TSTP Solution File: SYO244^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO244^5 : 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 : n014.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 09:03:38 EDT 2024

% Result   : Theorem 0.14s 0.41s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  189 (   7 unt;  14 typ;   0 def)
%            Number of atoms       : 1467 ( 314 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives : 1866 ( 301   ~; 423   |;  96   &; 874   @)
%                                         (  14 <=>;  78  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  753 ( 753   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  26 usr;  19 con; 0-2 aty)
%                                         (  39  !!;  41  ??;   0 @@+;   0 @@-)
%            Number of variables   :  274 ( 114   ^ 117   !;  42   ?; 274   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_12,type,
    sK0: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_13,type,
    sK1: ( ( a > $o ) > $o ) > $o ).

thf(func_def_14,type,
    sK2: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_15,type,
    sK3: ( a > $o ) > $o ).

thf(func_def_17,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(func_def_20,type,
    sK6: a ).

thf(func_def_21,type,
    sK7: ( a > $o ) > $o ).

thf(func_def_22,type,
    sK8: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).

thf(func_def_23,type,
    sK9: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).

thf(func_def_24,type,
    sK10: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_25,type,
    sK11: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_26,type,
    sK12: ( ( a > $o ) > $o ) > a > $o ).

thf(f659,plain,
    $false,
    inference(avatar_sat_refutation,[],[f87,f91,f98,f102,f109,f113,f121,f125,f298,f329,f364,f440,f488,f519,f522,f562,f581,f642,f658]) ).

thf(f658,plain,
    ( ~ spl4_2
    | ~ spl4_5
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f657]) ).

thf(f657,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f653]) ).

thf(f653,plain,
    ( ( $true = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f650,f112]) ).

thf(f112,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( $true
        = ( sK1 @ ( sK9 @ X1 ) ) )
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f111]) ).

thf(f111,plain,
    ( spl4_9
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( $true
        = ( sK1 @ ( sK9 @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

thf(f650,plain,
    ( ( ( sK1 @ ( sK9 @ sK10 ) )
      = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f643]) ).

thf(f643,plain,
    ( ( $true = $false )
    | ( ( sK1 @ ( sK9 @ sK10 ) )
      = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f97,f608]) ).

thf(f608,plain,
    ( ( ( sK10 @ ( sK9 @ sK10 ) @ sK6 )
      = $false )
    | ~ spl4_2
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f607]) ).

thf(f607,plain,
    ( ( ( sK10 @ ( sK9 @ sK10 ) @ sK6 )
      = $false )
    | ( $true = $false )
    | ~ spl4_2
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(forward_demodulation,[],[f599,f112]) ).

thf(f599,plain,
    ( ( ( sK1 @ ( sK9 @ sK10 ) )
      = $false )
    | ( ( sK10 @ ( sK9 @ sK10 ) @ sK6 )
      = $false )
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f591]) ).

thf(f591,plain,
    ( ( ( sK10 @ ( sK9 @ sK10 ) @ sK6 )
      = $false )
    | ( $true = $false )
    | ( ( sK1 @ ( sK9 @ sK10 ) )
      = $false )
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(superposition,[],[f86,f105]) ).

thf(f105,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( $false
          = ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) )
        | ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
          = $false ) )
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f104]) ).

thf(f104,plain,
    ( spl4_7
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( $false
          = ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) )
        | ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

thf(f86,plain,
    ( ! [X2: ( a > $o ) > $o] :
        ( ( $true
          = ( X2 @ ( sK10 @ X2 ) ) )
        | ( $false
          = ( sK1 @ X2 ) ) )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f85]) ).

thf(f85,plain,
    ( spl4_2
  <=> ! [X2: ( a > $o ) > $o] :
        ( ( $true
          = ( X2 @ ( sK10 @ X2 ) ) )
        | ( $false
          = ( sK1 @ X2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

thf(f97,plain,
    ( ! [X2: ( a > $o ) > $o] :
        ( ( $true
          = ( sK10 @ X2 @ sK6 ) )
        | ( $false
          = ( sK1 @ X2 ) ) )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f96,plain,
    ( spl4_5
  <=> ! [X2: ( a > $o ) > $o] :
        ( ( $false
          = ( sK1 @ X2 ) )
        | ( $true
          = ( sK10 @ X2 @ sK6 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

thf(f642,plain,
    ( ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f641]) ).

thf(f641,plain,
    ( $false
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f637]) ).

thf(f637,plain,
    ( ( $true = $false )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f632,f112]) ).

thf(f632,plain,
    ( ( $false
      = ( sK1 @ ( sK9 @ sK11 ) ) )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f629]) ).

thf(f629,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK1 @ ( sK9 @ sK11 ) ) )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f101,f606]) ).

thf(f606,plain,
    ( ( $false
      = ( sK11 @ ( sK9 @ sK11 ) @ sK6 ) )
    | ~ spl4_4
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f605]) ).

thf(f605,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK11 @ ( sK9 @ sK11 ) @ sK6 ) )
    | ~ spl4_4
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(forward_demodulation,[],[f600,f112]) ).

thf(f600,plain,
    ( ( $false
      = ( sK11 @ ( sK9 @ sK11 ) @ sK6 ) )
    | ( $false
      = ( sK1 @ ( sK9 @ sK11 ) ) )
    | ~ spl4_4
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f587]) ).

thf(f587,plain,
    ( ( $false
      = ( sK11 @ ( sK9 @ sK11 ) @ sK6 ) )
    | ( $true = $false )
    | ( $false
      = ( sK1 @ ( sK9 @ sK11 ) ) )
    | ~ spl4_4
    | ~ spl4_7 ),
    inference(superposition,[],[f105,f94]) ).

