TSTP Solution File: SEV046^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV046^5 : 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 : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:11:50 EDT 2024

% Result   : Theorem 0.18s 0.46s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   47
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  181 (  41 unt;  17 typ;   0 def)
%            Number of atoms       : 1473 ( 179 equ;   0 cnn)
%            Maximal formula atoms :    2 (   8 avg)
%            Number of connectives : 4236 ( 132   ~; 121   |; 160   &;2963   @)
%                                         (   2 <=>; 350  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  230 ( 230   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  15 usr;   9 con; 0-3 aty)
%                                         ( 508  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  715 ( 539   ^ 175   !;   0   ?; 715   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_7,type,
    b: $tType ).

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

thf(func_def_1,type,
    b: $tType ).

thf(func_def_19,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_20,type,
    sK2: a > b > b > $o ).

thf(func_def_21,type,
    sK3: a > a > $o ).

thf(func_def_22,type,
    sK4: a > b ).

thf(func_def_23,type,
    sK5: a > b ).

thf(func_def_24,type,
    sK6: a > b ).

thf(func_def_25,type,
    sK7: a ).

thf(func_def_26,type,
    sK8: a > b ).

thf(func_def_27,type,
    sK9: a ).

thf(func_def_28,type,
    sK10: a > b ).

thf(func_def_29,type,
    sK11: a > b ).

thf(func_def_30,type,
    sK12: a ).

thf(func_def_31,type,
    sK13: a ).

thf(f829,plain,
    $false,
    inference(avatar_sat_refutation,[],[f25,f577,f828]) ).

thf(f828,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f827]) ).

thf(f827,plain,
    ( $false
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f826]) ).

thf(f826,plain,
    ( ( $false = $true )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f825]) ).

thf(f825,plain,
    ( ( $true = ~ $true )
    | ~ spl0_1 ),
    inference(forward_demodulation,[],[f815,f662]) ).

thf(f662,plain,
    ( ( ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) )
      = $true )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f660]) ).

thf(f660,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f636,f608]) ).

thf(f608,plain,
    ( ( $true
      = ( sK3 @ sK12 @ sK13 ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f600]) ).

thf(f600,plain,
    ( ( $true
      = ( $true
       => ( sK3 @ sK12 @ sK13 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f103,f595]) ).

thf(f595,plain,
    ( ( $true
      = ( sK3 @ sK13 @ sK12 ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f593]) ).

thf(f593,plain,
    ( ( $false
      = ( ( sK3 @ sK13 @ sK12 )
       => ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f592]) ).

thf(f592,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK12 )
           => ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ sK12 ) ) )
        @ sK13 ) )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f591]) ).

thf(f591,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK12 )
           => ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ sK12 ) ) ) )
      = $false )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f590]) ).

thf(f590,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) )
        @ sK12 ) )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f584]) ).

thf(f584,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f583]) ).

thf(f583,plain,
    ( ( $false
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
       => ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f582]) ).

thf(f582,plain,
    ( ( $false
      = ( ^ [Y0: a > b] :
            ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y1 @ Y2 )
                     => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y2 @ Y1 )
                     => ( sK2 @ Y2 @ ( sK10 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) )
        @ sK11 ) )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f581]) ).

thf(f581,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y1 @ Y2 )
                     => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y2 @ Y1 )
                     => ( sK2 @ Y2 @ ( sK10 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f580]) ).

thf(f580,plain,
    ( ( $false
      = ( ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y2 @ Y3 )
                         => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) )
        @ sK10 ) )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y2 @ Y3 )
                         => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f20,plain,
    ( spl0_1
  <=> ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y2 @ Y3 )
                         => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f103,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ( sK3 @ X2 @ X1 )
       => ( sK3 @ X1 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f102]) ).

thf(f102,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ X1 )
           => ( sK3 @ X1 @ Y0 ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f101]) ).

thf(f101,plain,
    ! [X1: a] :
      ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ X1 )
           => ( sK3 @ X1 @ Y0 ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f100]) ).

thf(f100,plain,
    ! [X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK3 @ Y0 @ Y1 ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f99]) ).

thf(f99,plain,
    ( ( !! @ a
      @ ^ [Y0: a] :
          ( !! @ a
          @ ^ [Y1: a] :
              ( ( sK3 @ Y1 @ Y0 )
             => ( sK3 @ Y0 @ Y1 ) ) ) )
    = $true ),
    inference(boolean_simplification,[],[f98]) ).

thf(f98,plain,
    ( $true
    = ( $true
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK3 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(backward_demodulation,[],[f93,f97]) ).

thf(f97,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( ( sK2 @ Y1 )
                  = ( sK2 @ Y0 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f93]) ).

thf(f93,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( ( sK2 @ Y1 )
                  = ( sK2 @ Y0 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK3 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(boolean_simplification,[],[f92]) ).

thf(f92,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( ( sK2 @ Y1 )
                  = ( sK2 @ Y0 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK3 @ Y0 @ Y1 ) ) ) )
      & $true ) ),
    inference(backward_demodulation,[],[f15,f90]) ).

