TSTP Solution File: SET613^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET613^5 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 03:12:26 EDT 2024

% Result   : Theorem 0.12s 0.37s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   71 (  10 unt;   6 typ;   0 def)
%            Number of atoms       :  497 ( 128 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  596 ( 103   ~; 128   |;  91   &; 269   @)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   33 (  20   ^   8   !;   4   ?;  33   :)
%                                         (   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(f123,plain,
    $false,
    inference(avatar_sat_refutation,[],[f97,f100,f104,f108,f116,f122]) ).

thf(f122,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f121]) ).

thf(f121,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f117]) ).

thf(f117,plain,
    ( ( $false = $true )
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(superposition,[],[f90,f82]) ).

thf(f82,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f80]) ).

thf(f80,plain,
    ( spl2_1
  <=> ( ( sK1 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f90,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f88]) ).

thf(f88,plain,
    ( spl2_3
  <=> ( ( sK1 @ sK4 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f116,plain,
    ( ~ spl2_2
    | ~ spl2_4 ),
    inference(avatar_contradiction_clause,[],[f115]) ).

thf(f115,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f112]) ).

thf(f112,plain,
    ( ( $false = $true )
    | ~ spl2_2
    | ~ spl2_4 ),
    inference(superposition,[],[f86,f95]) ).

thf(f95,plain,
    ( ( $false
      = ( sK0 @ sK4 ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f93]) ).

thf(f93,plain,
    ( spl2_4
  <=> ( $false
      = ( sK0 @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f86,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f84]) ).

thf(f84,plain,
    ( spl2_2
  <=> ( ( sK0 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f108,plain,
    ( spl2_1
    | spl2_4 ),
    inference(avatar_split_clause,[],[f30,f93,f80]) ).

thf(f30,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( $false
      = ( sK0 @ sK4 ) ) ),
    inference(duplicate_literal_removal,[],[f29]) ).

thf(f29,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( $false
      = ( sK0 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f27]) ).

thf(f27,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) ) ),
    inference(duplicate_literal_removal,[],[f26]) ).

thf(f26,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) ) ),
    inference(not_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( ~ ( sK1 @ sK4 ) )
      = $false )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) )
    | ( $false
      = ( sK0 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ( ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( ( ~ ( sK1 @ sK4 ) )
      = $false )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( $false
      = ( ( sK0 @ sK4 )
        & ~ ( sK1 @ sK4 ) ) )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) )
    | ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f16]) ).

thf(f16,plain,
    ( ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $false )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) )
    | ( $false
      = ( ( sK0 @ sK4 )
        & ~ ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $false )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $false )
    | ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( $false
      = ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) )
        & ( ( sK0 @ sK4 )
          | ( sK1 @ sK4 ) ) ) )
    | ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( ( ( ( sK0 @ sK4 )
        & ~ ( sK1 @ sK4 ) )
      | ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) ) )
   != ( ~ ( ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) )
      & ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a] :
          ( ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) ) )
      @ sK4 )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ~ ( sK0 @ Y0 )
            & ( sK1 @ Y0 ) ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] :
          ( ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ~ ( sK0 @ Y0 )
            & ( sK1 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ~ ( sK0 @ Y0 )
            & ( sK1 @ Y0 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ^ [Y0: a] :
              ( ~ ( ( X0 @ Y0 )
                  & ( X1 @ Y0 ) )
              & ( ( X0 @ Y0 )
                | ( X1 @ Y0 ) ) ) )
       != ( ^ [Y0: a] :
              ( ( ( X0 @ Y0 )
                & ~ ( X1 @ Y0 ) )
              | ( ~ ( X0 @ Y0 )
                & ( X1 @ Y0 ) ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ~ ( ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) )
            & ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( ( ( sK0 @ Y0 )
              & ~ ( sK1 @ Y0 ) )
            | ( ~ ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

thf(f1,conjecture,
    ! [X1: a > $o,X0: a > $o] :
      ( ( ^ [X3: a] :
            ( ( ( X0 @ X3 )
              & ~ ( X1 @ X3 ) )
            | ( ~ ( X0 @ X3 )
              & ( X1 @ X3 ) ) ) )
      = ( ^ [X2: a] :
            ( ( ( X0 @ X2 )
              | ( X1 @ X2 ) )
            & ~ ( ( X0 @ X2 )
                & ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_87_pme) ).

thf(f104,plain,
    ( spl2_2
    | spl2_3 ),
    inference(avatar_split_clause,[],[f45,f88,f84]) ).

thf(f45,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f44]) ).

thf(f44,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f42]) ).

thf(f42,plain,
    ( ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK4 ) ) )
    | ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f40]) ).

thf(f40,plain,
    ( ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) ) )
    | ( ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f31]) ).

