TSTP Solution File: SEV447^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV447^1 : TPTP v8.2.0. Released v7.0.0.
% 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 : n025.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 04:13:49 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   84 (   6 unt;  10 typ;   0 def)
%            Number of atoms       :  552 ( 148 equ;   0 cnn)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  576 ( 126   ~; 129   |;  17   &; 287   @)
%                                         (  14 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;  15 con; 0-3 aty)
%            Number of variables   :   62 (   0   ^  36   !;  23   ?;  62   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    sK1: $tType ).

thf(func_def_0,type,
    'const/sets/IN': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).

thf(func_def_4,type,
    sK0: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_5,type,
    sK2: sK1 > $o ).

thf(func_def_6,type,
    sK3: sK1 > $o ).

thf(func_def_7,type,
    sK4: sK1 ).

thf(func_def_9,type,
    ph6: 
      !>[X0: $tType] : X0 ).

thf(func_def_11,type,
    sK7: sK1 ).

thf(func_def_12,type,
    sK8: sK1 ).

thf(func_def_13,type,
    sK9: sK1 ).

thf(f183,plain,
    $false,
    inference(avatar_sat_refutation,[],[f42,f47,f52,f54,f66,f75,f102,f129,f167,f173,f182]) ).

thf(f182,plain,
    ( ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f181]) ).

thf(f181,plain,
    ( $false
    | ~ spl5_1
    | spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f180,f40]) ).

thf(f40,plain,
    ( ( ( sK2 @ sK4 )
      = $true )
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f39]) ).

thf(f39,plain,
    ( spl5_3
  <=> ( ( sK2 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

thf(f180,plain,
    ( ( ( sK2 @ sK4 )
     != $true )
    | ~ spl5_1
    | spl5_2 ),
    inference(superposition,[],[f175,f27]) ).

thf(f27,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > $o,X2: X0] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).

thf(f175,plain,
    ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
     != $true )
    | ~ spl5_1
    | spl5_2 ),
    inference(superposition,[],[f37,f32]) ).

thf(f32,plain,
    ( ( sK2 = sK3 )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f31,plain,
    ( spl5_1
  <=> ( sK2 = sK3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

thf(f37,plain,
    ( ( $true
     != ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
    | spl5_2 ),
    inference(avatar_component_clause,[],[f35]) ).

thf(f35,plain,
    ( spl5_2
  <=> ( $true
      = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

thf(f173,plain,
    ( ~ spl5_5
    | spl5_6
    | ~ spl5_7 ),
    inference(avatar_contradiction_clause,[],[f172]) ).

thf(f172,plain,
    ( $false
    | ~ spl5_5
    | spl5_6
    | ~ spl5_7 ),
    inference(subsumption_resolution,[],[f171,f65]) ).

thf(f65,plain,
    ( ( ( sK2 @ sK7 )
      = $true )
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f63]) ).

thf(f63,plain,
    ( spl5_7
  <=> ( ( sK2 @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

thf(f171,plain,
    ( ( ( sK2 @ sK7 )
     != $true )
    | ~ spl5_5
    | spl5_6 ),
    inference(trivial_inequality_removal,[],[f170]) ).

thf(f170,plain,
    ( ( ( sK2 @ sK7 )
     != $true )
    | ( $true != $true )
    | ~ spl5_5
    | spl5_6 ),
    inference(superposition,[],[f60,f87]) ).

thf(f87,plain,
    ( ! [X0: sK1] :
        ( ( $true
          = ( sK3 @ X0 ) )
        | ( ( sK2 @ X0 )
         != $true ) )
    | ~ spl5_5 ),
    inference(superposition,[],[f27,f51]) ).

thf(f51,plain,
    ( ! [X3: sK1] :
        ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
          = $true )
        | ( $true
         != ( sK2 @ X3 ) ) )
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f50]) ).

thf(f50,plain,
    ( spl5_5
  <=> ! [X3: sK1] :
        ( ( $true
         != ( sK2 @ X3 ) )
        | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

thf(f60,plain,
    ( ( ( sK3 @ sK7 )
     != $true )
    | spl5_6 ),
    inference(avatar_component_clause,[],[f59]) ).

thf(f59,plain,
    ( spl5_6
  <=> ( ( sK3 @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

thf(f167,plain,
    ( ~ spl5_4
    | ~ spl5_6
    | ~ spl5_9 ),
    inference(avatar_contradiction_clause,[],[f166]) ).