thf(f90,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] :
          ( !! @ a
          @ ^ [Y1: a] :
              ( !! @ a
              @ ^ [Y2: a] :
                  ( ( ( sK3 @ Y1 @ Y0 )
                    & ( sK3 @ Y2 @ Y1 ) )
                 => ( sK3 @ Y2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( ( sK2 @ Y1 )
                  = ( sK2 @ Y0 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK3 @ Y0 @ Y1 ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK3 @ Y1 @ Y0 )
                      & ( sK3 @ Y2 @ Y1 ) )
                   => ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( $false
    = ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( ( sK2 @ Y1 )
                    = ( sK2 @ Y0 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ Y0 @ Y0 )
             => ( ( !! @ b
                  @ ^ [Y1: b] :
                      ( !! @ b
                      @ ^ [Y2: b] :
                          ( !! @ b
                          @ ^ [Y3: b] :
                              ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                                & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                             => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
                & ( !! @ b
                  @ ^ [Y1: b] :
                      ( !! @ b
                      @ ^ [Y2: b] :
                          ( ( sK2 @ Y0 @ Y2 @ Y1 )
                         => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK3 @ Y0 @ Y1 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK3 @ Y1 @ Y0 )
                        & ( sK3 @ Y2 @ Y1 ) )
                     => ( sK3 @ Y2 @ Y0 ) ) ) ) ) )
     => ( ( !! @ ( a > b )
          @ ^ [Y0: a > b] :
              ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y3 @ Y2 )
                           => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ( !! @ ( a > b )
          @ ^ [Y0: a > b] :
              ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( ( ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK3 @ Y3 @ Y4 )
                                 => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK3 @ Y3 @ Y4 )
                                 => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y4 @ Y3 )
                               => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f12]) ).

thf(f12,plain,
    ( $false
    = ( ^ [Y0: a > a > $o] :
          ( ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 @ Y1 )
                     => ( ( sK2 @ Y2 )
                        = ( sK2 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 @ Y1 )
                 => ( ( !! @ b
                      @ ^ [Y2: b] :
                          ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( ( ( sK2 @ Y1 @ Y3 @ Y4 )
                                    & ( sK2 @ Y1 @ Y2 @ Y3 ) )
                                 => ( sK2 @ Y1 @ Y2 @ Y4 ) ) ) ) )
                    & ( !! @ b
                      @ ^ [Y2: b] :
                          ( !! @ b
                          @ ^ [Y3: b] :
                              ( ( sK2 @ Y1 @ Y3 @ Y2 )
                             => ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 @ Y1 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y1 )
                            & ( Y0 @ Y3 @ Y2 ) )
                         => ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
         => ( ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y4 @ Y3 )
                               => ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
            & ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( ( ( !! @ a
                              @ ^ [Y4: a] :
                                  ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( ( Y0 @ Y4 @ Y5 )
                                     => ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
                            & ( !! @ a
                              @ ^ [Y4: a] :
                                  ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( ( Y0 @ Y4 @ Y5 )
                                     => ( sK2 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y0 @ Y5 @ Y4 )
                                   => ( sK2 @ Y5 @ ( Y1 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
      @ sK3 ) ),
    inference(sigma_clausification,[],[f11]) ).

thf(f11,plain,
    ( $false
    = ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 @ Y1 )
                     => ( ( sK2 @ Y2 )
                        = ( sK2 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 @ Y1 )
                 => ( ( !! @ b
                      @ ^ [Y2: b] :
                          ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( ( ( sK2 @ Y1 @ Y3 @ Y4 )
                                    & ( sK2 @ Y1 @ Y2 @ Y3 ) )
                                 => ( sK2 @ Y1 @ Y2 @ Y4 ) ) ) ) )
                    & ( !! @ b
                      @ ^ [Y2: b] :
                          ( !! @ b
                          @ ^ [Y3: b] :
                              ( ( sK2 @ Y1 @ Y3 @ Y2 )
                             => ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 @ Y1 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y1 )
                            & ( Y0 @ Y3 @ Y2 ) )
                         => ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
         => ( ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y4 @ Y3 )
                               => ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
            & ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( ( ( !! @ a
                              @ ^ [Y4: a] :
                                  ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( ( Y0 @ Y4 @ Y5 )
                                     => ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
                            & ( !! @ a
                              @ ^ [Y4: a] :
                                  ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( ( Y0 @ Y4 @ Y5 )
                                     => ( sK2 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y0 @ Y5 @ Y4 )
                                   => ( sK2 @ Y5 @ ( Y1 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( $false
    = ( ^ [Y0: a > b > b > $o] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 @ Y2 )
                         => ( ( Y0 @ Y3 )
                            = ( Y0 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 @ Y2 )
                     => ( ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( !! @ b
                                  @ ^ [Y5: b] :
                                      ( ( ( Y0 @ Y2 @ Y4 @ Y5 )
                                        & ( Y0 @ Y2 @ Y3 @ Y4 ) )
                                     => ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
                        & ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( ( Y0 @ Y2 @ Y4 @ Y3 )
                                 => ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 @ Y2 )
                         => ( Y1 @ Y2 @ Y3 ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( ( Y1 @ Y3 @ Y2 )
                                & ( Y1 @ Y4 @ Y3 ) )
                             => ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
             => ( ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y1 @ Y4 @ Y5 )
                                   => ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y1 @ Y5 @ Y4 )
                                   => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
                & ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y4: a > b] :
                              ( ( ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( ( Y1 @ Y5 @ Y6 )
                                         => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( ( Y1 @ Y5 @ Y6 )
                                         => ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
                             => ( !! @ a
                                @ ^ [Y5: a] :
                                    ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( ( Y1 @ Y6 @ Y5 )
                                       => ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_clausification,[],[f7]) ).