thf(f31,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( $false
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) )
    | ( $false
      = ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) ) )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f100,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f64,f93,f88]) ).

thf(f64,plain,
    ( ( $false
      = ( sK0 @ sK4 ) )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f63]) ).

thf(f63,plain,
    ( ( $false
      = ( sK0 @ sK4 ) )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f62]) ).

thf(f62,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( ( ~ ( sK0 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f60]) ).

thf(f60,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( sK0 @ sK4 ) )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f59]) ).

thf(f59,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( $false
      = ( sK0 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( $false
      = ( ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) ) )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f57]) ).

thf(f57,plain,
    ( ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $true )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f49]) ).

thf(f49,plain,
    ( ( ( ~ ( sK1 @ sK4 ) )
      = $true )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $true )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ( ( ( ( sK0 @ sK4 )
        & ~ ( sK1 @ sK4 ) )
      = $true )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $true )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ( ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $true )
    | ( ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( $true
      = ( ~ ( ( sK0 @ sK4 )
            & ( sK1 @ sK4 ) )
        & ( ( sK0 @ sK4 )
          | ( sK1 @ sK4 ) ) ) )
    | ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f97,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f73,f84,f80]) ).

thf(f73,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f70]) ).

thf(f70,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f68]) ).

thf(f68,plain,
    ( ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( ( ( sK0 @ sK4 )
        & ~ ( sK1 @ sK4 ) )
      = $true )
    | ( ( ~ ( sK0 @ sK4 )
        & ( sK1 @ sK4 ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f65]) ).

thf(f65,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f46]) ).

thf(f46,plain,
    ( ( $true
      = ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) ) )
    | ( ( ( ( sK0 @ sK4 )
          & ~ ( sK1 @ sK4 ) )
        | ( ~ ( sK0 @ sK4 )
          & ( sK1 @ sK4 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET613^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % 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
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon May 20 12:49:38 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a TH0_THM_EQU_NAR problem
% 0.12/0.35  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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36  % (23353)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)
% 0.12/0.36  % (23352)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.36  % (23354)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)
% 0.12/0.36  % (23355)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.12/0.36  % (23356)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)
% 0.12/0.36  % (23349)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.12/0.36  % (23352)Instruction limit reached!
% 0.12/0.36  % (23352)------------------------------
% 0.12/0.36  % (23352)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (23352)Termination reason: Unknown
% 0.12/0.36  % (23352)Termination phase: Saturation
% 0.12/0.36  % (23353)Instruction limit reached!
% 0.12/0.36  % (23353)------------------------------
% 0.12/0.36  % (23353)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  
% 0.12/0.36  % (23352)Memory used [KB]: 5500
% 0.12/0.36  % (23352)Time elapsed: 0.003 s
% 0.12/0.36  % (23352)Instructions burned: 2 (million)
% 0.12/0.36  % (23352)------------------------------
% 0.12/0.36  % (23352)------------------------------
% 0.12/0.36  % (23353)Termination reason: Unknown
% 0.12/0.36  % (23353)Termination phase: Saturation
% 0.12/0.36  
% 0.12/0.36  % (23353)Memory used [KB]: 5500
% 0.12/0.36  % (23353)Time elapsed: 0.003 s
% 0.12/0.36  % (23353)Instructions burned: 2 (million)
% 0.12/0.36  % (23353)------------------------------
% 0.12/0.36  % (23353)------------------------------
% 0.12/0.37  % (23356)Refutation not found, incomplete strategy
% 0.12/0.37  % (23356)------------------------------
% 0.12/0.37  % (23356)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (23356)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.37  
% 0.12/0.37  
% 0.12/0.37  % (23356)Memory used [KB]: 5500
% 0.12/0.37  % (23356)Time elapsed: 0.003 s
% 0.12/0.37  % (23356)Instructions burned: 2 (million)
% 0.12/0.37  % (23356)------------------------------
% 0.12/0.37  % (23356)------------------------------
% 0.12/0.37  % (23354)First to succeed.
% 0.12/0.37  % (23349)Also succeeded, but the first one will report.
% 0.12/0.37  % (23354)Refutation found. Thanks to Tanya!
% 0.12/0.37  % SZS status Theorem for theBenchmark
% 0.12/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37  % (23354)------------------------------
% 0.12/0.37  % (23354)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (23354)Termination reason: Refutation
% 0.12/0.37  
% 0.12/0.37  % (23354)Memory used [KB]: 5500
% 0.12/0.37  % (23354)Time elapsed: 0.006 s
% 0.12/0.37  % (23354)Instructions burned: 4 (million)
% 0.12/0.37  % (23354)------------------------------
% 0.12/0.37  % (23354)------------------------------
% 0.12/0.37  % (23348)Success in time 0.017 s
% 0.12/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------