thf(f166,plain,
    ( $false
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_9 ),
    inference(subsumption_resolution,[],[f162,f61]) ).

thf(f61,plain,
    ( ( ( sK3 @ sK7 )
      = $true )
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f59]) ).

thf(f162,plain,
    ( ( ( sK3 @ sK7 )
     != $true )
    | ~ spl5_4
    | ~ spl5_9 ),
    inference(trivial_inequality_removal,[],[f161]) ).

thf(f161,plain,
    ( ( $true = $false )
    | ( ( sK3 @ sK7 )
     != $true )
    | ~ spl5_4
    | ~ spl5_9 ),
    inference(superposition,[],[f82,f74]) ).

thf(f74,plain,
    ( ( ( sK2 @ sK7 )
      = $false )
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f72]) ).

thf(f72,plain,
    ( spl5_9
  <=> ( ( sK2 @ sK7 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

thf(f82,plain,
    ( ! [X0: sK1] :
        ( ( ( sK2 @ X0 )
          = $true )
        | ( $true
         != ( sK3 @ X0 ) ) )
    | ~ spl5_4 ),
    inference(superposition,[],[f46,f27]) ).

thf(f46,plain,
    ( ! [X3: sK1] :
        ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
         != $true )
        | ( $true
          = ( sK2 @ X3 ) ) )
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f45]) ).

thf(f45,plain,
    ( spl5_4
  <=> ! [X3: sK1] :
        ( ( $true
          = ( sK2 @ X3 ) )
        | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
         != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

thf(f129,plain,
    ( ~ spl5_1
    | ~ spl5_2
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f128]) ).

thf(f128,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2
    | spl5_3 ),
    inference(subsumption_resolution,[],[f125,f41]) ).

thf(f41,plain,
    ( ( ( sK2 @ sK4 )
     != $true )
    | spl5_3 ),
    inference(avatar_component_clause,[],[f39]) ).

thf(f125,plain,
    ( ( ( sK2 @ sK4 )
      = $true )
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f27,f116]) ).

thf(f116,plain,
    ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
      = $true )
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f36,f32]) ).

thf(f36,plain,
    ( ( $true
      = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f35]) ).

thf(f102,plain,
    ( ~ spl5_6
    | ~ spl5_8 ),
    inference(avatar_contradiction_clause,[],[f101]) ).

thf(f101,plain,
    ( $false
    | ~ spl5_6
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f100]) ).

thf(f100,plain,
    ( ( $true = $false )
    | ~ spl5_6
    | ~ spl5_8 ),
    inference(forward_demodulation,[],[f61,f70]) ).

thf(f70,plain,
    ( ( ( sK3 @ sK7 )
      = $false )
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f68]) ).

thf(f68,plain,
    ( spl5_8
  <=> ( ( sK3 @ sK7 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

thf(f75,plain,
    ( spl5_8
    | spl5_9
    | spl5_1 ),
    inference(avatar_split_clause,[],[f57,f31,f72,f68]) ).

thf(f57,plain,
    ( ( ( sK2 @ sK7 )
      = $false )
    | ( ( sK3 @ sK7 )
      = $false )
    | spl5_1 ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f55,plain,
    ( ( ( sK2 @ sK7 )
     != ( sK3 @ sK7 ) )
    | spl5_1 ),
    inference(negative_extensionality,[],[f33]) ).

thf(f33,plain,
    ( ( sK2 != sK3 )
    | spl5_1 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f66,plain,
    ( spl5_6
    | spl5_7
    | spl5_1 ),
    inference(avatar_split_clause,[],[f56,f31,f63,f59]) ).

thf(f56,plain,
    ( ( ( sK3 @ sK7 )
      = $true )
    | ( ( sK2 @ sK7 )
      = $true )
    | spl5_1 ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f54,plain,
    ( spl5_3
    | ~ spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f53,f35,f31,f39]) ).

thf(f53,plain,
    ( ( sK2 != sK3 )
    | ( $true
      = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
    | ( ( sK2 @ sK4 )
      = $true ) ),
    inference(forward_demodulation,[],[f24,f27]) ).