thf(f7,plain,
    ( $false
    = ( !! @ ( a > b > b > $o )
      @ ^ [Y0: a > b > b > $o] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 @ Y2 )
                         => ( ( Y0 @ Y3 )
                            = ( Y0 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 @ Y2 )
                     => ( ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( !! @ b
                                  @ ^ [Y5: b] :
                                      ( ( ( Y0 @ Y2 @ Y4 @ Y5 )
                                        & ( Y0 @ Y2 @ Y3 @ Y4 ) )
                                     => ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
                        & ( !! @ b
                          @ ^ [Y3: b] :
                              ( !! @ b
                              @ ^ [Y4: b] :
                                  ( ( Y0 @ Y2 @ Y4 @ Y3 )
                                 => ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 @ Y2 )
                         => ( Y1 @ Y2 @ Y3 ) ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( ( Y1 @ Y3 @ Y2 )
                                & ( Y1 @ Y4 @ Y3 ) )
                             => ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
             => ( ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y1 @ Y4 @ Y5 )
                                   => ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( !! @ a
                                @ ^ [Y5: a] :
                                    ( ( Y1 @ Y5 @ Y4 )
                                   => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
                & ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( !! @ ( a > b )
                      @ ^ [Y3: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y4: a > b] :
                              ( ( ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( ( Y1 @ Y5 @ Y6 )
                                         => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y5: a] :
                                      ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( ( Y1 @ Y5 @ Y6 )
                                         => ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
                             => ( !! @ a
                                @ ^ [Y5: a] :
                                    ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( ( Y1 @ Y6 @ Y5 )
                                       => ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f6]) ).

thf(f6,plain,
    ( $true
    = ( ~ ( !! @ ( a > b > b > $o )
          @ ^ [Y0: a > b > b > $o] :
              ( !! @ ( a > a > $o )
              @ ^ [Y1: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 @ Y2 )
                             => ( ( Y0 @ Y3 )
                                = ( Y0 @ Y2 ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 @ Y2 )
                         => ( ( !! @ b
                              @ ^ [Y3: b] :
                                  ( !! @ b
                                  @ ^ [Y4: b] :
                                      ( !! @ b
                                      @ ^ [Y5: b] :
                                          ( ( ( Y0 @ Y2 @ Y4 @ Y5 )
                                            & ( Y0 @ Y2 @ Y3 @ Y4 ) )
                                         => ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !! @ b
                              @ ^ [Y3: b] :
                                  ( !! @ b
                                  @ ^ [Y4: b] :
                                      ( ( Y0 @ Y2 @ Y4 @ Y3 )
                                     => ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 @ Y2 )
                             => ( Y1 @ Y2 @ Y3 ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( ( Y1 @ Y3 @ Y2 )
                                    & ( Y1 @ Y4 @ Y3 ) )
                                 => ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
                 => ( ( !! @ ( a > b )
                      @ ^ [Y2: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y3: a > b] :
                              ( ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y1 @ Y4 @ Y5 )
                                       => ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y1 @ Y5 @ Y4 )
                                       => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
                    & ( !! @ ( a > b )
                      @ ^ [Y2: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y3: a > b] :
                              ( !! @ ( a > b )
                              @ ^ [Y4: a > b] :
                                  ( ( ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( Y1 @ Y5 @ Y6 )
                                             => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( Y1 @ Y5 @ Y6 )
                                             => ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
                                 => ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( !! @ a
                                        @ ^ [Y6: a] :
                                            ( ( Y1 @ Y6 @ Y5 )
                                           => ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,plain,
    ( $true
    = ( ~ ( !! @ ( a > b > b > $o )
          @ ^ [Y0: a > b > b > $o] :
              ( !! @ ( a > a > $o )
              @ ^ [Y1: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 @ Y2 )
                             => ( ( Y0 @ Y3 )
                                = ( Y0 @ Y2 ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 @ Y2 )
                         => ( ( !! @ b
                              @ ^ [Y3: b] :
                                  ( !! @ b
                                  @ ^ [Y4: b] :
                                      ( !! @ b
                                      @ ^ [Y5: b] :
                                          ( ( ( Y0 @ Y2 @ Y4 @ Y5 )
                                            & ( Y0 @ Y2 @ Y3 @ Y4 ) )
                                         => ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !! @ b
                              @ ^ [Y3: b] :
                                  ( !! @ b
                                  @ ^ [Y4: b] :
                                      ( ( Y0 @ Y2 @ Y4 @ Y3 )
                                     => ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 @ Y2 )
                             => ( Y1 @ Y2 @ Y3 ) ) ) )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( ( Y1 @ Y3 @ Y2 )
                                    & ( Y1 @ Y4 @ Y3 ) )
                                 => ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
                 => ( ( !! @ ( a > b )
                      @ ^ [Y2: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y3: a > b] :
                              ( ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y1 @ Y4 @ Y5 )
                                       => ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y1 @ Y5 @ Y4 )
                                       => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
                    & ( !! @ ( a > b )
                      @ ^ [Y2: a > b] :
                          ( !! @ ( a > b )
                          @ ^ [Y3: a > b] :
                              ( !! @ ( a > b )
                              @ ^ [Y4: a > b] :
                                  ( ( ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( Y1 @ Y5 @ Y6 )
                                             => ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( Y1 @ Y5 @ Y6 )
                                             => ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
                                 => ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( !! @ a
                                        @ ^ [Y6: a] :
                                            ( ( Y1 @ Y6 @ Y5 )
                                           => ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > a > $o,X1: a > b > b > $o] :
        ( ( ! [X2: a,X3: a,X4: a] :
              ( ( ( X0 @ X2 @ X3 )
                & ( X0 @ X3 @ X4 ) )
             => ( X0 @ X2 @ X4 ) )
          & ! [X5: a,X6: a] :
              ( ( X0 @ X5 @ X6 )
             => ( X0 @ X6 @ X5 ) )
          & ! [X7: a] :
              ( ( X0 @ X7 @ X7 )
             => ( ! [X8: b,X9: b] :
                    ( ( X1 @ X7 @ X8 @ X9 )
                   => ( X1 @ X7 @ X9 @ X8 ) )
                & ! [X10: b,X11: b,X12: b] :
                    ( ( ( X1 @ X7 @ X12 @ X11 )
                      & ( X1 @ X7 @ X11 @ X10 ) )
                   => ( X1 @ X7 @ X12 @ X10 ) ) ) )
          & ! [X13: a,X14: a] :
              ( ( X0 @ X13 @ X14 )
             => ( ( X1 @ X13 )
                = ( X1 @ X14 ) ) ) )
       => ( ! [X15: a > b,X16: a > b,X17: a > b] :
              ( ( ! [X18: a,X19: a] :
                    ( ( X0 @ X19 @ X18 )
                   => ( X1 @ X19 @ ( X15 @ X19 ) @ ( X16 @ X18 ) ) )
                & ! [X20: a,X21: a] :
                    ( ( X0 @ X21 @ X20 )
                   => ( X1 @ X21 @ ( X17 @ X21 ) @ ( X15 @ X20 ) ) ) )
             => ! [X22: a,X23: a] :
                  ( ( X0 @ X22 @ X23 )
                 => ( X1 @ X22 @ ( X17 @ X22 ) @ ( X16 @ X23 ) ) ) )
          & ! [X24: a > b,X25: a > b] :
              ( ! [X26: a,X27: a] :
                  ( ( X0 @ X27 @ X26 )
                 => ( X1 @ X27 @ ( X24 @ X27 ) @ ( X25 @ X26 ) ) )
             => ! [X28: a,X29: a] :
                  ( ( X0 @ X28 @ X29 )
                 => ( X1 @ X28 @ ( X25 @ X28 ) @ ( X24 @ X29 ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ! [X0: a > a > $o,X1: a > b > b > $o] :
      ( ( ! [X2: a,X3: a,X4: a] :
            ( ( ( X0 @ X2 @ X3 )
              & ( X0 @ X3 @ X4 ) )
           => ( X0 @ X2 @ X4 ) )
        & ! [X2: a,X3: a] :
            ( ( X0 @ X2 @ X3 )
           => ( X0 @ X3 @ X2 ) )
        & ! [X2: a] :
            ( ( X0 @ X2 @ X2 )
           => ( ! [X5: b,X3: b] :
                  ( ( X1 @ X2 @ X5 @ X3 )
                 => ( X1 @ X2 @ X3 @ X5 ) )
              & ! [X4: b,X3: b,X5: b] :
                  ( ( ( X1 @ X2 @ X5 @ X3 )
                    & ( X1 @ X2 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X5 @ X4 ) ) ) )
        & ! [X2: a,X3: a] :
            ( ( X0 @ X2 @ X3 )
           => ( ( X1 @ X2 )
              = ( X1 @ X3 ) ) ) )
     => ( ! [X3: a > b,X4: a > b,X2: a > b] :
            ( ( ! [X6: a,X5: a] :
                  ( ( X0 @ X5 @ X6 )
                 => ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
              & ! [X6: a,X5: a] :
                  ( ( X0 @ X5 @ X6 )
                 => ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) ) )
           => ! [X5: a,X6: a] :
                ( ( X0 @ X5 @ X6 )
               => ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) )
        & ! [X2: a > b,X3: a > b] :
            ( ! [X6: a,X5: a] :
                ( ( X0 @ X5 @ X6 )
               => ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
           => ! [X5: a,X6: a] :
                ( ( X0 @ X5 @ X6 )
               => ( X1 @ X5 @ ( X3 @ X5 ) @ ( X2 @ X6 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM507_pme) ).

