TSTP Solution File: SYO246^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO246^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n026.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 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  126 (   7 unt;  14 typ;   0 def)
%            Number of atoms       : 1000 ( 235 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives : 1432 ( 158   ~; 238   |; 100   &; 763   @)
%                                         (   8 <=>;  91  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  723 ( 723   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  20 usr;  13 con; 0-3 aty)
%                                         (  36  !!;  38  ??;   0 @@+;   0 @@-)
%            Number of variables   :  268 ( 106   ^ 114   !;  46   ?; 268   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_2,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_13,type,
    sK0: ( ( a > $o ) > $o ) > $o ).

thf(func_def_14,type,
    sK1: ( a > $o ) > $o ).

thf(func_def_15,type,
    sK2: ( ( a > $o ) > $o ) > a > $o ).

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

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

thf(func_def_19,type,
    ph6: 
      !>[X0: $tType] : X0 ).

thf(func_def_20,type,
    sK7: a ).

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

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

thf(func_def_23,type,
    sK10: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_24,type,
    sK11: ( ( a > $o ) > $o ) > a > $o ).

thf(f260,plain,
    $false,
    inference(avatar_sat_refutation,[],[f65,f69,f73,f74,f81,f85,f90,f91,f153,f201,f229,f259]) ).

thf(f259,plain,
    ( ~ spl5_2
    | ~ spl5_3
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(avatar_contradiction_clause,[],[f258]) ).

thf(f258,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f254]) ).

thf(f254,plain,
    ( ( $false = $true )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(backward_demodulation,[],[f89,f248]) ).

thf(f248,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f247]) ).

thf(f247,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ( $false = $true )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(superposition,[],[f68,f243]) ).

thf(f243,plain,
    ( ( $false
      = ( sK11 @ sK9 @ sK7 ) )
    | ~ spl5_2
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f242]) ).

thf(f242,plain,
    ( ( $false
      = ( sK11 @ sK9 @ sK7 ) )
    | ( $false = $true )
    | ~ spl5_2
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(forward_demodulation,[],[f240,f89]) ).

thf(f240,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ( $false
      = ( sK11 @ sK9 @ sK7 ) )
    | ~ spl5_2
    | ~ spl5_5 ),
    inference(trivial_inequality_removal,[],[f236]) ).

thf(f236,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ( $false = $true )
    | ( $false
      = ( sK11 @ sK9 @ sK7 ) )
    | ~ spl5_2
    | ~ spl5_5 ),
    inference(superposition,[],[f64,f77]) ).

thf(f77,plain,
    ( ! [X2: a > $o] :
        ( ( $false
          = ( sK9 @ X2 ) )
        | ( ( X2 @ sK7 )
          = $false ) )
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f76]) ).

thf(f76,plain,
    ( spl5_5
  <=> ! [X2: a > $o] :
        ( ( ( X2 @ sK7 )
          = $false )
        | ( $false
          = ( sK9 @ X2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

thf(f64,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( X1 @ ( sK11 @ X1 ) ) )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f63]) ).

thf(f63,plain,
    ( spl5_2
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( $true
          = ( X1 @ ( sK11 @ X1 ) ) )
        | ( $false
          = ( sK0 @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

thf(f68,plain,
    ( ! [X1: ( a > $o ) > $o] :
        ( ( ( sK11 @ X1 @ sK7 )
          = $true )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f67]) ).

thf(f67,plain,
    ( spl5_3
  <=> ! [X1: ( a > $o ) > $o] :
        ( ( ( sK11 @ X1 @ sK7 )
          = $true )
        | ( $false
          = ( sK0 @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

thf(f89,plain,
    ( ( $true
      = ( sK0 @ sK9 ) )
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f87]) ).

thf(f87,plain,
    ( spl5_8
  <=> ( $true
      = ( sK0 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

thf(f229,plain,
    ( ~ spl5_1
    | ~ spl5_4
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(avatar_contradiction_clause,[],[f228]) ).

thf(f228,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f224]) ).

thf(f224,plain,
    ( ( $false = $true )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(backward_demodulation,[],[f89,f222]) ).

thf(f222,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f221]) ).

thf(f221,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ( $false = $true )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(superposition,[],[f72,f217]) ).

thf(f217,plain,
    ( ( $false
      = ( sK10 @ sK9 @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(trivial_inequality_removal,[],[f216]) ).

thf(f216,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK10 @ sK9 @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_5
    | ~ spl5_8 ),
    inference(forward_demodulation,[],[f215,f89]) ).

