TSTP Solution File: SYO016^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO016^1 : TPTP v8.2.0. Released v3.7.0.
% 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 : n016.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 09:02:14 EDT 2024

% Result   : Theorem 0.11s 0.37s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  116 (  15 unt;  11 typ;   0 def)
%            Number of atoms       :  762 ( 116 equ;   0 cnn)
%            Maximal formula atoms :    9 (   7 avg)
%            Number of connectives :  668 ( 121   ~; 151   |;   0   &; 333   @)
%                                         (  11 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   66 (  66   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  22 usr;  14 con; 0-2 aty)
%                                         (  20  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   52 (  41   ^  10   !;   0   ?;  52   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

thf(func_def_2,type,
    h: $o > $o ).

thf(func_def_12,type,
    sK1: $o > $o ).

thf(func_def_14,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(func_def_16,type,
    sK3: $o > $o ).

thf(func_def_17,type,
    sK4: $o > $o ).

thf(func_def_18,type,
    sK5: $o > $o ).

thf(func_def_19,type,
    sK6: $o > $o ).

thf(func_def_20,type,
    sK7: $o > $o ).

thf(func_def_21,type,
    sK8: $o > $o ).

thf(func_def_22,type,
    sK9: $o > $o ).

thf(f521,plain,
    $false,
    inference(avatar_sat_refutation,[],[f44,f58,f75,f81,f161,f189,f191,f207,f301,f307,f361,f366,f384,f520]) ).

thf(f520,plain,
    ( spl0_2
    | ~ spl0_6
    | ~ spl0_12
    | ~ spl0_13
    | ~ spl0_14 ),
    inference(avatar_contradiction_clause,[],[f519]) ).

thf(f519,plain,
    ( $false
    | spl0_2
    | ~ spl0_6
    | ~ spl0_12
    | ~ spl0_13
    | ~ spl0_14 ),
    inference(subsumption_resolution,[],[f480,f187]) ).

thf(f187,plain,
    ( ( $false
      = ( h @ $true ) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f185]) ).

thf(f185,plain,
    ( spl0_12
  <=> ( $false
      = ( h @ $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

thf(f480,plain,
    ( ( $false
     != ( h @ $true ) )
    | spl0_2
    | ~ spl0_6
    | ~ spl0_13
    | ~ spl0_14 ),
    inference(trivial_inequality_removal,[],[f477]) ).

thf(f477,plain,
    ( ( $false = $true )
    | ( $false
     != ( h @ $true ) )
    | spl0_2
    | ~ spl0_6
    | ~ spl0_13
    | ~ spl0_14 ),
    inference(constrained_superposition,[],[f468,f365]) ).

thf(f365,plain,
    ( ( $true
      = ( sK5 @ ( h @ $true ) ) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f363]) ).

thf(f363,plain,
    ( spl0_14
  <=> ( $true
      = ( sK5 @ ( h @ $true ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

thf(f468,plain,
    ( ( $false
      = ( sK5 @ $false ) )
    | spl0_2
    | ~ spl0_6
    | ~ spl0_13 ),
    inference(subsumption_resolution,[],[f464,f32]) ).

thf(f32,plain,
    ( ( $true
     != ( h @ $false ) )
    | spl0_2 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f31,plain,
    ( spl0_2
  <=> ( $true
      = ( h @ $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f464,plain,
    ( ( $false
      = ( sK5 @ $false ) )
    | ( $true
      = ( h @ $false ) )
    | ~ spl0_6
    | ~ spl0_13 ),
    inference(beta_eta_normalization,[],[f463]) ).

thf(f463,plain,
    ( ( ( ^ [Y0: $o] :
            ( h
            @ ( ^ [Y1: $o] : $false
              @ Y0 ) )
        @ ( h @ $false ) )
      = $true )
    | ( $false
      = ( sK5 @ $false ) )
    | ~ spl0_6
    | ~ spl0_13 ),
    inference(superposition,[],[f360,f57]) ).