thf(f94,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( X1 @ ( sK11 @ X1 ) ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f93]) ).

thf(f93,plain,
    ( spl4_4
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( $false
          = ( sK1 @ X1 ) )
        | ( $true
          = ( X1 @ ( sK11 @ X1 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

thf(f101,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( sK11 @ X1 @ sK6 ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f100]) ).

thf(f100,plain,
    ( spl4_6
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( $false
          = ( sK1 @ X1 ) )
        | ( $true
          = ( sK11 @ X1 @ sK6 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

thf(f581,plain,
    ( ~ spl4_6
    | spl4_20
    | ~ spl4_31 ),
    inference(avatar_contradiction_clause,[],[f580]) ).

thf(f580,plain,
    ( $false
    | ~ spl4_6
    | spl4_20
    | ~ spl4_31 ),
    inference(subsumption_resolution,[],[f576,f383]) ).

thf(f383,plain,
    ( ( $false
     != ( sK1 @ sK7 ) )
    | spl4_20 ),
    inference(avatar_component_clause,[],[f382]) ).

thf(f382,plain,
    ( spl4_20
  <=> ( $false
      = ( sK1 @ sK7 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

thf(f576,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_6
    | ~ spl4_31 ),
    inference(trivial_inequality_removal,[],[f573]) ).

thf(f573,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ( $true = $false )
    | ~ spl4_6
    | ~ spl4_31 ),
    inference(superposition,[],[f101,f558]) ).

thf(f558,plain,
    ( ( $false
      = ( sK11 @ sK7 @ sK6 ) )
    | ~ spl4_31 ),
    inference(avatar_component_clause,[],[f556]) ).

thf(f556,plain,
    ( spl4_31
  <=> ( $false
      = ( sK11 @ sK7 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).

thf(f562,plain,
    ( spl4_31
    | ~ spl4_4
    | ~ spl4_8
    | spl4_20 ),
    inference(avatar_split_clause,[],[f561,f382,f107,f93,f556]) ).

thf(f107,plain,
    ( spl4_8
  <=> ! [X2: a > $o] :
        ( ( ( sK7 @ X2 )
          = $false )
        | ( ( X2 @ sK6 )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

thf(f561,plain,
    ( ( $false
      = ( sK11 @ sK7 @ sK6 ) )
    | ~ spl4_4
    | ~ spl4_8
    | spl4_20 ),
    inference(subsumption_resolution,[],[f502,f383]) ).

thf(f502,plain,
    ( ( $false
      = ( sK11 @ sK7 @ sK6 ) )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_4
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f495]) ).

thf(f495,plain,
    ( ( $false
      = ( sK11 @ sK7 @ sK6 ) )
    | ( $true = $false )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_4
    | ~ spl4_8 ),
    inference(superposition,[],[f108,f94]) ).

thf(f108,plain,
    ( ! [X2: a > $o] :
        ( ( ( sK7 @ X2 )
          = $false )
        | ( ( X2 @ sK6 )
          = $false ) )
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f107]) ).

thf(f522,plain,
    ( ~ spl4_10
    | ~ spl4_20 ),
    inference(avatar_contradiction_clause,[],[f521]) ).

thf(f521,plain,
    ( $false
    | ~ spl4_10
    | ~ spl4_20 ),
    inference(trivial_inequality_removal,[],[f520]) ).

thf(f520,plain,
    ( ( $true = $false )
    | ~ spl4_10
    | ~ spl4_20 ),
    inference(forward_demodulation,[],[f117,f384]) ).

thf(f384,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_20 ),
    inference(avatar_component_clause,[],[f382]) ).

thf(f117,plain,
    ( ( $true
      = ( sK1 @ sK7 ) )
    | ~ spl4_10 ),
    inference(avatar_component_clause,[],[f115]) ).

thf(f115,plain,
    ( spl4_10
  <=> ( $true
      = ( sK1 @ sK7 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

thf(f519,plain,
    ( ~ spl4_4
    | ~ spl4_6
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(avatar_contradiction_clause,[],[f518]) ).

thf(f518,plain,
    ( $false
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f514]) ).

thf(f514,plain,
    ( ( $true = $false )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f513,f124]) ).

thf(f124,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( $true
        = ( sK1 @ ( sK8 @ X1 ) ) )
    | ~ spl4_12 ),
    inference(avatar_component_clause,[],[f123]) ).

thf(f123,plain,
    ( spl4_12
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( $true
        = ( sK1 @ ( sK8 @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

thf(f513,plain,
    ( ( ( sK1 @ ( sK8 @ sK11 ) )
      = $false )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f509]) ).

thf(f509,plain,
    ( ( ( sK1 @ ( sK8 @ sK11 ) )
      = $false )
    | ( $true = $false )
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f101,f506]) ).

thf(f506,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK6 ) )
    | ~ spl4_4
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f505]) ).

thf(f505,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK6 ) )
    | ~ spl4_4
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(forward_demodulation,[],[f499,f124]) ).

thf(f499,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK6 ) )
    | ( ( sK1 @ ( sK8 @ sK11 ) )
      = $false )
    | ~ spl4_4
    | ~ spl4_11 ),
    inference(trivial_inequality_removal,[],[f494]) ).

thf(f494,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK6 ) )
    | ( $true = $false )
    | ( ( sK1 @ ( sK8 @ sK11 ) )
      = $false )
    | ~ spl4_4
    | ~ spl4_11 ),
    inference(superposition,[],[f120,f94]) ).