thf(f636,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( sK3 @ X1 @ X2 )
         => ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ X2 ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f635]) ).

thf(f635,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ Y0 ) ) )
          @ X2 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f625]) ).

thf(f625,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ Y0 ) ) ) )
        = $true )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f624]) ).

thf(f624,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) )
          @ X1 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f585]) ).

thf(f585,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f583]) ).

thf(f815,plain,
    ( ( $true
      = ( ~ ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f800]) ).

thf(f800,plain,
    ( ( $true
      = ( ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) )
       => $false ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f796,f759]) ).

thf(f759,plain,
    ( ( $false
      = ( sK2 @ sK12 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f743,f599]) ).

thf(f599,plain,
    ( ( $false
      = ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f598]) ).

thf(f598,plain,
    ( ( $false
      = ( $true
       => ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
    | ~ spl0_1 ),
    inference(backward_demodulation,[],[f593,f595]) ).

thf(f743,plain,
    ( ! [X2: b,X1: b] :
        ( ( sK2 @ sK12 @ X1 @ X2 )
        = ( sK2 @ sK13 @ X1 @ X2 ) )
    | ~ spl0_1 ),
    inference(argument_congruence,[],[f740]) ).

thf(f740,plain,
    ( ! [X1: b] :
        ( ( sK2 @ sK13 @ X1 )
        = ( sK2 @ sK12 @ X1 ) )
    | ~ spl0_1 ),
    inference(argument_congruence,[],[f733]) ).

thf(f733,plain,
    ( ( ( sK2 @ sK12 )
      = ( sK2 @ sK13 ) )
    | ~ spl0_1 ),
    inference(equality_proxy_clausification,[],[f607]) ).

thf(f607,plain,
    ( ( $true
      = ( ( sK2 @ sK13 )
        = ( sK2 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f605]) ).