thf(f215,plain,
    ( ( $false
      = ( sK0 @ sK9 ) )
    | ( $false
      = ( sK10 @ sK9 @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(trivial_inequality_removal,[],[f211]) ).

thf(f211,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK0 @ sK9 ) )
    | ( $false
      = ( sK10 @ sK9 @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(superposition,[],[f61,f77]) ).

thf(f61,plain,
    ( ! [X2: ( a > $o ) > $o] :
        ( ( ( X2 @ ( sK10 @ X2 ) )
          = $true )
        | ( $false
          = ( sK0 @ X2 ) ) )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f60,plain,
    ( spl5_1
  <=> ! [X2: ( a > $o ) > $o] :
        ( ( $false
          = ( sK0 @ X2 ) )
        | ( ( X2 @ ( sK10 @ X2 ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

thf(f72,plain,
    ( ! [X2: ( a > $o ) > $o] :
        ( ( $true
          = ( sK10 @ X2 @ sK7 ) )
        | ( $false
          = ( sK0 @ X2 ) ) )
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f71]) ).

thf(f71,plain,
    ( spl5_4
  <=> ! [X2: ( a > $o ) > $o] :
        ( ( $false
          = ( sK0 @ X2 ) )
        | ( $true
          = ( sK10 @ X2 @ sK7 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

thf(f201,plain,
    ( ~ spl5_1
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(avatar_contradiction_clause,[],[f200]) ).

thf(f200,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f193]) ).

thf(f193,plain,
    ( ( $false = $true )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(superposition,[],[f191,f84]) ).

thf(f84,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( sK0 @ ( sK8 @ X1 ) )
        = $true )
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f83]) ).

thf(f83,plain,
    ( spl5_7
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( sK0 @ ( sK8 @ X1 ) )
        = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

thf(f191,plain,
    ( ( $false
      = ( sK0 @ ( sK8 @ sK10 ) ) )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f190]) ).

thf(f190,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK0 @ ( sK8 @ sK10 ) ) )
    | ~ spl5_1
    | ~ spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(superposition,[],[f72,f186]) ).

thf(f186,plain,
    ( ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f185]) ).

thf(f185,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(forward_demodulation,[],[f184,f84]) ).

thf(f184,plain,
    ( ( $false
      = ( sK0 @ ( sK8 @ sK10 ) ) )
    | ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_6 ),
    inference(trivial_inequality_removal,[],[f179]) ).

thf(f179,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK0 @ ( sK8 @ sK10 ) ) )
    | ( $false
      = ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
    | ~ spl5_1
    | ~ spl5_6 ),
    inference(superposition,[],[f61,f80]) ).

thf(f80,plain,
    ( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( $false
          = ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
        | ( $false
          = ( X1 @ ( sK8 @ X1 ) @ sK7 ) ) )
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f79]) ).

thf(f79,plain,
    ( spl5_6
  <=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
        ( ( $false
          = ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
        | ( $false
          = ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

thf(f153,plain,
    ( ~ spl5_2
    | ~ spl5_3
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(avatar_contradiction_clause,[],[f152]) ).

thf(f152,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f146]) ).

thf(f146,plain,
    ( ( $false = $true )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(superposition,[],[f84,f143]) ).

thf(f143,plain,
    ( ( $false
      = ( sK0 @ ( sK8 @ sK11 ) ) )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f141]) ).

thf(f141,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK0 @ ( sK8 @ sK11 ) ) )
    | ~ spl5_2
    | ~ spl5_3
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(superposition,[],[f138,f68]) ).

thf(f138,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
    | ~ spl5_2
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f137]) ).

thf(f137,plain,
    ( ( $false = $true )
    | ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
    | ~ spl5_2
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(forward_demodulation,[],[f135,f84]) ).

thf(f135,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
    | ( $false
      = ( sK0 @ ( sK8 @ sK11 ) ) )
    | ~ spl5_2
    | ~ spl5_6 ),
    inference(trivial_inequality_removal,[],[f130]) ).

thf(f130,plain,
    ( ( $false
      = ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
    | ( $false = $true )
    | ( $false
      = ( sK0 @ ( sK8 @ sK11 ) ) )
    | ~ spl5_2
    | ~ spl5_6 ),
    inference(superposition,[],[f80,f64]) ).

thf(f91,plain,
    ( spl5_7
    | spl5_8 ),
    inference(avatar_split_clause,[],[f35,f87,f83]) ).

thf(f35,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( sK0 @ ( sK8 @ X1 ) )
        = $true )
      | ( $true
        = ( sK0 @ sK9 ) ) ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
      | ( $true
        = ( sK0 @ sK9 ) ) ),
    inference(binary_proxy_clausification,[],[f31]) ).