thf(f57,plain,
    ( ! [X1: $o > $o] :
        ( ( $false
          = ( X1 @ ( h @ $true ) ) )
        | ( ( X1 @ ( h @ $false ) )
          = $true ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f56]) ).

thf(f56,plain,
    ( spl0_6
  <=> ! [X1: $o > $o] :
        ( ( $false
          = ( X1 @ ( h @ $true ) ) )
        | ( ( X1 @ ( h @ $false ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f360,plain,
    ( ( $false
      = ( sK5 @ ( h @ $false ) ) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f358]) ).

thf(f358,plain,
    ( spl0_13
  <=> ( $false
      = ( sK5 @ ( h @ $false ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

thf(f384,plain,
    ( spl0_2
    | ~ spl0_6
    | ~ spl0_9 ),
    inference(avatar_contradiction_clause,[],[f383]) ).

thf(f383,plain,
    ( $false
    | spl0_2
    | ~ spl0_6
    | ~ spl0_9 ),
    inference(trivial_inequality_removal,[],[f367]) ).

thf(f367,plain,
    ( ( $false = $true )
    | spl0_2
    | ~ spl0_6
    | ~ spl0_9 ),
    inference(superposition,[],[f151,f305]) ).

thf(f305,plain,
    ( ( ( sK1 @ $false )
      = $false )
    | spl0_2
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f129,f32]) ).

thf(f129,plain,
    ( ( $true
      = ( h @ $false ) )
    | ( ( sK1 @ $false )
      = $false )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f98]) ).

thf(f98,plain,
    ( ( ( ^ [Y0: $o] :
            ( h
            @ ( ^ [Y1: $o] : $false
              @ Y0 ) )
        @ ( h @ $false ) )
      = $true )
    | ( ( sK1 @ $false )
      = $false )
    | ~ spl0_6 ),
    inference(superposition,[],[f16,f57]) ).

thf(f16,plain,
    ( $false
    = ( sK1 @ ( h @ $false ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( $false
    = ( ( sK1
        @ ( h
          @ ( !! @ ( $o > $o )
            @ ^ [Y0: $o > $o] :
                ( ( Y0 @ ( h @ $true ) )
               => ( Y0 @ ( h @ $false ) ) ) ) ) )
     => ( sK1 @ ( h @ $false ) ) ) ),
    inference(beta_eta_normalization,[],[f14]) ).

thf(f14,plain,
    ( $false
    = ( ^ [Y0: $o > $o] :
          ( ( Y0
            @ ( h
              @ ( !! @ ( $o > $o )
                @ ^ [Y1: $o > $o] :
                    ( ( Y1 @ ( h @ $true ) )
                   => ( Y1 @ ( h @ $false ) ) ) ) ) )
         => ( Y0 @ ( h @ $false ) ) )
      @ sK1 ) ),
    inference(sigma_clausification,[],[f13]) ).

thf(f13,plain,
    ( $true
   != ( !! @ ( $o > $o )
      @ ^ [Y0: $o > $o] :
          ( ( Y0
            @ ( h
              @ ( !! @ ( $o > $o )
                @ ^ [Y1: $o > $o] :
                    ( ( Y1 @ ( h @ $true ) )
                   => ( Y1 @ ( h @ $false ) ) ) ) ) )
         => ( Y0 @ ( h @ $false ) ) ) ) ),
    inference(beta_eta_normalization,[],[f12]) ).

thf(f12,plain,
    ( ( ^ [Y0: $o,Y1: $o] :
          ( !! @ ( $o > $o )
          @ ^ [Y2: $o > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) )
      @ ( h
        @ ( ^ [Y0: $o,Y1: $o] :
              ( !! @ ( $o > $o )
              @ ^ [Y2: $o > $o] :
                  ( ( Y2 @ Y0 )
                 => ( Y2 @ Y1 ) ) )
          @ ( h @ $true )
          @ ( h @ $false ) ) )
      @ ( h @ $false ) )
   != $true ),
    inference(definition_unfolding,[],[f11,f10,f10]) ).

thf(f10,plain,
    ( leibeq
    = ( ^ [Y0: $o,Y1: $o] :
          ( !! @ ( $o > $o )
          @ ^ [Y2: $o > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f6]) ).