thf(f605,plain,
    ( ( ( $true
       => ( ( sK2 @ sK13 )
          = ( sK2 @ sK12 ) ) )
      = $true )
    | ~ spl0_1 ),
    inference(superposition,[],[f231,f595]) ).

thf(f231,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ( sK3 @ X2 @ X1 )
       => ( ( sK2 @ X2 )
          = ( sK2 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f230]) ).

thf(f230,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ X1 )
           => ( ( sK2 @ Y0 )
              = ( sK2 @ X1 ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f227]) ).

thf(f227,plain,
    ! [X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ X1 )
           => ( ( sK2 @ Y0 )
              = ( sK2 @ X1 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f226]) ).

thf(f226,plain,
    ! [X1: a] :
      ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( ( sK2 @ Y1 )
                  = ( sK2 @ Y0 ) ) ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f156]) ).

thf(f156,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] :
          ( !! @ a
          @ ^ [Y1: a] :
              ( ( sK3 @ Y1 @ Y0 )
             => ( ( sK2 @ Y1 )
                = ( sK2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f97]) ).

thf(f796,plain,
    ( ! [X2: b,X1: b] :
        ( ( ( sK2 @ sK12 @ X2 @ X1 )
         => ( sK2 @ sK12 @ X1 @ X2 ) )
        = $true )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f795]) ).

thf(f795,plain,
    ( ! [X2: b,X1: b] :
        ( $true
        = ( ^ [Y0: b] :
              ( ( sK2 @ sK12 @ Y0 @ X1 )
             => ( sK2 @ sK12 @ X1 @ Y0 ) )
          @ X2 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f787]) ).

thf(f787,plain,
    ( ! [X1: b] :
        ( $true
        = ( !! @ b
          @ ^ [Y0: b] :
              ( ( sK2 @ sK12 @ Y0 @ X1 )
             => ( sK2 @ sK12 @ X1 @ Y0 ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f785]) ).

thf(f785,plain,
    ( ! [X1: b] :
        ( $true
        = ( ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( sK2 @ sK12 @ Y1 @ Y0 )
                 => ( sK2 @ sK12 @ Y0 @ Y1 ) ) )
          @ X1 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f784]) ).

thf(f784,plain,
    ( ( ( !! @ b
        @ ^ [Y0: b] :
            ( !! @ b
            @ ^ [Y1: b] :
                ( ( sK2 @ sK12 @ Y1 @ Y0 )
               => ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f783]) ).

thf(f783,plain,
    ( ( $true
      = ( $true
        & ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( sK2 @ sK12 @ Y1 @ Y0 )
                 => ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(backward_demodulation,[],[f652,f780]) ).

thf(f780,plain,
    ( ( $true
      = ( !! @ b
        @ ^ [Y0: b] :
            ( !! @ b
            @ ^ [Y1: b] :
                ( !! @ b
                @ ^ [Y2: b] :
                    ( ( ( sK2 @ sK12 @ Y1 @ Y2 )
                      & ( sK2 @ sK12 @ Y0 @ Y1 ) )
                   => ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f652]) ).

thf(f652,plain,
    ( ( ( ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( ( ( sK2 @ sK12 @ Y1 @ Y2 )
                        & ( sK2 @ sK12 @ Y0 @ Y1 ) )
                     => ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) )
        & ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( sK2 @ sK12 @ Y1 @ Y0 )
                 => ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f638]) ).

thf(f638,plain,
    ( ( $true
      = ( $true
       => ( ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( ( sK2 @ sK12 @ Y1 @ Y2 )
                          & ( sK2 @ sK12 @ Y0 @ Y1 ) )
                       => ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) )
          & ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( ( sK2 @ sK12 @ Y1 @ Y0 )
                   => ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f165,f634]) ).

thf(f634,plain,
    ( ( $true
      = ( sK3 @ sK12 @ sK12 ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f629]) ).

thf(f629,plain,
    ( ( $true
      = ( $true
       => ( sK3 @ sK12 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f609,f608]) ).

thf(f609,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( sK3 @ X0 @ sK13 )
         => ( sK3 @ X0 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f602]) ).

thf(f602,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( $true
            & ( sK3 @ X0 @ sK13 ) )
         => ( sK3 @ X0 @ sK12 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f137,f595]) ).

thf(f137,plain,
    ! [X2: a,X3: a,X1: a] :
      ( ( ( ( sK3 @ X2 @ X1 )
          & ( sK3 @ X3 @ X2 ) )
       => ( sK3 @ X3 @ X1 ) )
      = $true ),
    inference(beta_eta_normalization,[],[f136]) ).

thf(f136,plain,
    ! [X2: a,X3: a,X1: a] :
      ( ( ^ [Y0: a] :
            ( ( ( sK3 @ X2 @ X1 )
              & ( sK3 @ Y0 @ X2 ) )
           => ( sK3 @ Y0 @ X1 ) )
        @ X3 )
      = $true ),
    inference(pi_clausification,[],[f133]) ).

thf(f133,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK3 @ X2 @ X1 )
              & ( sK3 @ Y0 @ X2 ) )
           => ( sK3 @ Y0 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f132]) ).

thf(f132,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ X1 )
                  & ( sK3 @ Y1 @ Y0 ) )
               => ( sK3 @ Y1 @ X1 ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f129]) ).

thf(f129,plain,
    ! [X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ X1 )
                  & ( sK3 @ Y1 @ Y0 ) )
               => ( sK3 @ Y1 @ X1 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f128]) ).

thf(f128,plain,
    ! [X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK3 @ Y1 @ Y0 )
                      & ( sK3 @ Y2 @ Y1 ) )
                   => ( sK3 @ Y2 @ Y0 ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f90]) ).

