TSTP Solution File: SEU856^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU856^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : n004.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 03:51:56 EDT 2024

% Result   : Theorem 0.23s 0.40s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   98 (   1 unt;   8 typ;   0 def)
%            Number of atoms       :  471 ( 108 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :  530 ( 150   ~; 148   |;  55   &; 161   @)
%                                         (  14 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;  15 con; 0-2 aty)
%            Number of variables   :   66 (  40   ^  19   !;   6   ?;  66   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    a: $tType ).

thf(func_def_0,type,
    a: $tType ).

thf(func_def_9,type,
    sK0: a > $o ).

thf(func_def_10,type,
    sK1: a > $o ).

thf(func_def_12,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_13,type,
    sK4: a ).

thf(func_def_14,type,
    sK5: a ).

thf(func_def_15,type,
    sK6: a ).

thf(f191,plain,
    $false,
    inference(avatar_sat_refutation,[],[f20,f21,f89,f100,f107,f117,f121,f124,f137,f146,f160,f166,f169,f189]) ).

thf(f189,plain,
    ( ~ spl2_2
    | spl2_13
    | ~ spl2_14 ),
    inference(avatar_contradiction_clause,[],[f188]) ).

thf(f188,plain,
    ( $false
    | ~ spl2_2
    | spl2_13
    | ~ spl2_14 ),
    inference(subsumption_resolution,[],[f179,f140]) ).

thf(f140,plain,
    ( ( $false
     != ( sK1 @ sK6 ) )
    | spl2_13 ),
    inference(avatar_component_clause,[],[f139]) ).

thf(f139,plain,
    ( spl2_13
  <=> ( $false
      = ( sK1 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

thf(f179,plain,
    ( ( $false
      = ( sK1 @ sK6 ) )
    | ~ spl2_2
    | ~ spl2_14 ),
    inference(trivial_inequality_removal,[],[f174]) ).

thf(f174,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK1 @ sK6 ) )
    | ~ spl2_2
    | ~ spl2_14 ),
    inference(superposition,[],[f154,f145]) ).

thf(f145,plain,
    ( ( $false
      = ( sK0 @ sK6 ) )
    | ~ spl2_14 ),
    inference(avatar_component_clause,[],[f143]) ).

thf(f143,plain,
    ( spl2_14
  <=> ( $false
      = ( sK0 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

thf(f154,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK0 @ X1 ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl2_2 ),
    inference(not_proxy_clausification,[],[f153]) ).

thf(f153,plain,
    ( ! [X1: a] :
        ( ( ( ~ ( sK0 @ X1 ) )
          = $false )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f149]) ).

thf(f149,plain,
    ( ! [X1: a] :
        ( ( ~ ( sK0 @ X1 )
          & ( sK1 @ X1 ) )
        = $false )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f148]) ).

thf(f148,plain,
    ( ! [X1: a] :
        ( $false
        = ( ( ~ ( sK1 @ X1 )
            & ( sK0 @ X1 ) )
          | ( ~ ( sK0 @ X1 )
            & ( sK1 @ X1 ) ) ) )
    | ~ spl2_2 ),
    inference(beta_eta_normalization,[],[f147]) ).

thf(f147,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] : $false
          @ X1 )
        = ( ^ [Y0: a] :
              ( ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) )
              | ( ~ ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) ) )
          @ X1 ) )
    | ~ spl2_2 ),
    inference(argument_congruence,[],[f18]) ).

thf(f18,plain,
    ( ( ( ^ [Y0: a] : $false )
      = ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f17,plain,
    ( spl2_2
  <=> ( ( ^ [Y0: a] : $false )
      = ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f169,plain,
    ( ~ spl2_12
    | ~ spl2_13 ),
    inference(avatar_contradiction_clause,[],[f168]) ).

thf(f168,plain,
    ( $false
    | ~ spl2_12
    | ~ spl2_13 ),
    inference(trivial_inequality_removal,[],[f167]) ).