thf(f120,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
          = $false )
        | ( $false
          = ( X1 @ ( sK8 @ X1 ) @ sK6 ) ) )
    | ~ spl4_11 ),
    inference(avatar_component_clause,[],[f119]) ).

thf(f119,plain,
    ( spl4_11
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( $false
          = ( X1 @ ( sK8 @ X1 ) @ sK6 ) )
        | ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

thf(f488,plain,
    ( ~ spl4_2
    | ~ spl4_5
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(avatar_contradiction_clause,[],[f487]) ).

thf(f487,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f483]) ).

thf(f483,plain,
    ( ( $true = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f469,f124]) ).

thf(f469,plain,
    ( ( ( sK1 @ ( sK8 @ sK10 ) )
      = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f465]) ).

thf(f465,plain,
    ( ( ( sK1 @ ( sK8 @ sK10 ) )
      = $false )
    | ( $true = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f97,f458]) ).

thf(f458,plain,
    ( ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK6 ) )
    | ~ spl4_2
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f457]) ).

thf(f457,plain,
    ( ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK6 ) )
    | ( $true = $false )
    | ~ spl4_2
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(forward_demodulation,[],[f452,f124]) ).

thf(f452,plain,
    ( ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK6 ) )
    | ( ( sK1 @ ( sK8 @ sK10 ) )
      = $false )
    | ~ spl4_2
    | ~ spl4_11 ),
    inference(trivial_inequality_removal,[],[f444]) ).

thf(f444,plain,
    ( ( ( sK1 @ ( sK8 @ sK10 ) )
      = $false )
    | ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK6 ) )
    | ( $true = $false )
    | ~ spl4_2
    | ~ spl4_11 ),
    inference(superposition,[],[f86,f120]) ).

thf(f440,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(avatar_contradiction_clause,[],[f439]) ).

thf(f439,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f436]) ).

thf(f436,plain,
    ( ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f124,f431]) ).

thf(f431,plain,
    ( ( $false
      = ( sK1 @ ( sK8 @ sK12 ) ) )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f425]) ).

thf(f425,plain,
    ( ( $false
      = ( sK1 @ ( sK8 @ sK12 ) ) )
    | ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(superposition,[],[f409,f90]) ).

thf(f90,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( sK12 @ X1 @ sK6 ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f89]) ).

thf(f89,plain,
    ( spl4_3
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( $false
          = ( sK1 @ X1 ) )
        | ( $true
          = ( sK12 @ X1 @ sK6 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

thf(f409,plain,
    ( ( ( sK12 @ ( sK8 @ sK12 ) @ sK6 )
      = $false )
    | ~ spl4_1
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(trivial_inequality_removal,[],[f408]) ).

thf(f408,plain,
    ( ( ( sK12 @ ( sK8 @ sK12 ) @ sK6 )
      = $false )
    | ( $true = $false )
    | ~ spl4_1
    | ~ spl4_11
    | ~ spl4_12 ),
    inference(forward_demodulation,[],[f407,f124]) ).

thf(f407,plain,
    ( ( $false
      = ( sK1 @ ( sK8 @ sK12 ) ) )
    | ( ( sK12 @ ( sK8 @ sK12 ) @ sK6 )
      = $false )
    | ~ spl4_1
    | ~ spl4_11 ),
    inference(trivial_inequality_removal,[],[f398]) ).

thf(f398,plain,
    ( ( $true = $false )
    | ( ( sK12 @ ( sK8 @ sK12 ) @ sK6 )
      = $false )
    | ( $false
      = ( sK1 @ ( sK8 @ sK12 ) ) )
    | ~ spl4_1
    | ~ spl4_11 ),
    inference(superposition,[],[f83,f120]) ).

thf(f83,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( X1 @ ( sK12 @ X1 ) ) )
        | ( $false
          = ( sK1 @ X1 ) ) )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f82]) ).

thf(f82,plain,
    ( spl4_1
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( X1 @ ( sK12 @ X1 ) ) )
        | ( $false
          = ( sK1 @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

thf(f364,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f363]) ).

thf(f363,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f359]) ).

thf(f359,plain,
    ( ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f358,f112]) ).

thf(f358,plain,
    ( ( ( sK1 @ ( sK9 @ sK12 ) )
      = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f354]) ).

thf(f354,plain,
    ( ( ( sK1 @ ( sK9 @ sK12 ) )
      = $false )
    | ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f90,f347]) ).

thf(f347,plain,
    ( ( ( sK12 @ ( sK9 @ sK12 ) @ sK6 )
      = $false )
    | ~ spl4_1
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f346]) ).

thf(f346,plain,
    ( ( $true = $false )
    | ( ( sK12 @ ( sK9 @ sK12 ) @ sK6 )
      = $false )
    | ~ spl4_1
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(forward_demodulation,[],[f343,f112]) ).

thf(f343,plain,
    ( ( ( sK12 @ ( sK9 @ sK12 ) @ sK6 )
      = $false )
    | ( ( sK1 @ ( sK9 @ sK12 ) )
      = $false )
    | ~ spl4_1
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f336]) ).

thf(f336,plain,
    ( ( $true = $false )
    | ( ( sK1 @ ( sK9 @ sK12 ) )
      = $false )
    | ( ( sK12 @ ( sK9 @ sK12 ) @ sK6 )
      = $false )
    | ~ spl4_1
    | ~ spl4_7 ),
    inference(superposition,[],[f83,f105]) ).