thf(f31,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( sK0 @ sK9 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK7 )
                & ( sK9 @ Y0 ) ) ) ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f30]) ).

thf(f30,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) )
          @ sK9 ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
    inference(sigma_clausification,[],[f29]) ).

thf(f29,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) ) ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f28]) ).

thf(f28,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) ) ) )
      | ( ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ( X1 @ Y0 @ sK7 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) )
          @ ( sK8 @ X1 ) )
        = $false ) ),
    inference(sigma_clausification,[],[f27]) ).

thf(f27,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ( X1 @ Y0 @ sK7 )
                & ( Y0 @ ( X1 @ Y0 ) ) ) ) )
        = $false )
      | ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f26]) ).

thf(f26,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) ) ) )
      | ( $false
        = ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK0 @ Y1 )
                 => ( ( Y0 @ Y1 @ sK7 )
                    & ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( $false
      = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
        @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK0 @ Y1 )
               => ( ( Y0 @ Y1 @ sK7 )
                  & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
    | ( $false
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK0 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK7 )
                  & ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f23]) ).

thf(f23,plain,
    ( ( !! @ ( ( a > $o ) > $o )
      @ ^ [Y0: ( a > $o ) > $o] :
          ( ( sK0 @ Y0 )
         => ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ sK7 )
                & ( Y0 @ Y1 ) ) ) ) )
   != ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
      @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK0 @ Y1 )
             => ( ( Y0 @ Y1 @ sK7 )
                & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f22]) ).

thf(f22,plain,
    ( ( ^ [Y0: a] :
          ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y2: ( a > $o ) > $o] :
                  ( ( sK0 @ Y2 )
                 => ( ( Y1 @ Y2 @ Y0 )
                    & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
      @ sK7 )
   != ( ^ [Y0: a] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK0 @ Y1 )
             => ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                    & ( Y1 @ Y2 ) ) ) ) )
      @ sK7 ) ),
    inference(negative_extensionality,[],[f19]) ).