thf(f167,plain,
    ( ( $true = $false )
    | ~ spl2_12
    | ~ spl2_13 ),
    inference(forward_demodulation,[],[f136,f141]) ).

thf(f141,plain,
    ( ( $false
      = ( sK1 @ sK6 ) )
    | ~ spl2_13 ),
    inference(avatar_component_clause,[],[f139]) ).

thf(f136,plain,
    ( ( $true
      = ( sK1 @ sK6 ) )
    | ~ spl2_12 ),
    inference(avatar_component_clause,[],[f134]) ).

thf(f134,plain,
    ( spl2_12
  <=> ( $true
      = ( sK1 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

thf(f166,plain,
    ( ~ spl2_11
    | ~ spl2_14 ),
    inference(avatar_contradiction_clause,[],[f165]) ).

thf(f165,plain,
    ( $false
    | ~ spl2_11
    | ~ spl2_14 ),
    inference(trivial_inequality_removal,[],[f161]) ).

thf(f161,plain,
    ( ( $true = $false )
    | ~ spl2_11
    | ~ spl2_14 ),
    inference(superposition,[],[f145,f132]) ).

thf(f132,plain,
    ( ( $true
      = ( sK0 @ sK6 ) )
    | ~ spl2_11 ),
    inference(avatar_component_clause,[],[f130]) ).

thf(f130,plain,
    ( spl2_11
  <=> ( $true
      = ( sK0 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

thf(f160,plain,
    ( spl2_14
    | ~ spl2_2
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f157,f139,f17,f143]) ).

thf(f157,plain,
    ( ( $false
      = ( sK0 @ sK6 ) )
    | ~ spl2_2
    | ~ spl2_13 ),
    inference(trivial_inequality_removal,[],[f156]) ).

thf(f156,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK0 @ sK6 ) )
    | ~ spl2_2
    | ~ spl2_13 ),
    inference(superposition,[],[f141,f152]) ).

thf(f152,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK1 @ X1 ) )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl2_2 ),
    inference(not_proxy_clausification,[],[f151]) ).

thf(f151,plain,
    ( ! [X1: a] :
        ( ( $false
          = ( sK0 @ X1 ) )
        | ( $false
          = ( ~ ( sK1 @ X1 ) ) ) )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f150]) ).

thf(f150,plain,
    ( ! [X1: a] :
        ( ( ~ ( sK1 @ X1 )
          & ( sK0 @ X1 ) )
        = $false )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f148]) ).

thf(f146,plain,
    ( spl2_13
    | spl2_14
    | spl2_1 ),
    inference(avatar_split_clause,[],[f128,f13,f143,f139]) ).

thf(f13,plain,
    ( spl2_1
  <=> ( sK1 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f128,plain,
    ( ( $false
      = ( sK1 @ sK6 ) )
    | ( $false
      = ( sK0 @ sK6 ) )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f126]) ).

thf(f126,plain,
    ( ( ( sK1 @ sK6 )
     != ( sK0 @ sK6 ) )
    | spl2_1 ),
    inference(negative_extensionality,[],[f15]) ).

thf(f15,plain,
    ( ( sK1 != sK0 )
    | spl2_1 ),
    inference(avatar_component_clause,[],[f13]) ).

thf(f137,plain,
    ( spl2_11
    | spl2_12
    | spl2_1 ),
    inference(avatar_split_clause,[],[f127,f13,f134,f130]) ).

thf(f127,plain,
    ( ( $true
      = ( sK0 @ sK6 ) )
    | ( $true
      = ( sK1 @ sK6 ) )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f126]) ).

thf(f124,plain,
    ( ~ spl2_1
    | ~ spl2_9
    | spl2_10 ),
    inference(avatar_contradiction_clause,[],[f123]) ).

thf(f123,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_9
    | spl2_10 ),
    inference(subsumption_resolution,[],[f112,f97]) ).