thf(f6,plain,
    ( leibeq
    = ( ^ [Y0: $o,Y1: $o] :
          ( !! @ ( $o > $o )
          @ ^ [Y2: $o > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ( leibeq
    = ( ^ [X0: $o,X1: $o] :
        ! [X2: $o > $o] :
          ( ( X2 @ X0 )
         => ( X2 @ X1 ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( leibeq
    = ( ^ [X0: $o,X1: $o] :
        ! [X2: $o > $o] :
          ( ( X2 @ X0 )
         => ( X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq) ).

thf(f11,plain,
    ( $true
   != ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ) ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ( $true
   != ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ) ),
    inference(flattening,[],[f8]) ).

thf(f8,plain,
    ( $true
   != ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(f151,plain,
    ( ( ( sK1 @ $false )
      = $true )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f149]) ).

thf(f149,plain,
    ( spl0_9
  <=> ( ( sK1 @ $false )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

thf(f366,plain,
    ( spl0_14
    | spl0_9
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f355,f185,f149,f363]) ).

thf(f355,plain,
    ( ( $true
      = ( sK5 @ ( h @ $true ) ) )
    | ( ( sK1 @ $false )
      = $true )
    | ~ spl0_12 ),
    inference(binary_proxy_clausification,[],[f353]) ).

thf(f353,plain,
    ( ( $false
      = ( ( sK5 @ ( h @ $true ) )
       => ( sK5 @ ( h @ $false ) ) ) )
    | ( ( sK1 @ $false )
      = $true )
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f352]) ).

thf(f352,plain,
    ( ( ( ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) )
        @ sK5 )
      = $false )
    | ( ( sK1 @ $false )
      = $true )
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f348]) ).

thf(f348,plain,
    ( ( $true
     != ( !! @ ( $o > $o )
        @ ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) ) ) )
    | ( ( sK1 @ $false )
      = $true )
    | ~ spl0_12 ),
    inference(constrained_superposition,[],[f17,f187]) ).

thf(f17,plain,
    ( $true
    = ( sK1
      @ ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f361,plain,
    ( spl0_13
    | spl0_9
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f354,f185,f149,f358]) ).

thf(f354,plain,
    ( ( $false
      = ( sK5 @ ( h @ $false ) ) )
    | ( ( sK1 @ $false )
      = $true )
    | ~ spl0_12 ),
    inference(binary_proxy_clausification,[],[f353]) ).

thf(f307,plain,
    ( ~ spl0_1
    | ~ spl0_7 ),
    inference(avatar_contradiction_clause,[],[f306]) ).

thf(f306,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f225,f29]) ).

thf(f29,plain,
    ( ( $true
      = ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f27]) ).

thf(f27,plain,
    ( spl0_1
  <=> ( $true
      = ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f225,plain,
    ( ( $true
     != ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) )
    | ~ spl0_7 ),
    inference(trivial_inequality_removal,[],[f224]) ).

thf(f224,plain,
    ( ( $false = $true )
    | ( $true
     != ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) )
    | ~ spl0_7 ),
    inference(constrained_superposition,[],[f17,f74]) ).

thf(f74,plain,
    ( ( $false
      = ( sK1 @ $true ) )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f72]) ).

thf(f72,plain,
    ( spl0_7
  <=> ( $false
      = ( sK1 @ $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

thf(f301,plain,
    ( ~ spl0_2
    | spl0_5
    | ~ spl0_10 ),
    inference(avatar_contradiction_clause,[],[f300]) ).

thf(f300,plain,
    ( $false
    | ~ spl0_2
    | spl0_5
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f291,f156]) ).

thf(f156,plain,
    ( ( ( h @ $true )
      = $true )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f154]) ).

thf(f154,plain,
    ( spl0_10
  <=> ( ( h @ $true )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

thf(f291,plain,
    ( ( ( h @ $true )
     != $true )
    | ~ spl0_2
    | spl0_5
    | ~ spl0_10 ),
    inference(trivial_inequality_removal,[],[f279]) ).