thf(f329,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(avatar_contradiction_clause,[],[f328]) ).

thf(f328,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f325]) ).

thf(f325,plain,
    ( ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(superposition,[],[f117,f323]) ).

thf(f323,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f317]) ).

thf(f317,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ( $true = $false )
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(superposition,[],[f315,f90]) ).

thf(f315,plain,
    ( ( $false
      = ( sK12 @ sK7 @ sK6 ) )
    | ~ spl4_1
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f314]) ).

thf(f314,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK12 @ sK7 @ sK6 ) )
    | ~ spl4_1
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(forward_demodulation,[],[f309,f117]) ).

thf(f309,plain,
    ( ( $false
      = ( sK12 @ sK7 @ sK6 ) )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_1
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f305]) ).

thf(f305,plain,
    ( ( $false
      = ( sK12 @ sK7 @ sK6 ) )
    | ( $true = $false )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_1
    | ~ spl4_8 ),
    inference(superposition,[],[f83,f108]) ).

thf(f298,plain,
    ( ~ spl4_2
    | ~ spl4_5
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(avatar_contradiction_clause,[],[f297]) ).

thf(f297,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f294]) ).

thf(f294,plain,
    ( ( $true = $false )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(superposition,[],[f117,f291]) ).

thf(f291,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f288]) ).

thf(f288,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_2
    | ~ spl4_5
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(superposition,[],[f97,f281]) ).

thf(f281,plain,
    ( ( $false
      = ( sK10 @ sK7 @ sK6 ) )
    | ~ spl4_2
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f280]) ).

thf(f280,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK10 @ sK7 @ sK6 ) )
    | ~ spl4_2
    | ~ spl4_8
    | ~ spl4_10 ),
    inference(forward_demodulation,[],[f279,f117]) ).

thf(f279,plain,
    ( ( $false
      = ( sK1 @ sK7 ) )
    | ( $false
      = ( sK10 @ sK7 @ sK6 ) )
    | ~ spl4_2
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f270]) ).

thf(f270,plain,
    ( ( $false
      = ( sK10 @ sK7 @ sK6 ) )
    | ( $true = $false )
    | ( $false
      = ( sK1 @ sK7 ) )
    | ~ spl4_2
    | ~ spl4_8 ),
    inference(superposition,[],[f86,f108]) ).

thf(f125,plain,
    ( spl4_10
    | spl4_12 ),
    inference(avatar_split_clause,[],[f53,f123,f115]) ).

thf(f53,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $true
        = ( sK1 @ ( sK8 @ X1 ) ) )
      | ( $true
        = ( sK1 @ sK7 ) ) ),
    inference(binary_proxy_clausification,[],[f51]) ).

thf(f51,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $true
        = ( sK1 @ sK7 ) )
      | ( ( ( sK1 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
        = $false ) ),
    inference(beta_eta_normalization,[],[f50]) ).

thf(f50,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) )
          @ ( sK8 @ X1 ) )
        = $false )
      | ( $true
        = ( sK1 @ sK7 ) ) ),
    inference(sigma_clausification,[],[f49]) ).

thf(f49,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $true
        = ( sK1 @ sK7 ) )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( sK1 @ sK7 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK6 )
                & ( sK7 @ Y0 ) ) ) ) )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f46]) ).

thf(f46,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) )
      | ( ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK6 )
                    & ( Y0 @ Y1 ) ) ) )
          @ sK7 )
        = $false ) ),
    inference(sigma_clausification,[],[f45]) ).

thf(f45,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK6 )
                    & ( Y0 @ Y1 ) ) ) ) ) )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f44]) ).

thf(f44,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK1 @ Y1 )
                 => ( ( Y0 @ Y1 @ sK6 )
                    & ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
          @ X1 ) )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK6 )
                    & ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(pi_clausification,[],[f43]) ).

thf(f43,plain,
    ( ( $false
      = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
        @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK1 @ Y1 )
               => ( ( Y0 @ Y1 @ sK6 )
                  & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
    | ( $false
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK1 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK6 )
                  & ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
      @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK1 @ Y1 )
             => ( ( Y0 @ Y1 @ sK6 )
                & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
   != ( !! @ ( ( a > $o ) > $o )
      @ ^ [Y0: ( a > $o ) > $o] :
          ( ( sK1 @ Y0 )
         => ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ sK6 )
                & ( Y0 @ Y1 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f40]) ).

thf(f40,plain,
    ( ( ^ [Y0: a] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK1 @ Y1 )
             => ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                    & ( Y1 @ Y2 ) ) ) ) )
      @ sK6 )
   != ( ^ [Y0: a] :
          ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y2: ( a > $o ) > $o] :
                  ( ( sK1 @ Y2 )
                 => ( ( Y1 @ Y2 @ Y0 )
                    & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
      @ sK6 ) ),
    inference(negative_extensionality,[],[f15]) ).