thf(f165,plain,
    ! [X1: a] :
      ( ( ( sK3 @ X1 @ X1 )
       => ( ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( ( sK2 @ X1 @ Y1 @ Y2 )
                          & ( sK2 @ X1 @ Y0 @ Y1 ) )
                       => ( sK2 @ X1 @ Y0 @ Y2 ) ) ) ) )
          & ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( ( sK2 @ X1 @ Y1 @ Y0 )
                   => ( sK2 @ X1 @ Y0 @ Y1 ) ) ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f164]) ).

thf(f164,plain,
    ! [X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f158]) ).

thf(f158,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] :
          ( ( sK3 @ Y0 @ Y0 )
         => ( ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( !! @ b
                      @ ^ [Y3: b] :
                          ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                            & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                         => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( ( sK2 @ Y0 @ Y2 @ Y1 )
                     => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(boolean_simplification,[],[f157]) ).

thf(f157,plain,
    ( $true
    = ( $true
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ Y0 )
           => ( ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( !! @ b
                        @ ^ [Y3: b] :
                            ( ( ( sK2 @ Y0 @ Y2 @ Y3 )
                              & ( sK2 @ Y0 @ Y1 @ Y2 ) )
                           => ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( sK2 @ Y0 @ Y2 @ Y1 )
                       => ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
    inference(backward_demodulation,[],[f97,f156]) ).

thf(f577,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f576]) ).

thf(f576,plain,
    ( $false
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f575]) ).

thf(f575,plain,
    ( ( $false = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f574]) ).

thf(f574,plain,
    ( ( $true = ~ $true )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f565,f328]) ).

thf(f328,plain,
    ( ( $true
      = ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f322,f74]) ).

thf(f74,plain,
    ( ( ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) )
      = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f73]) ).

thf(f73,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f71,f52]) ).

thf(f52,plain,
    ( ( ( sK3 @ sK9 @ sK7 )
      = $true )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ( ( ( ( sK3 @ sK9 @ sK7 )
       => ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
      = $false )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f46]) ).

thf(f46,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK7 )
           => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK7 ) ) )
        @ sK9 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f43]) ).

thf(f43,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK7 )
           => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK7 ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f42]) ).

thf(f42,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) )
        @ sK7 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f34]) ).

thf(f34,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y0 @ Y1 )
                   => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y0 @ Y1 )
                   => ( sK2 @ Y0 @ ( sK6 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
       => ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f32]) ).

thf(f32,plain,
    ( ( $false
      = ( ^ [Y0: a > b] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y2 @ Y1 )
                     => ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) )
        @ sK6 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f31]) ).

thf(f31,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK3 @ Y2 @ Y1 )
                     => ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f30]) ).

thf(f30,plain,
    ( ( $false
      = ( ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
                  & ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( sK4 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) )
        @ sK5 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f29]) ).

thf(f29,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
                  & ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( sK4 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f28]) ).

thf(f28,plain,
    ( ( ( ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( !! @ ( a > b )
                @ ^ [Y2: a > b] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( sK3 @ Y4 @ Y3 )
                             => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
        @ sK4 )
      = $false )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f24]) ).

thf(f24,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( !! @ ( a > b )
                @ ^ [Y2: a > b] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( sK3 @ Y4 @ Y3 )
                             => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f23]) ).

thf(f23,plain,
    ( spl0_2
  <=> ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( !! @ ( a > b )
                @ ^ [Y2: a > b] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( sK3 @ Y4 @ Y3 )
                             => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f71,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( sK3 @ X1 @ X2 )
         => ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ X2 ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f70]) ).

thf(f70,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ Y0 ) ) )
          @ X2 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f67]) ).

thf(f67,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ Y0 ) ) ) )
        = $true )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f66]) ).

thf(f66,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) )
          @ X1 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f56]) ).

thf(f56,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(not_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( $false
      = ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK3 @ Y0 @ Y1 )
                     => ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK3 @ Y0 @ Y1 )
                     => ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f44]) ).

thf(f44,plain,
    ( ( $false
      = ( ^ [Y0: a > b] :
            ~ ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
        @ sK8 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f38]) ).

thf(f38,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ~ ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f37]) ).

thf(f37,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
           => $false ) ) )
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f31,f34]) ).

thf(f322,plain,
    ( ! [X2: b,X1: b] :
        ( ( sK2 @ sK7 @ X1 @ X2 )
        = ( sK2 @ sK9 @ X1 @ X2 ) )
    | ~ spl0_2 ),
    inference(argument_congruence,[],[f315]) ).

thf(f315,plain,
    ( ! [X1: b] :
        ( ( sK2 @ sK7 @ X1 )
        = ( sK2 @ sK9 @ X1 ) )
    | ~ spl0_2 ),
    inference(argument_congruence,[],[f308]) ).

thf(f308,plain,
    ( ( ( sK2 @ sK7 )
      = ( sK2 @ sK9 ) )
    | ~ spl0_2 ),
    inference(equality_proxy_clausification,[],[f241]) ).

thf(f241,plain,
    ( ( $true
      = ( ( sK2 @ sK9 )
        = ( sK2 @ sK7 ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f235]) ).

thf(f235,plain,
    ( ( $true
      = ( $true
       => ( ( sK2 @ sK9 )
          = ( sK2 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f231,f52]) ).

thf(f565,plain,
    ( ( $true
      = ( ~ ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f560]) ).

thf(f560,plain,
    ( ( $true
      = ( ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) )
       => $false ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f442,f334]) ).

thf(f334,plain,
    ( ( $false
      = ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f54,f322]) ).