thf(f279,plain,
    ( ( $false = $true )
    | ( ( h @ $true )
     != $true )
    | ~ spl0_2
    | spl0_5
    | ~ spl0_10 ),
    inference(constrained_superposition,[],[f248,f246]) ).

thf(f246,plain,
    ( ( ( sK3 @ ( h @ $true ) )
      = $true )
    | spl0_5
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f242,f53]) ).

thf(f53,plain,
    ( ( $true
     != ( sK1 @ $true ) )
    | spl0_5 ),
    inference(avatar_component_clause,[],[f52]) ).

thf(f52,plain,
    ( spl0_5
  <=> ( $true
      = ( sK1 @ $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f242,plain,
    ( ( ( sK3 @ ( h @ $true ) )
      = $true )
    | ( $true
      = ( sK1 @ $true ) )
    | ~ spl0_10 ),
    inference(binary_proxy_clausification,[],[f240]) ).

thf(f240,plain,
    ( ( $false
      = ( ( sK3 @ ( h @ $true ) )
       => ( sK3 @ ( h @ $false ) ) ) )
    | ( $true
      = ( sK1 @ $true ) )
    | ~ spl0_10 ),
    inference(beta_eta_normalization,[],[f239]) ).

thf(f239,plain,
    ( ( ( ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) )
        @ sK3 )
      = $false )
    | ( $true
      = ( sK1 @ $true ) )
    | ~ spl0_10 ),
    inference(sigma_clausification,[],[f232]) ).

thf(f232,plain,
    ( ( $true
      = ( sK1 @ $true ) )
    | ( $true
     != ( !! @ ( $o > $o )
        @ ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) ) ) )
    | ~ spl0_10 ),
    inference(constrained_superposition,[],[f17,f156]) ).

thf(f248,plain,
    ( ( $false
      = ( sK3 @ $true ) )
    | ~ spl0_2
    | spl0_5
    | ~ spl0_10 ),
    inference(superposition,[],[f245,f33]) ).

thf(f33,plain,
    ( ( $true
      = ( h @ $false ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f245,plain,
    ( ( ( sK3 @ ( h @ $false ) )
      = $false )
    | spl0_5
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f241,f53]) ).

thf(f241,plain,
    ( ( ( sK3 @ ( h @ $false ) )
      = $false )
    | ( $true
      = ( sK1 @ $true ) )
    | ~ spl0_10 ),
    inference(binary_proxy_clausification,[],[f240]) ).

thf(f207,plain,
    ( ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f206]) ).

thf(f206,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f194]) ).

thf(f194,plain,
    ( ( $false = $true )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f42,f33]) ).

thf(f42,plain,
    ( ( $false
      = ( h @ $false ) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f40]) ).

thf(f40,plain,
    ( spl0_4
  <=> ( $false
      = ( h @ $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f191,plain,
    ( spl0_12
    | spl0_2
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f138,f56,f31,f185]) ).

thf(f138,plain,
    ( ( $true
      = ( h @ $false ) )
    | ( $false
      = ( h @ $true ) )
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f86]) ).

thf(f86,plain,
    ( ( ( h @ $true )
      = ( h @ $false ) )
    | ~ spl0_6 ),
    inference(leibniz_equality_elimination,[],[f57]) ).

thf(f189,plain,
    ( ~ spl0_2
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f84,f52,f31]) ).

thf(f84,plain,
    ( ( $true
     != ( h @ $false ) )
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f82]) ).

thf(f82,plain,
    ( ( $true
     != ( h @ $false ) )
    | ( $false = $true )
    | ~ spl0_5 ),
    inference(constrained_superposition,[],[f54,f16]) ).

thf(f54,plain,
    ( ( $true
      = ( sK1 @ $true ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f52]) ).

thf(f161,plain,
    ( spl0_10
    | spl0_4
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f106,f56,f40,f154]) ).

thf(f106,plain,
    ( ( ( h @ $true )
      = $true )
    | ( $false
      = ( h @ $false ) )
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f87]) ).