thf(f15,plain,
    ( ( ^ [Y0: a] :
          ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y2: ( a > $o ) > $o] :
                  ( ( sK1 @ Y2 )
                 => ( ( Y1 @ Y2 @ Y0 )
                    & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
   != ( ^ [Y0: a] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK1 @ Y1 )
             => ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                    & ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( $true
          = ( X1 @ ( sK0 @ X1 ) ) ) )
    & ! [X4: ( a > $o ) > $o] :
        ( ( $true
          = ( X4 @ ( sK2 @ X4 ) ) )
        | ( $true
         != ( sK1 @ X4 ) ) )
    & ( ( ^ [Y0: a] :
            ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
            @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y2: ( a > $o ) > $o] :
                    ( ( sK1 @ Y2 )
                   => ( ( Y1 @ Y2 @ Y0 )
                      & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
     != ( ^ [Y0: a] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK1 @ Y1 )
               => ( ?? @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( Y2 @ Y0 )
                      & ( Y1 @ Y2 ) ) ) ) ) ) )
    & ( $true
      = ( sK1 @ sK3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
      ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( ( X1 @ ( X0 @ X1 ) )
          = $true ) )
   => ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( $true
          = ( X1 @ ( sK0 @ X1 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X3: ( ( a > $o ) > $o ) > $o] :
        ( ! [X4: ( a > $o ) > $o] :
            ( ? [X5: a > $o] :
                ( $true
                = ( X4 @ X5 ) )
            | ( $true
             != ( X3 @ X4 ) ) )
        & ( ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X3 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X3 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) ) )
        & ? [X6: ( a > $o ) > $o] :
            ( ( X3 @ X6 )
            = $true ) )
   => ( ! [X4: ( a > $o ) > $o] :
          ( ? [X5: a > $o] :
              ( $true
              = ( X4 @ X5 ) )
          | ( $true
           != ( sK1 @ X4 ) ) )
      & ( ( ^ [Y0: a] :
              ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
              @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                  ( !! @ ( ( a > $o ) > $o )
                  @ ^ [Y2: ( a > $o ) > $o] :
                      ( ( sK1 @ Y2 )
                     => ( ( Y1 @ Y2 @ Y0 )
                        & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
       != ( ^ [Y0: a] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK1 @ Y1 )
                 => ( ?? @ ( a > $o )
                    @ ^ [Y2: a > $o] :
                        ( ( Y2 @ Y0 )
                        & ( Y1 @ Y2 ) ) ) ) ) ) )
      & ? [X6: ( a > $o ) > $o] :
          ( $true
          = ( sK1 @ X6 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X4: ( a > $o ) > $o] :
      ( ? [X5: a > $o] :
          ( $true
          = ( X4 @ X5 ) )
     => ( $true
        = ( X4 @ ( sK2 @ X4 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X6: ( a > $o ) > $o] :
        ( $true
        = ( sK1 @ X6 ) )
   => ( $true
      = ( sK1 @ sK3 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
      ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( ( X1 @ ( X0 @ X1 ) )
          = $true ) )
    & ? [X3: ( ( a > $o ) > $o ) > $o] :
        ( ! [X4: ( a > $o ) > $o] :
            ( ? [X5: a > $o] :
                ( $true
                = ( X4 @ X5 ) )
            | ( $true
             != ( X3 @ X4 ) ) )
        & ( ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X3 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X3 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) ) )
        & ? [X6: ( a > $o ) > $o] :
            ( ( X3 @ X6 )
            = $true ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
      ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( ( X1 @ ( X0 @ X1 ) )
          = $true ) )
    & ? [X3: ( ( a > $o ) > $o ) > $o] :
        ( ! [X5: ( a > $o ) > $o] :
            ( ? [X6: a > $o] :
                ( $true
                = ( X5 @ X6 ) )
            | ( $true
             != ( X3 @ X5 ) ) )
        & ( ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X3 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X3 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) ) )
        & ? [X4: ( a > $o ) > $o] :
            ( $true
            = ( X3 @ X4 ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ? [X3: ( ( a > $o ) > $o ) > $o] :
        ( ( ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X3 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X3 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) ) )
        & ? [X4: ( a > $o ) > $o] :
            ( $true
            = ( X3 @ X4 ) )
        & ! [X5: ( a > $o ) > $o] :
            ( ? [X6: a > $o] :
                ( $true
                = ( X5 @ X6 ) )
            | ( $true
             != ( X3 @ X5 ) ) ) )
    & ? [X0: ( ( a > $o ) > $o ) > a > $o] :
      ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           != $true )
        | ( ( X1 @ ( X0 @ X1 ) )
          = $true ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
        ! [X1: ( a > $o ) > $o] :
          ( ? [X2: a > $o] :
              ( ( X1 @ X2 )
              = $true )
         => ( ( X1 @ ( X0 @ X1 ) )
            = $true ) )
     => ! [X3: ( ( a > $o ) > $o ) > $o] :
          ( ( ? [X4: ( a > $o ) > $o] :
                ( $true
                = ( X3 @ X4 ) )
            & ! [X5: ( a > $o ) > $o] :
                ( ( $true
                  = ( X3 @ X5 ) )
               => ? [X6: a > $o] :
                    ( $true
                    = ( X5 @ X6 ) ) ) )
         => ( ( ^ [Y0: a] :
                  ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                  @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                      ( !! @ ( ( a > $o ) > $o )
                      @ ^ [Y2: ( a > $o ) > $o] :
                          ( ( X3 @ Y2 )
                         => ( ( Y1 @ Y2 @ Y0 )
                            & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
            = ( ^ [Y0: a] :
                  ( !! @ ( ( a > $o ) > $o )
                  @ ^ [Y1: ( a > $o ) > $o] :
                      ( ( X3 @ Y1 )
                     => ( ?? @ ( a > $o )
                        @ ^ [Y2: a > $o] :
                            ( ( Y2 @ Y0 )
                            & ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
        ! [X1: ( a > $o ) > $o] :
          ( ? [X2: a > $o] : ( X1 @ X2 )
         => ( X1 @ ( X0 @ X1 ) ) )
     => ! [X3: ( ( a > $o ) > $o ) > $o] :
          ( ( ? [X4: ( a > $o ) > $o] : ( X3 @ X4 )
            & ! [X5: ( a > $o ) > $o] :
                ( ( X3 @ X5 )
               => ? [X6: a > $o] : ( X5 @ X6 ) ) )
         => ( ( ^ [X7: a] :
                ? [X8: ( ( a > $o ) > $o ) > a > $o] :
                ! [X9: ( a > $o ) > $o] :
                  ( ( X3 @ X9 )
                 => ( ( X9 @ ( X8 @ X9 ) )
                    & ( X8 @ X9 @ X7 ) ) ) )
            = ( ^ [X10: a] :
                ! [X11: ( a > $o ) > $o] :
                  ( ( X3 @ X11 )
                 => ? [X12: a > $o] :
                      ( ( X11 @ X12 )
                      & ( X12 @ X10 ) ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
        ! [X1: ( a > $o ) > $o] :
          ( ? [X2: a > $o] : ( X1 @ X2 )
         => ( X1 @ ( X0 @ X1 ) ) )
     => ! [X3: ( ( a > $o ) > $o ) > $o] :
          ( ( ? [X1: ( a > $o ) > $o] : ( X3 @ X1 )
            & ! [X1: ( a > $o ) > $o] :
                ( ( X3 @ X1 )
               => ? [X4: a > $o] : ( X1 @ X4 ) ) )
         => ( ( ^ [X5: a] :
                ? [X0: ( ( a > $o ) > $o ) > a > $o] :
                ! [X6: ( a > $o ) > $o] :
                  ( ( X3 @ X6 )
                 => ( ( X6 @ ( X0 @ X6 ) )
                    & ( X0 @ X6 @ X5 ) ) ) )
            = ( ^ [X5: a] :
                ! [X6: ( a > $o ) > $o] :
                  ( ( X3 @ X6 )
                 => ? [X7: a > $o] :
                      ( ( X6 @ X7 )
                      & ( X7 @ X5 ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
      ! [X1: ( a > $o ) > $o] :
        ( ? [X2: a > $o] : ( X1 @ X2 )
       => ( X1 @ ( X0 @ X1 ) ) )
   => ! [X3: ( ( a > $o ) > $o ) > $o] :
        ( ( ? [X1: ( a > $o ) > $o] : ( X3 @ X1 )
          & ! [X1: ( a > $o ) > $o] :
              ( ( X3 @ X1 )
             => ? [X4: a > $o] : ( X1 @ X4 ) ) )
       => ( ( ^ [X5: a] :
              ? [X0: ( ( a > $o ) > $o ) > a > $o] :
              ! [X6: ( a > $o ) > $o] :
                ( ( X3 @ X6 )
               => ( ( X6 @ ( X0 @ X6 ) )
                  & ( X0 @ X6 @ X5 ) ) ) )
          = ( ^ [X5: a] :
              ! [X6: ( a > $o ) > $o] :
                ( ( X3 @ X6 )
               => ? [X7: a > $o] :
                    ( ( X6 @ X7 )
                    & ( X7 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM535B) ).