thf(f54,plain,
    ( ( $false
      = ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f53]) ).

thf(f53,plain,
    ( ( $false
      = ( $true
       => ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f47,f52]) ).

thf(f442,plain,
    ( ! [X0: b] :
        ( $true
        = ( ( sK2 @ sK7 @ X0 @ ( sK8 @ sK7 ) )
         => ( sK2 @ sK7 @ X0 @ ( sK5 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f422]) ).

thf(f422,plain,
    ( ! [X0: b] :
        ( $true
        = ( ( $true
            & ( sK2 @ sK7 @ X0 @ ( sK8 @ sK7 ) ) )
         => ( sK2 @ sK7 @ X0 @ ( sK5 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f391,f215]) ).

thf(f215,plain,
    ( ( $true
      = ( sK2 @ sK7 @ ( sK8 @ sK7 ) @ ( sK5 @ sK7 ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f203]) ).

thf(f203,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK7 @ ( sK8 @ sK7 ) @ ( sK5 @ sK7 ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f62,f197]) ).

thf(f197,plain,
    ( ( $true
      = ( sK3 @ sK7 @ sK7 ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f195]) ).

thf(f195,plain,
    ( ( ( $true
       => ( sK3 @ sK7 @ sK7 ) )
      = $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f151,f108]) ).

thf(f108,plain,
    ( ( $true
      = ( sK3 @ sK7 @ sK9 ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f106]) ).

thf(f106,plain,
    ( ( $true
      = ( $true
       => ( sK3 @ sK7 @ sK9 ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f103,f52]) ).

thf(f151,plain,
    ( ! [X0: a] :
        ( ( ( sK3 @ X0 @ sK9 )
         => ( sK3 @ X0 @ sK7 ) )
        = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f145]) ).

thf(f145,plain,
    ( ! [X0: a] :
        ( ( ( $true
            & ( sK3 @ X0 @ sK9 ) )
         => ( sK3 @ X0 @ sK7 ) )
        = $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f137,f52]) ).

thf(f62,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( sK3 @ X1 @ X2 )
         => ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ X2 ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f61]) ).

thf(f61,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ Y0 ) ) )
          @ X2 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f60]) ).

thf(f60,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ Y0 ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f59]) ).

thf(f59,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) )
          @ X1 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f57]) ).

thf(f57,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f48,f56]) ).

thf(f391,plain,
    ( ! [X2: b,X3: b,X1: b] :
        ( $true
        = ( ( ( sK2 @ sK7 @ X2 @ X3 )
            & ( sK2 @ sK7 @ X1 @ X2 ) )
         => ( sK2 @ sK7 @ X1 @ X3 ) ) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f390,f322]) ).

thf(f390,plain,
    ( ! [X2: b,X3: b,X1: b] :
        ( $true
        = ( ( ( sK2 @ sK7 @ X2 @ X3 )
            & ( sK2 @ sK7 @ X1 @ X2 ) )
         => ( sK2 @ sK9 @ X1 @ X3 ) ) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f389,f322]) ).

thf(f389,plain,
    ( ! [X2: b,X3: b,X1: b] :
        ( $true
        = ( ( ( sK2 @ sK7 @ X2 @ X3 )
            & ( sK2 @ sK9 @ X1 @ X2 ) )
         => ( sK2 @ sK9 @ X1 @ X3 ) ) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f388,f322]) ).

thf(f388,plain,
    ( ! [X2: b,X3: b,X1: b] :
        ( $true
        = ( ( ( sK2 @ sK9 @ X2 @ X3 )
            & ( sK2 @ sK9 @ X1 @ X2 ) )
         => ( sK2 @ sK9 @ X1 @ X3 ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f387]) ).

thf(f387,plain,
    ( ! [X2: b,X3: b,X1: b] :
        ( ( ^ [Y0: b] :
              ( ( ( sK2 @ sK9 @ X2 @ Y0 )
                & ( sK2 @ sK9 @ X1 @ X2 ) )
             => ( sK2 @ sK9 @ X1 @ Y0 ) )
          @ X3 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f386]) ).

thf(f386,plain,
    ( ! [X2: b,X1: b] :
        ( ( !! @ b
          @ ^ [Y0: b] :
              ( ( ( sK2 @ sK9 @ X2 @ Y0 )
                & ( sK2 @ sK9 @ X1 @ X2 ) )
             => ( sK2 @ sK9 @ X1 @ Y0 ) ) )
        = $true )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f385]) ).

thf(f385,plain,
    ( ! [X2: b,X1: b] :
        ( ( ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( ( sK2 @ sK9 @ Y0 @ Y1 )
                    & ( sK2 @ sK9 @ X1 @ Y0 ) )
                 => ( sK2 @ sK9 @ X1 @ Y1 ) ) )
          @ X2 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f381]) ).

thf(f381,plain,
    ( ! [X1: b] :
        ( $true
        = ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( ( sK2 @ sK9 @ Y0 @ Y1 )
                    & ( sK2 @ sK9 @ X1 @ Y0 ) )
                 => ( sK2 @ sK9 @ X1 @ Y1 ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f379]) ).

thf(f379,plain,
    ( ! [X1: b] :
        ( $true
        = ( ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( ( ( sK2 @ sK9 @ Y1 @ Y2 )
                        & ( sK2 @ sK9 @ Y0 @ Y1 ) )
                     => ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) )
          @ X1 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f378]) ).