thf(f24,plain,
    ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
      = $true )
    | ( $true
      = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
    | ( sK2 != sK3 ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f20,plain,
    ( ( ! [X3: sK1] :
          ( ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
              = $true )
            | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
             != $true ) )
          & ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
             != $true )
            | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
              = $true ) ) )
      | ( sK2 = sK3 ) )
    & ( ( ( ( $true
            = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
          | ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
            = $true ) )
        & ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
           != $true )
          | ( $true
           != ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ) )
      | ( sK2 != sK3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f17,f19,f18]) ).

thf(f18,plain,
    ( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
        ( ( ! [X3: X0] :
              ( ( ( $true
                  = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
                | ( $true
                 != ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
              & ( ( $true
                 != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
                | ( $true
                  = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) )
          | ( X1 = X2 ) )
        & ( ? [X4: X0] :
              ( ( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
                  = $true )
                | ( $true
                  = ( 'const/sets/IN' @ X0 @ X4 @ X1 ) ) )
              & ( ( $true
                 != ( 'const/sets/IN' @ X0 @ X4 @ X1 ) )
                | ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
                 != $true ) ) )
          | ( X1 != X2 ) ) )
   => ( ( ! [X3: sK1] :
            ( ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
                = $true )
              | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
               != $true ) )
            & ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
               != $true )
              | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
                = $true ) ) )
        | ( sK2 = sK3 ) )
      & ( ? [X4: sK1] :
            ( ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
                = $true )
              | ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
                = $true ) )
            & ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
               != $true )
              | ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
               != $true ) ) )
        | ( sK2 != sK3 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f19,plain,
    ( ? [X4: sK1] :
        ( ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
            = $true )
          | ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
            = $true ) )
        & ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
           != $true )
          | ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
           != $true ) ) )
   => ( ( ( $true
          = ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
        | ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
          = $true ) )
      & ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
         != $true )
        | ( $true
         != ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
      ( ( ! [X3: X0] :
            ( ( ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
              | ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
            & ( ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
              | ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) )
        | ( X1 = X2 ) )
      & ( ? [X4: X0] :
            ( ( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
                = $true )
              | ( $true
                = ( 'const/sets/IN' @ X0 @ X4 @ X1 ) ) )
            & ( ( $true
               != ( 'const/sets/IN' @ X0 @ X4 @ X1 ) )
              | ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
               != $true ) ) )
        | ( X1 != X2 ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,plain,
    ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
      ( ( ! [X3: X0] :
            ( ( ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
              | ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
            & ( ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
              | ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) )
        | ( X1 = X2 ) )
      & ( ? [X3: X0] :
            ( ( ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
              | ( $true
                = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
            & ( ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
              | ( $true
               != ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) )
        | ( X1 != X2 ) ) ),
    inference(nnf_transformation,[],[f11]) ).

thf(f11,plain,
    ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
      ( ( X1 != X2 )
    <~> ? [X3: X0] :
          ( ( $true
            = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
        <=> ( $true
           != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
    inference(ennf_transformation,[],[f10]) ).

thf(f10,plain,
    ~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
        ( ? [X3: X0] :
            ( ( $true
              = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
          <=> ( $true
             != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
      <=> ( X1 != X2 ) ),
    inference(flattening,[],[f9]) ).

thf(f9,plain,
    ~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
        ( ? [X3: X0] :
            ( ( $true
             != ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
          <=> ( $true
              = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
      <=> ( X1 != X2 ) ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
      ? [X3: X0] :
        ( ( ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
          = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
        = ( X1 != X2 ) ),
    inference(rectify,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ! [X0: $tType,X2: X0 > $o,X3: X0 > $o] :
      ? [X4: X0] :
        ( ( ( ~ ( 'const/sets/IN' @ X0 @ X4 @ X2 ) )
          = ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
        = ( X2 != X3 ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o] :
    ? [X4: X0] :
      ( ( ( ~ ( 'const/sets/IN' @ X0 @ X4 @ X2 ) )
        = ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
      = ( X2 != X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_EQUAL_SETS_') ).

thf(f52,plain,
    ( spl5_1
    | spl5_5 ),
    inference(avatar_split_clause,[],[f48,f50,f31]) ).

thf(f48,plain,
    ! [X3: sK1] :
      ( ( sK2 = sK3 )
      | ( $true
       != ( sK2 @ X3 ) )
      | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
        = $true ) ),
    inference(forward_demodulation,[],[f25,f27]) ).