thf(f121,plain,
    ( spl4_10
    | spl4_11 ),
    inference(avatar_split_clause,[],[f54,f119,f115]) ).

thf(f54,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( X1 @ ( sK8 @ X1 ) @ sK6 ) )
      | ( $true
        = ( sK1 @ sK7 ) )
      | ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

thf(f52,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
          & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
      | ( $true
        = ( sK1 @ sK7 ) ) ),
    inference(binary_proxy_clausification,[],[f51]) ).

thf(f113,plain,
    ( spl4_8
    | spl4_9 ),
    inference(avatar_split_clause,[],[f61,f111,f107]) ).

thf(f61,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $true
        = ( sK1 @ ( sK9 @ X1 ) ) )
      | ( ( X2 @ sK6 )
        = $false )
      | ( ( sK7 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f59]) ).

thf(f59,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( X2 @ sK6 )
        = $false )
      | ( ( sK7 @ X2 )
        = $false )
      | ( $false
        = ( ( sK1 @ ( sK9 @ X1 ) )
         => ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
            & ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X2 @ sK6 )
          & ( sK7 @ X2 ) ) )
      | ( $false
        = ( ( sK1 @ ( sK9 @ X1 ) )
         => ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
            & ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f57]) ).

thf(f57,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X2 @ sK6 )
          & ( sK7 @ X2 ) ) )
      | ( $false
        = ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) )
          @ ( sK9 @ X1 ) ) ) ),
    inference(sigma_clausification,[],[f56]) ).

thf(f56,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( ( X2 @ sK6 )
          & ( sK7 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f55]) ).

thf(f55,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) )
      | ( ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( sK7 @ Y0 ) )
          @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f48]) ).

thf(f48,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( sK7 @ Y0 ) ) ) )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( X1 @ Y0 @ sK6 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f47]) ).

thf(f109,plain,
    ( spl4_7
    | spl4_8 ),
    inference(avatar_split_clause,[],[f62,f107,f104]) ).

thf(f62,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( sK7 @ X2 )
        = $false )
      | ( $false
        = ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) )
      | ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
        = $false )
      | ( ( X2 @ sK6 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f60]) ).

thf(f60,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( X2 @ sK6 )
        = $false )
      | ( $false
        = ( ( X1 @ ( sK9 @ X1 ) @ sK6 )
          & ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) ) )
      | ( ( sK7 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f59]) ).

thf(f102,plain,
    ( spl4_6
    | spl4_5 ),
    inference(avatar_split_clause,[],[f76,f96,f100]) ).

