @ sK0 ) @ ( setminus @ sK2 @ sK1 ) )
     != ( setminus @ sK2 @ ( union @ sK0 @ sK1 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f44,plain,
    ? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
      ( ( setminus @ X2 @ ( union @ X0 @ X1 ) )
     != ( intersection @ ( setminus @ X2 @ X0 ) @ ( setminus @ X2 @ X1 ) ) ),
    inference(ennf_transformation,[],[f43]) ).

thf(f43,plain,
    ~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
        ( ( setminus @ X2 @ ( union @ X0 @ X1 ) )
        = ( intersection @ ( setminus @ X2 @ X0 ) @ ( setminus @ X2 @ X1 ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,negated_conjecture,
    ~ ! [X2: $i > $o,X4: $i > $o,X0: $i > $o] :
        ( ( setminus @ X0 @ ( union @ X2 @ X4 ) )
        = ( intersection @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X4 ) ) ),
    inference(negated_conjecture,[],[f15]) ).

thf(f15,conjecture,
    ! [X2: $i > $o,X4: $i > $o,X0: $i > $o] :
      ( ( setminus @ X0 @ ( union @ X2 @ X4 ) )
      = ( intersection @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(f130,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f128]) ).

thf(f128,plain,
    ( spl3_3
  <=> ( ( sK2 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f152,plain,
    ( ~ spl3_1
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f151]) ).

thf(f151,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f148]) ).

thf(f148,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_5 ),
    inference(superposition,[],[f118,f138]) ).

thf(f138,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f136]) ).

thf(f136,plain,
    ( spl3_5
  <=> ( $true
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f118,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f116]) ).

thf(f116,plain,
    ( spl3_1
  <=> ( $false
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f145,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f144]) ).

thf(f144,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f140]) ).

thf(f140,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(superposition,[],[f122,f134]) ).

thf(f134,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f132]) ).

thf(f132,plain,
    ( spl3_4
  <=> ( ( sK0 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f122,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f120]) ).

thf(f120,plain,
    ( spl3_2
  <=> ( ( sK0 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f139,plain,
    ( spl3_3
    | spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f80,f136,f132,f128]) ).

thf(f80,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f79]) ).

thf(f79,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f78]) ).

thf(f78,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f77]) ).

thf(f77,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f76]) ).

thf(f76,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) ) ),
    inference(duplicate_literal_removal,[],[f75]) ).

thf(f75,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f74,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f73]) ).

thf(f73,plain,
    ( ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) )
    | ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $false
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f72]) ).

thf(f72,plain,
    ( ( $false
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f71]) ).

thf(f71,plain,
    ( ( $false
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) )
    | ( $false
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f70]) ).

thf(f70,plain,
    ( ( $false
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( $false
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f68]) ).

thf(f68,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f125,plain,
    spl3_2,
    inference(avatar_split_clause,[],[f94,f120]) ).

thf(f94,plain,
    ( ( sK0 @ sK5 )
    = $false ),
    inference(duplicate_literal_removal,[],[f93]) ).

thf(f93,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f92]) ).

thf(f92,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK0 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f86]) ).

thf(f86,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f85]) ).

thf(f85,plain,
    ( ( $false
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f84]) ).

thf(f84,plain,
    ( ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f82]) ).

thf(f82,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f67]) ).

thf(f124,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f101,f116]) ).

thf(f101,plain,
    ( $false
    = ( sK1 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f100]) ).

thf(f100,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f98]) ).

thf(f98,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f97]) ).

thf(f97,plain,
    ( ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f96]) ).

thf(f96,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f83]) ).

thf(f83,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET612^3 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37  % Computer : n019.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon May 20 13:31:53 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a TH0_THM_EQU_NAR problem
% 0.16/0.38  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40  % (23230)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.40  % (23233)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.40  % (23237)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.40  % (23233)Instruction limit reached!
% 0.16/0.40  % (23233)------------------------------
% 0.16/0.40  % (23233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40  % (23233)Termination reason: Unknown
% 0.16/0.40  % (23233)Termination phase: shuffling
% 0.16/0.40  
% 0.16/0.40  % (23233)Memory used [KB]: 895
% 0.16/0.40  % (23233)Time elapsed: 0.002 s
% 0.16/0.40  % (23233)Instructions burned: 2 (million)
% 0.16/0.40  % (23233)------------------------------
% 0.16/0.40  % (23233)------------------------------
% 0.16/0.40  % (23237)Instruction limit reached!
% 0.16/0.40  % (23237)------------------------------
% 0.16/0.40  % (23237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40  % (23237)Termination reason: Unknown
% 0.16/0.40  % (23237)Termination phase: Saturation
% 0.16/0.40  
% 0.16/0.40  % (23237)Memory used [KB]: 1023
% 0.16/0.40  % (23237)Time elapsed: 0.004 s
% 0.16/0.40  % (23237)Instructions burned: 4 (million)
% 0.16/0.40  % (23237)------------------------------
% 0.16/0.40  % (23237)------------------------------
% 0.16/0.40  % (23231)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.16/0.40  % (23232)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.16/0.40  % (23230)First to succeed.
% 0.16/0.40  % (23234)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.40  % (23231)Instruction limit reached!
% 0.16/0.40  % (23231)------------------------------
% 0.16/0.40  % (23231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40  % (23231)Termination reason: Unknown
% 0.16/0.40  % (23231)Termination phase: Saturation
% 0.16/0.40  
% 0.16/0.40  % (23231)Memory used [KB]: 5500
% 0.16/0.40  % (23231)Time elapsed: 0.004 s
% 0.16/0.40  % (23231)Instructions burned: 4 (million)
% 0.16/0.40  % (23231)------------------------------
% 0.16/0.40  % (23231)------------------------------
% 0.16/0.40  % (23234)Instruction limit reached!
% 0.16/0.40  % (23234)------------------------------
% 0.16/0.40  % (23234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40  % (23234)Termination reason: Unknown
% 0.16/0.40  % (23234)Termination phase: Property scanning
% 0.16/0.40  
% 0.16/0.40  % (23234)Memory used [KB]: 1023
% 0.16/0.40  % (23234)Time elapsed: 0.003 s
% 0.16/0.40  % (23234)Instructions burned: 3 (million)
% 0.16/0.40  % (23234)------------------------------
% 0.16/0.40  % (23234)------------------------------
% 0.16/0.40  % (23236)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.40  % (23230)Refutation found. Thanks to Tanya!
% 0.16/0.40  % SZS status Theorem for theBenchmark
% 0.16/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.40  % (23230)------------------------------
% 0.16/0.40  % (23230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40  % (23230)Termination reason: Refutation
% 0.16/0.40  
% 0.16/0.40  % (23230)Memory used [KB]: 5500
% 0.16/0.40  % (23230)Time elapsed: 0.007 s
% 0.16/0.40  % (23230)Instructions burned: 5 (million)
% 0.16/0.40  % (23230)------------------------------
% 0.16/0.40  % (23230)------------------------------
% 0.16/0.40  % (23229)Success in time 0.031 s
% 0.16/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------