thf(f19,plain,
    ( ( ^ [Y0: a] :
          ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
          @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y2: ( a > $o ) > $o] :
                  ( ( sK0 @ Y2 )
                 => ( ( Y1 @ Y2 @ Y0 )
                    & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
   != ( ^ [Y0: a] :
          ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y1: ( a > $o ) > $o] :
              ( ( sK0 @ Y1 )
             => ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                    & ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( ( ^ [Y0: a] :
            ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
            @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y2: ( a > $o ) > $o] :
                    ( ( sK0 @ Y2 )
                   => ( ( Y1 @ Y2 @ Y0 )
                      & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
     != ( ^ [Y0: a] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK0 @ Y1 )
               => ( ?? @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( Y2 @ Y0 )
                      & ( Y1 @ Y2 ) ) ) ) ) ) )
    & ( $true
      = ( sK0 @ sK1 ) )
    & ! [X2: ( a > $o ) > $o] :
        ( ( ( sK0 @ X2 )
         != $true )
        | ( ( X2 @ ( sK2 @ X2 ) )
          = $true ) )
    & ! [X4: ( ( a > $o ) > $o ) > $o] :
        ( ! [X6: ( a > $o ) > $o] :
            ( ( ( X4 @ X6 )
             != $true )
            | ( ( X6 @ ( sK3 @ X4 @ X6 ) )
              = $true ) )
        | ( ( $true
            = ( X4 @ ( sK4 @ X4 ) ) )
          & ! [X8: a > $o] :
              ( $true
             != ( sK4 @ X4 @ X8 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f13,f12,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: ( ( a > $o ) > $o ) > $o] :
        ( ( ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X0 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X0 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ? [X1: ( a > $o ) > $o] :
            ( ( X0 @ X1 )
            = $true )
        & ! [X2: ( a > $o ) > $o] :
            ( ( $true
             != ( X0 @ X2 ) )
            | ? [X3: a > $o] :
                ( ( X2 @ X3 )
                = $true ) ) )
   => ( ( ( ^ [Y0: a] :
              ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
              @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                  ( !! @ ( ( a > $o ) > $o )
                  @ ^ [Y2: ( a > $o ) > $o] :
                      ( ( sK0 @ Y2 )
                     => ( ( Y1 @ Y2 @ Y0 )
                        & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
       != ( ^ [Y0: a] :
              ( !! @ ( ( a > $o ) > $o )
              @ ^ [Y1: ( a > $o ) > $o] :
                  ( ( sK0 @ Y1 )
                 => ( ?? @ ( a > $o )
                    @ ^ [Y2: a > $o] :
                        ( ( Y2 @ Y0 )
                        & ( Y1 @ Y2 ) ) ) ) ) ) )
      & ? [X1: ( a > $o ) > $o] :
          ( ( sK0 @ X1 )
          = $true )
      & ! [X2: ( a > $o ) > $o] :
          ( ( ( sK0 @ X2 )
           != $true )
          | ? [X3: a > $o] :
              ( ( X2 @ X3 )
              = $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X1: ( a > $o ) > $o] :
        ( ( sK0 @ X1 )
        = $true )
   => ( $true
      = ( sK0 @ sK1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X2: ( a > $o ) > $o] :
      ( ? [X3: a > $o] :
          ( ( X2 @ X3 )
          = $true )
     => ( ( X2 @ ( sK2 @ X2 ) )
        = $true ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X4: ( ( a > $o ) > $o ) > $o] :
      ( ? [X5: ( ( a > $o ) > $o ) > a > $o] :
        ! [X6: ( a > $o ) > $o] :
          ( ( ( X4 @ X6 )
           != $true )
          | ( $true
            = ( X6 @ ( X5 @ X6 ) ) ) )
     => ! [X6: ( a > $o ) > $o] :
          ( ( ( X4 @ X6 )
           != $true )
          | ( ( X6 @ ( sK3 @ X4 @ X6 ) )
            = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X4: ( ( a > $o ) > $o ) > $o] :
      ( ? [X7: ( a > $o ) > $o] :
          ( ( ( X4 @ X7 )
            = $true )
          & ! [X8: a > $o] :
              ( ( X7 @ X8 )
             != $true ) )
     => ( ( $true
          = ( X4 @ ( sK4 @ X4 ) ) )
        & ! [X8: a > $o] :
            ( $true
           != ( sK4 @ X4 @ X8 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: ( ( a > $o ) > $o ) > $o] :
        ( ( ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X0 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X0 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ? [X1: ( a > $o ) > $o] :
            ( ( X0 @ X1 )
            = $true )
        & ! [X2: ( a > $o ) > $o] :
            ( ( $true
             != ( X0 @ X2 ) )
            | ? [X3: a > $o] :
                ( ( X2 @ X3 )
                = $true ) ) )
    & ! [X4: ( ( a > $o ) > $o ) > $o] :
        ( ? [X5: ( ( a > $o ) > $o ) > a > $o] :
          ! [X6: ( a > $o ) > $o] :
            ( ( ( X4 @ X6 )
             != $true )
            | ( $true
              = ( X6 @ ( X5 @ X6 ) ) ) )
        | ? [X7: ( a > $o ) > $o] :
            ( ( ( X4 @ X7 )
              = $true )
            & ! [X8: a > $o] :
                ( ( X7 @ X8 )
               != $true ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ? [X5: ( ( a > $o ) > $o ) > $o] :
        ( ( ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X5 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X5 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ? [X8: ( a > $o ) > $o] :
            ( ( X5 @ X8 )
            = $true )
        & ! [X6: ( a > $o ) > $o] :
            ( ( ( X5 @ X6 )
             != $true )
            | ? [X7: a > $o] :
                ( ( X6 @ X7 )
                = $true ) ) )
    & ! [X0: ( ( a > $o ) > $o ) > $o] :
        ( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
          ! [X4: ( a > $o ) > $o] :
            ( ( ( X0 @ X4 )
             != $true )
            | ( $true
              = ( X4 @ ( X3 @ X4 ) ) ) )
        | ? [X1: ( a > $o ) > $o] :
            ( ( ( X0 @ X1 )
              = $true )