thf(f25,plain,
    ! [X3: sK1] :
      ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
        = $true )
      | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
       != $true )
      | ( sK2 = sK3 ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f47,plain,
    ( spl5_1
    | spl5_4 ),
    inference(avatar_split_clause,[],[f43,f45,f31]) ).

thf(f43,plain,
    ! [X3: sK1] :
      ( ( $true
        = ( sK2 @ X3 ) )
      | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
       != $true )
      | ( sK2 = sK3 ) ),
    inference(forward_demodulation,[],[f26,f27]) ).

thf(f26,plain,
    ! [X3: sK1] :
      ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
       != $true )
      | ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
        = $true )
      | ( sK2 = sK3 ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f42,plain,
    ( ~ spl5_1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f29,f39,f35,f31]) ).

thf(f29,plain,
    ( ( ( sK2 @ sK4 )
     != $true )
    | ( sK2 != sK3 )
    | ( $true
     != ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ),
    inference(forward_demodulation,[],[f23,f27]) ).

thf(f23,plain,
    ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
     != $true )
    | ( $true
     != ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
    | ( sK2 != sK3 ) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV447^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14  % 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
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 19:18:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH1_THM_EQU_NAR problem
% 0.14/0.35  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
% 0.14/0.37  % (30121)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.37  % (30122)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)
% 0.14/0.37  % (30123)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)
% 0.14/0.37  % (30124)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37  % (30125)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)
% 0.14/0.37  % (30126)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)
% 0.14/0.37  % (30127)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.37  % (30128)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)
% 0.14/0.37  % Exception at run slice level
% 0.14/0.37  User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.14/0.37  % (30124)Instruction limit reached!
% 0.14/0.37  % (30124)------------------------------
% 0.14/0.37  % (30124)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (30124)Termination reason: Unknown
% 0.14/0.37  % (30124)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (30124)Memory used [KB]: 5500
% 0.14/0.37  % (30124)Time elapsed: 0.004 s
% 0.14/0.37  % (30124)Instructions burned: 3 (million)
% 0.14/0.37  % (30124)------------------------------
% 0.14/0.37  % (30124)------------------------------
% 0.14/0.38  % (30122)Instruction limit reached!
% 0.14/0.38  % (30122)------------------------------
% 0.14/0.38  % (30122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (30122)Termination reason: Unknown
% 0.14/0.38  % (30122)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (30122)Memory used [KB]: 5500
% 0.14/0.38  % (30122)Time elapsed: 0.005 s
% 0.14/0.38  % (30122)Instructions burned: 4 (million)
% 0.14/0.38  % (30122)------------------------------
% 0.14/0.38  % (30122)------------------------------
% 0.14/0.38  % (30128)Instruction limit reached!
% 0.14/0.38  % (30128)------------------------------
% 0.14/0.38  % (30128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (30128)Termination reason: Unknown
% 0.14/0.38  % (30128)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (30128)Memory used [KB]: 5500
% 0.14/0.38  % (30128)Time elapsed: 0.004 s
% 0.14/0.38  % (30128)Instructions burned: 3 (million)
% 0.14/0.38  % (30128)------------------------------
% 0.14/0.38  % (30128)------------------------------
% 0.21/0.39  % (30127)Instruction limit reached!
% 0.21/0.39  % (30127)------------------------------
% 0.21/0.39  % (30127)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (30127)Termination reason: Unknown
% 0.21/0.39  % (30127)Termination phase: Saturation
% 0.21/0.39  
% 0.21/0.39  % (30127)Memory used [KB]: 5628
% 0.21/0.39  % (30127)Time elapsed: 0.015 s
% 0.21/0.39  % (30126)First to succeed.
% 0.21/0.39  % (30127)Instructions burned: 18 (million)
% 0.21/0.39  % (30127)------------------------------
% 0.21/0.39  % (30127)------------------------------
% 0.21/0.39  % (30129)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.39  % (30126)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (30126)------------------------------
% 0.21/0.39  % (30126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (30126)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (30126)Memory used [KB]: 5628
% 0.21/0.39  % (30126)Time elapsed: 0.017 s
% 0.21/0.39  % (30126)Instructions burned: 18 (million)
% 0.21/0.39  % (30126)------------------------------
% 0.21/0.39  % (30126)------------------------------
% 0.21/0.39  % (30120)Success in time 0.026 s
% 0.21/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------