thf(f87,plain,
    ( ( ( h @ $true )
      = ( h @ $false ) )
    | ~ spl0_6 ),
    inference(leibniz_equality_elimination,[],[f57]) ).

thf(f81,plain,
    ( spl0_7
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f77,f31,f72]) ).

thf(f77,plain,
    ( ( $false
      = ( sK1 @ $true ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f16,f33]) ).

thf(f75,plain,
    ( spl0_7
    | spl0_6
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f64,f27,f56,f72]) ).

thf(f64,plain,
    ( ! [X1: $o > $o] :
        ( ( $false
          = ( X1 @ ( h @ $true ) ) )
        | ( ( X1 @ ( h @ $false ) )
          = $true )
        | ( $false
          = ( sK1 @ $true ) ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f63]) ).

thf(f63,plain,
    ( ! [X1: $o > $o] :
        ( ( $false
          = ( sK1 @ $true ) )
        | ( ( ( X1 @ ( h @ $true ) )
           => ( X1 @ ( h @ $false ) ) )
          = $true ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f62]) ).

thf(f62,plain,
    ( ! [X1: $o > $o] :
        ( ( $false
          = ( sK1 @ $true ) )
        | ( ( ^ [Y0: $o > $o] :
                ( ( Y0 @ ( h @ $true ) )
               => ( Y0 @ ( h @ $false ) ) )
            @ X1 )
          = $true ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f61]) ).

thf(f61,plain,
    ( ( $false
      = ( sK1 @ $true ) )
    | ( $false
     != ( !! @ ( $o > $o )
        @ ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) ) ) )
    | ~ spl0_1 ),
    inference(constrained_superposition,[],[f16,f29]) ).

thf(f58,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f50,f31,f56,f52]) ).

thf(f50,plain,
    ( ! [X1: $o > $o] :
        ( ( $true
          = ( sK1 @ $true ) )
        | ( $false
          = ( X1 @ ( h @ $true ) ) )
        | ( ( X1 @ ( h @ $false ) )
          = $true ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f49]) ).

thf(f49,plain,
    ( ! [X1: $o > $o] :
        ( ( $true
          = ( sK1 @ $true ) )
        | ( ( ( X1 @ ( h @ $true ) )
           => ( X1 @ ( h @ $false ) ) )
          = $true ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f48]) ).

thf(f48,plain,
    ( ! [X1: $o > $o] :
        ( ( $true
          = ( sK1 @ $true ) )
        | ( ( ^ [Y0: $o > $o] :
                ( ( Y0 @ ( h @ $true ) )
               => ( Y0 @ ( h @ $false ) ) )
            @ X1 )
          = $true ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f46]) ).

thf(f46,plain,
    ( ( $true
      = ( sK1 @ $true ) )
    | ( $false
     != ( !! @ ( $o > $o )
        @ ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) ) ) )
    | ~ spl0_2 ),
    inference(constrained_superposition,[],[f17,f33]) ).

thf(f44,plain,
    ( spl0_2
    | spl0_1 ),
    inference(avatar_split_clause,[],[f21,f27,f31]) ).

thf(f21,plain,
    ( ( $true
      = ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) ) )
    | ( $true
      = ( h @ $false ) ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f20,plain,
    ( ( h
      @ ( !! @ ( $o > $o )
        @ ^ [Y0: $o > $o] :
            ( ( Y0 @ ( h @ $true ) )
           => ( Y0 @ ( h @ $false ) ) ) ) )
   != ( h @ $false ) ),
    inference(trivial_inequality_removal,[],[f18]) ).