            & ! [X2: a > $o] :
                ( ( X1 @ X2 )
               != $true ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ? [X5: ( ( a > $o ) > $o ) > $o] :
        ( ( ( ^ [Y0: a] :
                ( !! @ ( ( a > $o ) > $o )
                @ ^ [Y1: ( a > $o ) > $o] :
                    ( ( X5 @ Y1 )
                   => ( ?? @ ( a > $o )
                      @ ^ [Y2: a > $o] :
                          ( ( Y2 @ Y0 )
                          & ( Y1 @ Y2 ) ) ) ) ) )
         != ( ^ [Y0: a] :
                ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                    ( !! @ ( ( a > $o ) > $o )
                    @ ^ [Y2: ( a > $o ) > $o] :
                        ( ( X5 @ Y2 )
                       => ( ( Y1 @ Y2 @ Y0 )
                          & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ? [X8: ( a > $o ) > $o] :
            ( ( X5 @ X8 )
            = $true )
        & ! [X6: ( a > $o ) > $o] :
            ( ( ( X5 @ X6 )
             != $true )
            | ? [X7: a > $o] :
                ( ( X6 @ X7 )
                = $true ) ) )
    & ! [X0: ( ( a > $o ) > $o ) > $o] :
        ( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
          ! [X4: ( a > $o ) > $o] :
            ( ( ( X0 @ X4 )
             != $true )
            | ( $true
              = ( X4 @ ( X3 @ X4 ) ) ) )
        | ? [X1: ( a > $o ) > $o] :
            ( ( ( X0 @ X1 )
              = $true )
            & ! [X2: a > $o] :
                ( ( X1 @ X2 )
               != $true ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
          ( ! [X1: ( a > $o ) > $o] :
              ( ( ( X0 @ X1 )
                = $true )
             => ? [X2: a > $o] :
                  ( ( X1 @ X2 )
                  = $true ) )
         => ? [X3: ( ( a > $o ) > $o ) > a > $o] :
            ! [X4: ( a > $o ) > $o] :
              ( ( ( X0 @ X4 )
                = $true )
             => ( $true
                = ( X4 @ ( X3 @ X4 ) ) ) ) )
     => ! [X5: ( ( a > $o ) > $o ) > $o] :
          ( ( ? [X8: ( a > $o ) > $o] :
                ( ( X5 @ X8 )
                = $true )
            & ! [X6: ( a > $o ) > $o] :
                ( ( ( X5 @ X6 )
                  = $true )
               => ? [X7: a > $o] :
                    ( ( X6 @ X7 )
                    = $true ) ) )
         => ( ( ^ [Y0: a] :
                  ( !! @ ( ( a > $o ) > $o )
                  @ ^ [Y1: ( a > $o ) > $o] :
                      ( ( X5 @ Y1 )
                     => ( ?? @ ( a > $o )
                        @ ^ [Y2: a > $o] :
                            ( ( Y2 @ Y0 )
                            & ( Y1 @ Y2 ) ) ) ) ) )
            = ( ^ [Y0: a] :
                  ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
                  @ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
                      ( !! @ ( ( a > $o ) > $o )
                      @ ^ [Y2: ( a > $o ) > $o] :
                          ( ( X5 @ Y2 )
                         => ( ( Y1 @ Y2 @ Y0 )
                            & ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
          ( ! [X1: ( a > $o ) > $o] :
              ( ( X0 @ X1 )
             => ? [X2: a > $o] : ( X1 @ X2 ) )
         => ? [X3: ( ( a > $o ) > $o ) > a > $o] :
            ! [X4: ( a > $o ) > $o] :
              ( ( X0 @ X4 )
             => ( X4 @ ( X3 @ X4 ) ) ) )
     => ! [X5: ( ( a > $o ) > $o ) > $o] :
          ( ( ! [X6: ( a > $o ) > $o] :
                ( ( X5 @ X6 )
               => ? [X7: a > $o] : ( X6 @ X7 ) )
            & ? [X8: ( a > $o ) > $o] : ( X5 @ X8 ) )
         => ( ( ^ [X9: a] :
                ? [X10: ( ( a > $o ) > $o ) > a > $o] :
                ! [X11: ( a > $o ) > $o] :
                  ( ( X5 @ X11 )
                 => ( ( X11 @ ( X10 @ X11 ) )
                    & ( X10 @ X11 @ X9 ) ) ) )
            = ( ^ [X12: a] :
                ! [X13: ( a > $o ) > $o] :
                  ( ( X5 @ X13 )
                 => ? [X14: a > $o] :
                      ( ( X13 @ X14 )
                      & ( X14 @ X12 ) ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
          ( ! [X1: ( a > $o ) > $o] :
              ( ( X0 @ X1 )
             => ? [X2: a > $o] : ( X1 @ X2 ) )
         => ? [X3: ( ( a > $o ) > $o ) > a > $o] :
            ! [X1: ( a > $o ) > $o] :
              ( ( X0 @ X1 )
             => ( X1 @ ( X3 @ X1 ) ) ) )
     => ! [X4: ( ( a > $o ) > $o ) > $o] :
          ( ( ! [X1: ( a > $o ) > $o] :
                ( ( X4 @ X1 )
               => ? [X5: a > $o] : ( X1 @ X5 ) )
            & ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
         => ( ( ^ [X6: a] :
                ? [X3: ( ( a > $o ) > $o ) > a > $o] :
                ! [X7: ( a > $o ) > $o] :
                  ( ( X4 @ X7 )
                 => ( ( X7 @ ( X3 @ X7 ) )
                    & ( X3 @ X7 @ X6 ) ) ) )
            = ( ^ [X6: a] :
                ! [X7: ( a > $o ) > $o] :
                  ( ( X4 @ X7 )
                 => ? [X8: a > $o] :
                      ( ( X7 @ X8 )
                      & ( X8 @ X6 ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ! [X0: ( ( a > $o ) > $o ) > $o] :
        ( ! [X1: ( a > $o ) > $o] :
            ( ( X0 @ X1 )
           => ? [X2: a > $o] : ( X1 @ X2 ) )
       => ? [X3: ( ( a > $o ) > $o ) > a > $o] :
          ! [X1: ( a > $o ) > $o] :
            ( ( X0 @ X1 )
           => ( X1 @ ( X3 @ X1 ) ) ) )
   => ! [X4: ( ( a > $o ) > $o ) > $o] :
        ( ( ! [X1: ( a > $o ) > $o] :
              ( ( X4 @ X1 )
             => ? [X5: a > $o] : ( X1 @ X5 ) )
          & ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
       => ( ( ^ [X6: a] :
              ? [X3: ( ( a > $o ) > $o ) > a > $o] :
              ! [X7: ( a > $o ) > $o] :
                ( ( X4 @ X7 )
               => ( ( X7 @ ( X3 @ X7 ) )
                  & ( X3 @ X7 @ X6 ) ) ) )
          = ( ^ [X6: a] :
              ! [X7: ( a > $o ) > $o] :
                ( ( X4 @ X7 )
               => ? [X8: a > $o] :
                    ( ( X7 @ X8 )
                    & ( X8 @ X6 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM535) ).