thf(f97,plain,
    ( ( $false
     != ( sK0 @ sK5 ) )
    | spl2_10 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f96,plain,
    ( spl2_10
  <=> ( $false
      = ( sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

thf(f112,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ~ spl2_1
    | ~ spl2_9 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK0 @ sK5 ) )
    | ~ spl2_1
    | ~ spl2_9 ),
    inference(superposition,[],[f93,f68]) ).

thf(f68,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK1 @ X1 ) )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ! [X1: a] :
        ( ( sK0 @ X1 )
        = ( sK1 @ X1 ) )
    | ~ spl2_1 ),
    inference(argument_congruence,[],[f14]) ).

thf(f14,plain,
    ( ( sK1 = sK0 )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f13]) ).

thf(f93,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl2_9 ),
    inference(avatar_component_clause,[],[f91]) ).

thf(f91,plain,
    ( spl2_9
  <=> ( ( sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

thf(f121,plain,
    ( ~ spl2_7
    | ~ spl2_10 ),
    inference(avatar_contradiction_clause,[],[f120]) ).

thf(f120,plain,
    ( $false
    | ~ spl2_7
    | ~ spl2_10 ),
    inference(trivial_inequality_removal,[],[f119]) ).

thf(f119,plain,
    ( ( $true = $false )
    | ~ spl2_7
    | ~ spl2_10 ),
    inference(forward_demodulation,[],[f84,f98]) ).

thf(f98,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ~ spl2_10 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f84,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f82]) ).

thf(f82,plain,
    ( spl2_7
  <=> ( $true
      = ( sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

thf(f117,plain,
    ( ~ spl2_8
    | ~ spl2_9 ),
    inference(avatar_contradiction_clause,[],[f116]) ).

thf(f116,plain,
    ( $false
    | ~ spl2_8
    | ~ spl2_9 ),
    inference(trivial_inequality_removal,[],[f110]) ).

thf(f110,plain,
    ( ( $true = $false )
    | ~ spl2_8
    | ~ spl2_9 ),
    inference(superposition,[],[f88,f93]) ).

thf(f88,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f86]) ).

thf(f86,plain,
    ( spl2_8
  <=> ( $true
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

thf(f107,plain,
    ( spl2_9
    | ~ spl2_1
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f104,f96,f13,f91]) ).

thf(f104,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl2_1
    | ~ spl2_10 ),
    inference(trivial_inequality_removal,[],[f102]) ).

thf(f102,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( $true = $false )
    | ~ spl2_1
    | ~ spl2_10 ),
    inference(superposition,[],[f98,f67]) ).

thf(f67,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK0 @ X1 ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f100,plain,
    ( spl2_10
    | spl2_9
    | spl2_2 ),
    inference(avatar_split_clause,[],[f77,f17,f91,f96]) ).

thf(f77,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | spl2_2 ),
    inference(not_proxy_clausification,[],[f76]) ).

thf(f76,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK0 @ sK5 ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f74,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | spl2_2 ),
    inference(not_proxy_clausification,[],[f73]) ).

thf(f73,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f71]) ).

thf(f71,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f70]) ).

thf(f70,plain,
    ( ( $false
     != ( ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) ) ) )
    | spl2_2 ),
    inference(beta_eta_normalization,[],[f69]) ).

thf(f69,plain,
    ( ( ( ^ [Y0: a] : $false
        @ sK5 )
     != ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) )
        @ sK5 ) )
    | spl2_2 ),
    inference(negative_extensionality,[],[f19]) ).

thf(f19,plain,
    ( ( ( ^ [Y0: a] : $false )
     != ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f89,plain,
    ( spl2_7
    | spl2_8
    | spl2_2 ),
    inference(avatar_split_clause,[],[f78,f17,f86,f82]) ).

thf(f78,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f72]) ).

thf(f72,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f71]) ).

thf(f21,plain,
    ( spl2_2
    | spl2_1 ),
    inference(avatar_split_clause,[],[f10,f13,f17]) ).