thf(f18,plain,
    ( ( $false = $true )
    | ( ( h
        @ ( !! @ ( $o > $o )
          @ ^ [Y0: $o > $o] :
              ( ( Y0 @ ( h @ $true ) )
             => ( Y0 @ ( h @ $false ) ) ) ) )
     != ( h @ $false ) ) ),
    inference(constrained_superposition,[],[f17,f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SYO016^1 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12  % 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
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon May 20 09:51:37 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  This is a TH0_THM_EQU_NAR problem
% 0.11/0.33  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
% 0.11/0.35  % (16565)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)
% 0.11/0.35  % (16563)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)
% 0.11/0.35  % (16564)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.35  % (16566)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)
% 0.11/0.35  % (16567)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.35  % (16568)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)
% 0.11/0.35  % (16562)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)
% 0.11/0.35  % (16564)Instruction limit reached!
% 0.11/0.35  % (16564)------------------------------
% 0.11/0.35  % (16564)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (16564)Termination reason: Unknown
% 0.11/0.35  % (16566)Refutation not found, incomplete strategy
% 0.11/0.35  % (16566)------------------------------
% 0.11/0.35  % (16566)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (16564)Termination phase: Saturation
% 0.11/0.35  % (16565)Instruction limit reached!
% 0.11/0.35  % (16565)------------------------------
% 0.11/0.35  % (16565)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  
% 0.11/0.35  % (16565)Termination reason: Unknown
% 0.11/0.35  % (16565)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (16564)Memory used [KB]: 5373
% 0.11/0.35  % (16564)Time elapsed: 0.003 s
% 0.11/0.35  % (16565)Memory used [KB]: 5500
% 0.11/0.35  % (16564)Instructions burned: 2 (million)
% 0.11/0.35  % (16565)Time elapsed: 0.003 s
% 0.11/0.35  % (16564)------------------------------
% 0.11/0.35  % (16564)------------------------------
% 0.11/0.35  % (16565)Instructions burned: 2 (million)
% 0.11/0.35  % (16565)------------------------------
% 0.11/0.35  % (16565)------------------------------
% 0.11/0.35  % (16566)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35  
% 0.11/0.35  
% 0.11/0.35  % (16566)Memory used [KB]: 5373
% 0.11/0.35  % (16568)Refutation not found, incomplete strategy
% 0.11/0.35  % (16568)------------------------------
% 0.11/0.35  % (16568)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (16568)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35  
% 0.11/0.35  
% 0.11/0.35  % (16568)Memory used [KB]: 5500
% 0.11/0.35  % (16568)Time elapsed: 0.002 s
% 0.11/0.35  % (16568)Instructions burned: 1 (million)
% 0.11/0.35  % (16568)------------------------------
% 0.11/0.35  % (16568)------------------------------
% 0.11/0.35  % (16566)Time elapsed: 0.003 s
% 0.11/0.35  % (16566)Instructions burned: 1 (million)
% 0.11/0.35  % (16566)------------------------------
% 0.11/0.35  % (16566)------------------------------
% 0.11/0.35  % (16563)Refutation not found, incomplete strategy
% 0.11/0.35  % (16563)------------------------------
% 0.11/0.35  % (16563)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (16563)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35  
% 0.11/0.35  
% 0.11/0.35  % (16563)Memory used [KB]: 5500
% 0.11/0.35  % (16563)Time elapsed: 0.003 s
% 0.11/0.35  % (16563)Instructions burned: 2 (million)
% 0.11/0.35  % (16563)------------------------------
% 0.11/0.35  % (16563)------------------------------
% 0.11/0.35  % (16561)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.11/0.35  % (16562)Instruction limit reached!
% 0.11/0.35  % (16562)------------------------------
% 0.11/0.35  % (16562)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (16562)Termination reason: Unknown
% 0.11/0.35  % (16562)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (16562)Memory used [KB]: 5500
% 0.11/0.35  % (16562)Time elapsed: 0.004 s
% 0.11/0.35  % (16562)Instructions burned: 4 (million)
% 0.11/0.35  % (16562)------------------------------
% 0.11/0.35  % (16562)------------------------------