thf(f90,plain,
    ( spl5_6
    | spl5_8 ),
    inference(avatar_split_clause,[],[f36,f87,f79]) ).

thf(f36,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
      | ( $false
        = ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
      | ( $true
        = ( sK0 @ sK9 ) ) ),
    inference(binary_proxy_clausification,[],[f34]) ).

thf(f34,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
          & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
      | ( $true
        = ( sK0 @ sK9 ) ) ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f85,plain,
    ( spl5_7
    | spl5_5 ),
    inference(avatar_split_clause,[],[f41,f76,f83]) ).

thf(f41,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( sK0 @ ( sK8 @ X1 ) )
        = $true )
      | ( ( X2 @ sK7 )
        = $false )
      | ( $false
        = ( sK9 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( sK9 @ X2 ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
      | ( ( X2 @ sK7 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f38]) ).

thf(f38,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X2 @ sK7 )
          & ( sK9 @ X2 ) ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f37]) ).

thf(f37,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
      | ( $false
        = ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK7 )
              & ( sK9 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f32]) ).

thf(f32,plain,
    ! [X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK7 )
              & ( sK9 @ Y0 ) ) ) )
      | ( $false
        = ( ( sK0 @ ( sK8 @ X1 ) )
         => ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
            & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f31]) ).

thf(f81,plain,
    ( spl5_5
    | spl5_6 ),
    inference(avatar_split_clause,[],[f42,f79,f76]) ).

thf(f42,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( ( X2 @ sK7 )
        = $false )
      | ( $false
        = ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
      | ( $false
        = ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
      | ( $false
        = ( sK9 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
      ( ( $false
        = ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
          & ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
      | ( ( X2 @ sK7 )
        = $false )
      | ( $false
        = ( sK9 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f74,plain,
    ( spl5_4
    | spl5_3 ),
    inference(avatar_split_clause,[],[f56,f67,f71]) ).

thf(f56,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK0 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK7 ) )
      | ( $false
        = ( sK0 @ X1 ) )
      | ( ( sK11 @ X1 @ sK7 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK0 @ X1 ) )
      | ( $false
        = ( sK0 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK7 ) )
      | ( ( ( sK11 @ X1 @ sK7 )
          & ( X1 @ ( sK11 @ X1 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

thf(f52,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( ( sK10 @ X2 @ sK7 )
          & ( X2 @ ( sK10 @ X2 ) ) ) )
      | ( ( ( sK11 @ X1 @ sK7 )
          & ( X1 @ ( sK11 @ X1 ) ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) )
      | ( $false
        = ( sK0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f51]) ).

thf(f51,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( ( sK0 @ X2 )
         => ( ( sK10 @ X2 @ sK7 )
            & ( X2 @ ( sK10 @ X2 ) ) ) )
        = $true )
      | ( ( ( sK11 @ X1 @ sK7 )
          & ( X1 @ ( sK11 @ X1 ) ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f50]) ).