thf(f10,plain,
    ( ( ( ^ [Y0: a] : $false )
      = ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) )
    | ( sK1 = sK0 ) ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ( ( ( ( ^ [Y0: a] : $false )
       != ( ^ [Y0: a] :
              ( ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) )
              | ( ~ ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) ) ) ) )
      | ( sK1 != sK0 ) )
    & ( ( ( ^ [Y0: a] : $false )
        = ( ^ [Y0: a] :
              ( ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) )
              | ( ~ ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) ) ) ) )
      | ( sK1 = sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).

thf(f8,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ( ( ^ [Y0: a] : $false )
           != ( ^ [Y0: a] :
                  ( ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) )
                  | ( ~ ( X0 @ Y0 )
                    & ( X1 @ Y0 ) ) ) ) )
          | ( X0 != X1 ) )
        & ( ( ( ^ [Y0: a] : $false )
            = ( ^ [Y0: a] :
                  ( ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) )
                  | ( ~ ( X0 @ Y0 )
                    & ( X1 @ Y0 ) ) ) ) )
          | ( X0 = X1 ) ) )
   => ( ( ( ( ^ [Y0: a] : $false )
         != ( ^ [Y0: a] :
                ( ( ~ ( sK1 @ Y0 )
                  & ( sK0 @ Y0 ) )
                | ( ~ ( sK0 @ Y0 )
                  & ( sK1 @ Y0 ) ) ) ) )
        | ( sK1 != sK0 ) )
      & ( ( ( ^ [Y0: a] : $false )
          = ( ^ [Y0: a] :
                ( ( ~ ( sK1 @ Y0 )
                  & ( sK0 @ Y0 ) )
                | ( ~ ( sK0 @ Y0 )
                  & ( sK1 @ Y0 ) ) ) ) )
        | ( sK1 = sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f7,plain,
    ? [X0: a > $o,X1: a > $o] :
      ( ( ( ( ^ [Y0: a] : $false )
         != ( ^ [Y0: a] :
                ( ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) )
                | ( ~ ( X0 @ Y0 )
                  & ( X1 @ Y0 ) ) ) ) )
        | ( X0 != X1 ) )
      & ( ( ( ^ [Y0: a] : $false )
          = ( ^ [Y0: a] :
                ( ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) )
                | ( ~ ( X0 @ Y0 )
                  & ( X1 @ Y0 ) ) ) ) )
        | ( X0 = X1 ) ) ),
    inference(nnf_transformation,[],[f6]) ).

thf(f6,plain,
    ? [X0: a > $o,X1: a > $o] :
      ( ( X0 = X1 )
    <~> ( ( ^ [Y0: a] : $false )
        = ( ^ [Y0: a] :
              ( ( ~ ( X1 @ Y0 )
                & ( X0 @ Y0 ) )
              | ( ~ ( X0 @ Y0 )
                & ( X1 @ Y0 ) ) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( X0 = X1 )
      <=> ( ( ^ [Y0: a] : $false )
          = ( ^ [Y0: a] :
                ( ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) )
                | ( ~ ( X0 @ Y0 )
                  & ( X1 @ Y0 ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( X0 = X1 )
      <=> ( ( ^ [X2: a] : $false )
          = ( ^ [X3: a] :
                ( ( ( X1 @ X3 )
                  & ~ ( X0 @ X3 ) )
                | ( ( X0 @ X3 )
                  & ~ ( X1 @ X3 ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( X0 = X1 )
      <=> ( ( ^ [X3: a] : $false )
          = ( ^ [X2: a] :
                ( ( ( X1 @ X2 )
                  & ~ ( X0 @ X2 ) )
                | ( ( X0 @ X2 )
                  & ~ ( X1 @ X2 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o] :
      ( ( X0 = X1 )
    <=> ( ( ^ [X3: a] : $false )
        = ( ^ [X2: a] :
              ( ( ( X1 @ X2 )
                & ~ ( X0 @ X2 ) )
              | ( ( X0 @ X2 )
                & ~ ( X1 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM46_pme) ).