% 0.11/0.36  % (16567)Instruction limit reached!
% 0.11/0.36  % (16567)------------------------------
% 0.11/0.36  % (16567)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36  % (16567)Termination reason: Unknown
% 0.11/0.36  % (16567)Termination phase: Saturation
% 0.11/0.36  
% 0.11/0.36  % (16567)Memory used [KB]: 5628
% 0.11/0.36  % (16567)Time elapsed: 0.012 s
% 0.11/0.36  % (16567)Instructions burned: 18 (million)
% 0.11/0.36  % (16567)------------------------------
% 0.11/0.36  % (16567)------------------------------
% 0.11/0.36  % (16569)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)
% 0.11/0.36  % (16570)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.11/0.36  % (16571)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.36  % (16573)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.36  % (16571)Refutation not found, incomplete strategy
% 0.11/0.36  % (16571)------------------------------
% 0.11/0.36  % (16571)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36  % (16571)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36  
% 0.11/0.36  
% 0.11/0.36  % (16571)Memory used [KB]: 5373
% 0.11/0.36  % (16571)Time elapsed: 0.002 s
% 0.11/0.36  % (16571)Instructions burned: 1 (million)
% 0.11/0.36  % (16571)------------------------------
% 0.11/0.36  % (16571)------------------------------
% 0.11/0.36  % (16574)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.11/0.36  % (16572)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.11/0.36  % (16570)Refutation not found, incomplete strategy
% 0.11/0.36  % (16570)------------------------------
% 0.11/0.36  % (16570)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36  % (16570)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36  
% 0.11/0.36  
% 0.11/0.36  % (16570)Memory used [KB]: 5500
% 0.11/0.36  % (16570)Time elapsed: 0.004 s
% 0.11/0.36  % (16570)Instructions burned: 4 (million)
% 0.11/0.36  % (16570)------------------------------
% 0.11/0.36  % (16570)------------------------------
% 0.11/0.36  % (16573)Instruction limit reached!
% 0.11/0.36  % (16573)------------------------------
% 0.11/0.36  % (16573)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36  % (16572)Refutation not found, incomplete strategy
% 0.11/0.36  % (16572)------------------------------
% 0.11/0.36  % (16572)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36  % (16572)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36  
% 0.11/0.36  
% 0.11/0.36  % (16572)Memory used [KB]: 5500
% 0.11/0.36  % (16572)Time elapsed: 0.003 s
% 0.11/0.36  % (16572)Instructions burned: 2 (million)
% 0.11/0.36  % (16572)------------------------------
% 0.11/0.36  % (16572)------------------------------
% 0.11/0.36  % (16573)Termination reason: Unknown
% 0.11/0.36  % (16573)Termination phase: Saturation
% 0.11/0.36  
% 0.11/0.36  % (16573)Memory used [KB]: 1023
% 0.11/0.36  % (16573)Time elapsed: 0.006 s
% 0.11/0.36  % (16573)Instructions burned: 8 (million)
% 0.11/0.36  % (16573)------------------------------
% 0.11/0.36  % (16573)------------------------------
% 0.11/0.37  % (16561)First to succeed.
% 0.11/0.37  % (16574)Instruction limit reached!
% 0.11/0.37  % (16574)------------------------------
% 0.11/0.37  % (16574)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37  % (16574)Termination reason: Unknown
% 0.11/0.37  % (16574)Termination phase: Saturation
% 0.11/0.37  
% 0.11/0.37  % (16574)Memory used [KB]: 5756
% 0.11/0.37  % (16574)Time elapsed: 0.011 s
% 0.11/0.37  % (16574)Instructions burned: 17 (million)
% 0.11/0.37  % (16574)------------------------------
% 0.11/0.37  % (16574)------------------------------
% 0.11/0.37  % (16561)Refutation found. Thanks to Tanya!
% 0.11/0.37  % SZS status Theorem for theBenchmark
% 0.11/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.38  % (16561)------------------------------
% 0.11/0.38  % (16561)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38  % (16561)Termination reason: Refutation
% 0.11/0.38  
% 0.11/0.38  % (16561)Memory used [KB]: 5884
% 0.11/0.38  % (16561)Time elapsed: 0.028 s
% 0.11/0.38  % (16561)Instructions burned: 34 (million)
% 0.11/0.38  % (16561)------------------------------
% 0.11/0.38  % (16561)------------------------------
% 0.11/0.38  % (16560)Success in time 0.037 s
% 0.11/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------