thf(f76,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X1 ) )
      | ( $true
        = ( sK11 @ X1 @ sK6 ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK6 ) ) ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f74,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( sK10 @ X2 @ sK6 ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $true
        = ( ( sK11 @ X1 @ sK6 )
          & ( X1 @ ( sK11 @ X1 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f73]) ).

thf(f73,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X1 ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK6 ) )
      | ( $true
        = ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) )
          @ ( sK11 @ X1 ) ) ) ),
    inference(sigma_clausification,[],[f72]) ).

thf(f72,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK6 ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f70]) ).

thf(f70,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ( sK10 @ X2 @ sK6 )
          & ( X2 @ ( sK10 @ X2 ) ) ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ( sK1 @ X2 )
         => ( ( sK10 @ X2 @ sK6 )
            & ( X2 @ ( sK10 @ X2 ) ) ) ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f68]) ).

thf(f68,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( sK10 @ Y0 @ sK6 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) )
          @ X2 ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) ) ),
    inference(pi_clausification,[],[f67]) ).

thf(f67,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X1 ) )
      | ( $true
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( sK10 @ Y0 @ sK6 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ( sK1 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK6 )
                & ( X1 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ( sK10 @ Y0 @ sK6 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f65]) ).

thf(f65,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK1 @ Y1 )
                 => ( ( Y0 @ Y1 @ sK6 )
                    & ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
          @ sK10 ) )
      | ( $true
        = ( ( sK1 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK6 )
                & ( X1 @ Y0 ) ) ) ) ) ),
    inference(sigma_clausification,[],[f64]) ).

thf(f64,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK1 @ Y1 )
                 => ( ( Y0 @ Y1 @ sK6 )
                    & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
      | ( $true
        = ( ( sK1 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK6 )
                & ( X1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f63]) ).

thf(f63,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK1 @ Y1 )
                 => ( ( Y0 @ Y1 @ sK6 )
                    & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
      | ( $true
        = ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK1 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK6 )
                    & ( Y0 @ Y1 ) ) ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f42]) ).

thf(f42,plain,
    ( ( $true
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK1 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK6 )
                  & ( Y0 @ Y1 ) ) ) ) ) )
    | ( $true
      = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
        @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK1 @ Y1 )
               => ( ( Y0 @ Y1 @ sK6 )
                  & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f41]) ).

thf(f98,plain,
    ( spl4_4
    | spl4_5 ),
    inference(avatar_split_clause,[],[f75,f96,f93]) ).

thf(f75,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X2 ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $true
        = ( X1 @ ( sK11 @ X1 ) ) )
      | ( $true
        = ( sK10 @ X2 @ sK6 ) ) ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f91,plain,
    ( spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f80,f89,f85]) ).

thf(f80,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( X2 @ ( sK10 @ X2 ) ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( sK12 @ X1 @ sK6 ) ) ),
    inference(binary_proxy_clausification,[],[f78]) ).

thf(f78,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ( sK12 @ X1 @ sK6 )
          & ( X1 @ ( sK12 @ X1 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( X2 @ ( sK10 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f77]) ).

thf(f77,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK1 @ X2 ) )
      | ( $true
        = ( X2 @ ( sK10 @ X2 ) ) )
      | ( $true
        = ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) )
          @ ( sK12 @ X1 ) ) )
      | ( $false
        = ( sK1 @ X1 ) ) ),
    inference(sigma_clausification,[],[f71]) ).

thf(f71,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( X2 @ ( sK10 @ X2 ) ) )
      | ( $true
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK6 )
              & ( X1 @ Y0 ) ) ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $false
        = ( sK1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f70]) ).

thf(f87,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f79,f85,f82]) ).