thf(f50,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( ( sK0 @ X2 )
         => ( ( sK10 @ X2 @ sK7 )
            & ( X2 @ ( sK10 @ X2 ) ) ) )
        = $true )
      | ( ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK7 )
              & ( X1 @ Y0 ) )
          @ ( sK11 @ X1 ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) ) ),
    inference(sigma_clausification,[],[f49]) ).

thf(f49,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ sK7 )
              & ( X1 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) )
      | ( ( ( sK0 @ X2 )
         => ( ( sK10 @ X2 @ sK7 )
            & ( X2 @ ( sK10 @ X2 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( ( sK0 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK7 )
                & ( X1 @ Y0 ) ) ) )
        = $true )
      | ( ( ( sK0 @ X2 )
         => ( ( sK10 @ X2 @ sK7 )
            & ( X2 @ ( sK10 @ X2 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f47]) ).

thf(f47,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( ( sK0 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK7 )
                & ( X1 @ Y0 ) ) ) )
        = $true )
      | ( ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ( sK10 @ Y0 @ sK7 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) )
          @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f46]) ).

thf(f46,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ( sK10 @ Y0 @ sK7 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
        = $true )
      | ( ( ( sK0 @ X1 )
         => ( ?? @ ( a > $o )
            @ ^ [Y0: a > $o] :
                ( ( Y0 @ sK7 )
                & ( X1 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f45]) ).

thf(f45,plain,
    ! [X1: ( a > $o ) > $o] :
      ( ( ( !! @ ( ( a > $o ) > $o )
          @ ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ( sK10 @ Y0 @ sK7 )
                & ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
        = $true )
      | ( ( ^ [Y0: ( a > $o ) > $o] :
              ( ( sK0 @ Y0 )
             => ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ sK7 )
                    & ( Y0 @ Y1 ) ) ) )
          @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f44]) ).

thf(f44,plain,
    ( ( $true
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK0 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK7 )
                  & ( Y0 @ Y1 ) ) ) ) ) )
    | ( ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK0 @ Y0 )
           => ( ( sK10 @ Y0 @ sK7 )
              & ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
      = $true ) ),
    inference(beta_eta_normalization,[],[f43]) ).

thf(f43,plain,
    ( ( $true
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK0 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK7 )
                  & ( Y0 @ Y1 ) ) ) ) ) )
    | ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK0 @ Y1 )
               => ( ( Y0 @ Y1 @ sK7 )
                  & ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
        @ sK10 )
      = $true ) ),
    inference(sigma_clausification,[],[f24]) ).

thf(f24,plain,
    ( ( $true
      = ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
        @ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
            ( !! @ ( ( a > $o ) > $o )
            @ ^ [Y1: ( a > $o ) > $o] :
                ( ( sK0 @ Y1 )
               => ( ( Y0 @ Y1 @ sK7 )
                  & ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
    | ( $true
      = ( !! @ ( ( a > $o ) > $o )
        @ ^ [Y0: ( a > $o ) > $o] :
            ( ( sK0 @ Y0 )
           => ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ sK7 )
                  & ( Y0 @ Y1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f23]) ).

thf(f73,plain,
    ( spl5_4
    | spl5_2 ),
    inference(avatar_split_clause,[],[f55,f63,f71]) ).

thf(f55,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $true
        = ( X1 @ ( sK11 @ X1 ) ) )
      | ( $false
        = ( sK0 @ X1 ) )
      | ( $false
        = ( sK0 @ X2 ) )
      | ( $true
        = ( sK10 @ X2 @ sK7 ) ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f69,plain,
    ( spl5_1
    | spl5_3 ),
    inference(avatar_split_clause,[],[f58,f67,f60]) ).

thf(f58,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( sK11 @ X1 @ sK7 )
        = $true )
      | ( ( X2 @ ( sK10 @ X2 ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) )
      | ( $false
        = ( sK0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

thf(f53,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( ( X2 @ ( sK10 @ X2 ) )
        = $true )
      | ( $false
        = ( sK0 @ X2 ) )
      | ( ( ( sK11 @ X1 @ sK7 )
          & ( X1 @ ( sK11 @ X1 ) ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

thf(f65,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f57,f63,f60]) ).