thf(f20,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f11,f17,f13]) ).

thf(f11,plain,
    ( ( ( ^ [Y0: a] : $false )
     != ( ^ [Y0: a] :
            ( ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) )
    | ( sK1 != sK0 ) ),
    inference(cnf_transformation,[],[f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU856^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.15  % 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
% 0.16/0.36  % Computer : n004.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   : Sun May 19 15:47:08 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a TH0_THM_EQU_NAR problem
% 0.16/0.37  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
% 0.23/0.39  % (18412)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.23/0.39  % (18414)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 (3000ds/27Mi)
% 0.23/0.39  % (18413)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 (3000ds/4Mi)
% 0.23/0.39  % (18415)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.23/0.39  % (18417)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.23/0.39  % (18416)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 (3000ds/2Mi)
% 0.23/0.39  % (18418)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.23/0.39  % (18415)Instruction limit reached!
% 0.23/0.39  % (18415)------------------------------
% 0.23/0.39  % (18415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (18416)Instruction limit reached!
% 0.23/0.39  % (18416)------------------------------
% 0.23/0.39  % (18416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (18415)Termination reason: Unknown
% 0.23/0.39  % (18415)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (18415)Memory used [KB]: 5500
% 0.23/0.39  % (18415)Time elapsed: 0.004 s
% 0.23/0.39  % (18415)Instructions burned: 2 (million)
% 0.23/0.39  % (18415)------------------------------
% 0.23/0.39  % (18415)------------------------------
% 0.23/0.39  % (18416)Termination reason: Unknown
% 0.23/0.39  % (18420)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.23/0.39  % (18416)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (18416)Memory used [KB]: 5500
% 0.23/0.39  % (18416)Time elapsed: 0.003 s
% 0.23/0.39  % (18416)Instructions burned: 2 (million)
% 0.23/0.39  % (18416)------------------------------
% 0.23/0.39  % (18416)------------------------------
% 0.23/0.39  % (18413)Instruction limit reached!
% 0.23/0.39  % (18413)------------------------------
% 0.23/0.39  % (18413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (18413)Termination reason: Unknown
% 0.23/0.39  % (18413)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (18413)Memory used [KB]: 5500
% 0.23/0.39  % (18413)Time elapsed: 0.005 s
% 0.23/0.39  % (18413)Instructions burned: 4 (million)
% 0.23/0.39  % (18413)------------------------------
% 0.23/0.39  % (18413)------------------------------
% 0.23/0.39  % (18420)Refutation not found, incomplete strategy
% 0.23/0.39  % (18420)------------------------------
% 0.23/0.39  % (18420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (18420)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.39  
% 0.23/0.39  
% 0.23/0.39  % (18420)Memory used [KB]: 5500
% 0.23/0.39  % (18420)Time elapsed: 0.004 s
% 0.23/0.39  % (18420)Instructions burned: 2 (million)
% 0.23/0.39  % (18420)------------------------------
% 0.23/0.39  % (18420)------------------------------
% 0.23/0.39  % (18417)First to succeed.
% 0.23/0.39  % (18418)Also succeeded, but the first one will report.
% 0.23/0.40  % (18417)Refutation found. Thanks to Tanya!
% 0.23/0.40  % SZS status Theorem for theBenchmark
% 0.23/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.40  % (18417)------------------------------
% 0.23/0.40  % (18417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (18417)Termination reason: Refutation
% 0.23/0.40  
% 0.23/0.40  % (18417)Memory used [KB]: 5500
% 0.23/0.40  % (18417)Time elapsed: 0.011 s
% 0.23/0.40  % (18417)Instructions burned: 7 (million)
% 0.23/0.40  % (18417)------------------------------
% 0.23/0.40  % (18417)------------------------------
% 0.23/0.40  % (18410)Success in time 0.021 s
% 0.23/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------