thf(f79,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( X1 @ ( sK12 @ X1 ) ) )
      | ( $false
        = ( sK1 @ X1 ) )
      | ( $true
        = ( X2 @ ( sK10 @ X2 ) ) )
      | ( $false
        = ( sK1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO244^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14  % 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 : n014.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   : Mon May 20 09:55:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_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
% 0.14/0.36  % (10175)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  % (10175)Instruction limit reached!
% 0.14/0.37  % (10175)------------------------------
% 0.14/0.37  % (10175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (10175)Termination reason: Unknown
% 0.14/0.37  % (10175)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (10175)Memory used [KB]: 895
% 0.14/0.37  % (10175)Time elapsed: 0.002 s
% 0.14/0.37  % (10175)Instructions burned: 2 (million)
% 0.14/0.37  % (10175)------------------------------
% 0.14/0.37  % (10175)------------------------------
% 0.14/0.37  % (10171)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  % (10176)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  % (10178)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  % (10177)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  % (10172)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  % (10178)Instruction limit reached!
% 0.14/0.37  % (10178)------------------------------
% 0.14/0.37  % (10178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (10178)Termination reason: Unknown
% 0.14/0.37  % (10178)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (10178)Memory used [KB]: 5500
% 0.14/0.37  % (10178)Time elapsed: 0.003 s
% 0.14/0.37  % (10178)Instructions burned: 3 (million)
% 0.14/0.37  % (10178)------------------------------
% 0.14/0.37  % (10178)------------------------------
% 0.14/0.37  % (10179)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)
% 0.14/0.37  % (10172)Instruction limit reached!
% 0.14/0.37  % (10172)------------------------------
% 0.14/0.37  % (10172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (10172)Termination reason: Unknown
% 0.14/0.37  % (10172)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (10172)Memory used [KB]: 5500
% 0.14/0.37  % (10172)Time elapsed: 0.005 s
% 0.14/0.37  % (10172)Instructions burned: 4 (million)
% 0.14/0.37  % (10172)------------------------------
% 0.14/0.37  % (10172)------------------------------
% 0.14/0.38  % (10174)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.38  % (10174)Instruction limit reached!
% 0.14/0.38  % (10174)------------------------------
% 0.14/0.38  % (10174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (10174)Termination reason: Unknown
% 0.14/0.38  % (10174)Termination phase: Preprocessing 1
% 0.14/0.38  
% 0.14/0.38  % (10174)Memory used [KB]: 895
% 0.14/0.38  % (10174)Time elapsed: 0.002 s
% 0.14/0.38  % (10174)Instructions burned: 2 (million)
% 0.14/0.38  % (10174)------------------------------
% 0.14/0.38  % (10174)------------------------------
% 0.14/0.38  % (10177)Instruction limit reached!
% 0.14/0.38  % (10177)------------------------------
% 0.14/0.38  % (10177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (10177)Termination reason: Unknown
% 0.14/0.38  % (10177)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (10177)Memory used [KB]: 5628
% 0.14/0.38  % (10177)Time elapsed: 0.011 s
% 0.14/0.38  % (10177)Instructions burned: 18 (million)
% 0.14/0.38  % (10177)------------------------------
% 0.14/0.38  % (10177)------------------------------
% 0.14/0.38  % (10179)Instruction limit reached!
% 0.14/0.38  % (10179)------------------------------
% 0.14/0.38  % (10179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (10179)Termination reason: Unknown
% 0.14/0.38  % (10179)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (10179)Memory used [KB]: 6012
% 0.14/0.38  % (10179)Time elapsed: 0.012 s
% 0.14/0.38  % (10179)Instructions burned: 39 (million)
% 0.14/0.38  % (10179)------------------------------
% 0.14/0.38  % (10179)------------------------------
% 0.14/0.38  % (10173)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)
% 0.14/0.39  % (10180)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)
% 0.14/0.39  % (10181)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)
% 0.14/0.39  % (10182)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)
% 0.14/0.39  % (10184)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.39  % (10181)Instruction limit reached!
% 0.14/0.39  % (10181)------------------------------
% 0.14/0.39  % (10181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (10181)Termination reason: Unknown
% 0.14/0.39  % (10181)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (10181)Memory used [KB]: 5500
% 0.14/0.39  % (10181)Time elapsed: 0.003 s
% 0.14/0.39  % (10181)Instructions burned: 5 (million)
% 0.14/0.39  % (10181)------------------------------
% 0.14/0.39  % (10181)------------------------------
% 0.14/0.40  % (10184)Instruction limit reached!
% 0.14/0.40  % (10184)------------------------------
% 0.14/0.40  % (10184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (10184)Termination reason: Unknown
% 0.14/0.40  % (10184)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (10184)Memory used [KB]: 1023
% 0.14/0.40  % (10184)Time elapsed: 0.005 s
% 0.14/0.40  % (10184)Instructions burned: 7 (million)
% 0.14/0.40  % (10184)------------------------------
% 0.14/0.40  % (10184)------------------------------
% 0.14/0.40  % (10180)Instruction limit reached!
% 0.14/0.40  % (10180)------------------------------
% 0.14/0.40  % (10180)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (10180)Termination reason: Unknown
% 0.14/0.40  % (10180)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (10180)Memory used [KB]: 5628
% 0.14/0.40  % (10180)Time elapsed: 0.012 s
% 0.14/0.40  % (10180)Instructions burned: 15 (million)
% 0.14/0.40  % (10180)------------------------------
% 0.14/0.40  % (10180)------------------------------
% 0.14/0.40  % (10176)First to succeed.
% 0.14/0.40  % (10186)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.40  % (10173)Instruction limit reached!
% 0.14/0.40  % (10173)------------------------------
% 0.14/0.40  % (10173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (10173)Termination reason: Unknown
% 0.14/0.40  % (10173)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (10173)Memory used [KB]: 5628
% 0.14/0.40  % (10173)Time elapsed: 0.020 s
% 0.14/0.40  % (10173)Instructions burned: 27 (million)
% 0.14/0.40  % (10173)------------------------------
% 0.14/0.40  % (10173)------------------------------
% 0.14/0.40  % (10186)Instruction limit reached!
% 0.14/0.40  % (10186)------------------------------
% 0.14/0.40  % (10186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (10186)Termination reason: Unknown
% 0.14/0.40  % (10186)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (10186)Memory used [KB]: 5500
% 0.14/0.40  % (10186)Time elapsed: 0.003 s
% 0.14/0.40  % (10186)Instructions burned: 5 (million)
% 0.14/0.40  % (10186)------------------------------
% 0.14/0.40  % (10186)------------------------------
% 0.14/0.41  % (10176)Refutation found. Thanks to Tanya!
% 0.14/0.41  % SZS status Theorem for theBenchmark
% 0.14/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41  % (10176)------------------------------
% 0.14/0.41  % (10176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (10176)Termination reason: Refutation
% 0.14/0.41  
% 0.14/0.41  % (10176)Memory used [KB]: 5884
% 0.14/0.41  % (10176)Time elapsed: 0.036 s
% 0.14/0.41  % (10176)Instructions burned: 54 (million)
% 0.14/0.41  % (10176)------------------------------
% 0.14/0.41  % (10176)------------------------------
% 0.14/0.41  % (10170)Success in time 0.043 s
% 0.14/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------