thf(f57,plain,
    ! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
      ( ( $false
        = ( sK0 @ X2 ) )
      | ( $true
        = ( X1 @ ( sK11 @ X1 ) ) )
      | ( ( X2 @ ( sK10 @ X2 ) )
        = $true )
      | ( $false
        = ( sK0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO246^5 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n026.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 10:37:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_EQU_NAR problem
% 0.14/0.36  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
% 0.14/0.37  % (4370)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37  % (4371)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 (2999ds/4Mi)
% 0.14/0.37  % (4372)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 (2999ds/27Mi)
% 0.14/0.37  % (4374)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 (2999ds/2Mi)
% 0.14/0.38  % (4375)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 (2999ds/275Mi)
% 0.14/0.38  % (4376)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38  % (4377)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.38  % (4374)Instruction limit reached!
% 0.14/0.38  % (4374)------------------------------
% 0.14/0.38  % (4374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (4374)Termination reason: Unknown
% 0.14/0.38  % (4374)Termination phase: Property scanning
% 0.14/0.38  
% 0.14/0.38  % (4374)Memory used [KB]: 895
% 0.14/0.38  % (4374)Time elapsed: 0.003 s
% 0.14/0.38  % (4374)Instructions burned: 2 (million)
% 0.14/0.38  % (4374)------------------------------
% 0.14/0.38  % (4374)------------------------------
% 0.14/0.38  % (4377)Instruction limit reached!
% 0.14/0.38  % (4377)------------------------------
% 0.14/0.38  % (4377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (4377)Termination reason: Unknown
% 0.14/0.38  % (4377)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (4377)Memory used [KB]: 5500
% 0.14/0.38  % (4377)Time elapsed: 0.005 s
% 0.14/0.38  % (4377)Instructions burned: 3 (million)
% 0.14/0.38  % (4377)------------------------------
% 0.14/0.38  % (4377)------------------------------
% 0.14/0.38  % (4371)Instruction limit reached!
% 0.14/0.38  % (4371)------------------------------
% 0.14/0.38  % (4371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (4371)Termination reason: Unknown
% 0.14/0.38  % (4371)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (4371)Memory used [KB]: 5500
% 0.14/0.38  % (4371)Time elapsed: 0.006 s
% 0.14/0.38  % (4371)Instructions burned: 5 (million)
% 0.14/0.38  % (4371)------------------------------
% 0.14/0.38  % (4371)------------------------------
% 0.14/0.38  % (4373)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38  % (4373)Instruction limit reached!
% 0.14/0.38  % (4373)------------------------------
% 0.14/0.38  % (4373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (4373)Termination reason: Unknown
% 0.14/0.38  % (4373)Termination phase: Preprocessing 3
% 0.14/0.38  
% 0.14/0.38  % (4373)Memory used [KB]: 895
% 0.14/0.38  % (4373)Time elapsed: 0.003 s
% 0.14/0.38  % (4373)Instructions burned: 2 (million)
% 0.14/0.38  % (4373)------------------------------
% 0.14/0.38  % (4373)------------------------------
% 0.14/0.39  % (4376)Instruction limit reached!
% 0.14/0.39  % (4376)------------------------------
% 0.14/0.39  % (4376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (4376)Termination reason: Unknown
% 0.14/0.39  % (4376)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (4376)Memory used [KB]: 5628
% 0.14/0.39  % (4376)Time elapsed: 0.014 s
% 0.14/0.39  % (4376)Instructions burned: 19 (million)
% 0.14/0.39  % (4376)------------------------------
% 0.14/0.39  % (4376)------------------------------
% 0.14/0.39  % (4378)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)
% 0.14/0.39  % (4379)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  % (4380)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  % (4372)First to succeed.
% 0.14/0.40  % (4380)Instruction limit reached!
% 0.14/0.40  % (4380)------------------------------
% 0.14/0.40  % (4380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (4380)Termination reason: Unknown
% 0.14/0.40  % (4380)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (4380)Memory used [KB]: 5500
% 0.14/0.40  % (4380)Time elapsed: 0.004 s
% 0.14/0.40  % (4380)Instructions burned: 3 (million)
% 0.14/0.40  % (4380)------------------------------
% 0.14/0.40  % (4380)------------------------------
% 0.14/0.40  % (4381)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)
% 0.14/0.40  % (4372)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (4372)------------------------------
% 0.14/0.40  % (4372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (4372)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (4372)Memory used [KB]: 5756
% 0.14/0.40  % (4372)Time elapsed: 0.026 s
% 0.14/0.40  % (4372)Instructions burned: 26 (million)
% 0.14/0.40  % (4372)------------------------------
% 0.14/0.40  % (4372)------------------------------
% 0.14/0.40  % (4369)Success in time 0.028 s
% 0.14/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------