thf(f378,plain,
    ( ( $true
      = ( !! @ b
        @ ^ [Y0: b] :
            ( !! @ b
            @ ^ [Y1: b] :
                ( !! @ b
                @ ^ [Y2: b] :
                    ( ( ( sK2 @ sK9 @ Y1 @ Y2 )
                      & ( sK2 @ sK9 @ Y0 @ Y1 ) )
                   => ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f377]) ).

thf(f377,plain,
    ( ( $true
      = ( ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( ( ( sK2 @ sK9 @ Y1 @ Y2 )
                        & ( sK2 @ sK9 @ Y0 @ Y1 ) )
                     => ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
        & $true ) )
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f190,f373]) ).

thf(f373,plain,
    ( ( ( !! @ b
        @ ^ [Y0: b] :
            ( !! @ b
            @ ^ [Y1: b] :
                ( ( sK2 @ sK9 @ Y1 @ Y0 )
               => ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f190]) ).

thf(f190,plain,
    ( ( ( ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( !! @ b
                  @ ^ [Y2: b] :
                      ( ( ( sK2 @ sK9 @ Y1 @ Y2 )
                        & ( sK2 @ sK9 @ Y0 @ Y1 ) )
                     => ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
        & ( !! @ b
          @ ^ [Y0: b] :
              ( !! @ b
              @ ^ [Y1: b] :
                  ( ( sK2 @ sK9 @ Y1 @ Y0 )
                 => ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f189]) ).

thf(f189,plain,
    ( ( $true
      = ( $true
       => ( ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( !! @ b
                    @ ^ [Y2: b] :
                        ( ( ( sK2 @ sK9 @ Y1 @ Y2 )
                          & ( sK2 @ sK9 @ Y0 @ Y1 ) )
                       => ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
          & ( !! @ b
            @ ^ [Y0: b] :
                ( !! @ b
                @ ^ [Y1: b] :
                    ( ( sK2 @ sK9 @ Y1 @ Y0 )
                   => ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f165,f163]) ).

thf(f163,plain,
    ( ( $true
      = ( sK3 @ sK9 @ sK9 ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f161]) ).

thf(f161,plain,
    ( ( $true
      = ( $true
       => ( sK3 @ sK9 @ sK9 ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f147,f108]) ).

thf(f147,plain,
    ( ! [X0: a] :
        ( ( ( sK3 @ sK7 @ X0 )
         => ( sK3 @ sK9 @ X0 ) )
        = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f143]) ).

thf(f143,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( ( sK3 @ sK7 @ X0 )
            & $true )
         => ( sK3 @ sK9 @ X0 ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f137,f52]) ).

thf(f25,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f18,f23,f20]) ).

thf(f18,plain,
    ( ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y2 @ Y3 )
                         => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
    | ( $false
      = ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( !! @ ( a > b )
                @ ^ [Y2: a > b] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( sK3 @ Y4 @ Y3 )
                             => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( $false
    = ( ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y2 @ Y3 )
                         => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK3 @ Y3 @ Y2 )
                         => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
      & ( !! @ ( a > b )
        @ ^ [Y0: a > b] :
            ( !! @ ( a > b )
            @ ^ [Y1: a > b] :
                ( !! @ ( a > b )
                @ ^ [Y2: a > b] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y3 @ Y4 )
                               => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( !! @ a
                          @ ^ [Y4: a] :
                              ( ( sK3 @ Y4 @ Y3 )
                             => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(boolean_simplification,[],[f16]) ).

thf(f16,plain,
    ( $false
    = ( $true
     => ( ( !! @ ( a > b )
          @ ^ [Y0: a > b] :
              ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y2 @ Y3 )
                           => ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK3 @ Y3 @ Y2 )
                           => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
        & ( !! @ ( a > b )
          @ ^ [Y0: a > b] :
              ( !! @ ( a > b )
              @ ^ [Y1: a > b] :
                  ( !! @ ( a > b )
                  @ ^ [Y2: a > b] :
                      ( ( ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK3 @ Y3 @ Y4 )
                                 => ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK3 @ Y3 @ Y4 )
                                 => ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( sK3 @ Y4 @ Y3 )
                               => ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(backward_demodulation,[],[f13,f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sun May 19 19:07:52 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a TH0_THM_EQU_NAR problem
% 0.11/0.32  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34  % (8983)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)
% 0.11/0.34  % (8984)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)
% 0.11/0.34  % (8982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34  % (8987)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)
% 0.11/0.34  % (8985)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34  % (8986)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)
% 0.11/0.34  % (8988)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.34  % (8989)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)
% 0.18/0.34  % (8985)Instruction limit reached!
% 0.18/0.34  % (8985)------------------------------
% 0.18/0.34  % (8985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34  % (8985)Termination reason: Unknown
% 0.18/0.34  % (8985)Termination phase: Preprocessing 3
% 0.18/0.34  % (8986)Instruction limit reached!
% 0.18/0.34  % (8986)------------------------------
% 0.18/0.34  % (8986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34  % (8986)Termination reason: Unknown
% 0.18/0.34  % (8986)Termination phase: Property scanning
% 0.18/0.34  
% 0.18/0.34  % (8986)Memory used [KB]: 1023
% 0.18/0.34  % (8986)Time elapsed: 0.003 s
% 0.18/0.34  % (8986)Instructions burned: 3 (million)
% 0.18/0.34  % (8986)------------------------------
% 0.18/0.34  % (8986)------------------------------
% 0.18/0.34  
% 0.18/0.34  % (8985)Memory used [KB]: 1023
% 0.18/0.34  % (8985)Time elapsed: 0.003 s
% 0.18/0.34  % (8985)Instructions burned: 3 (million)
% 0.18/0.34  % (8985)------------------------------
% 0.18/0.34  % (8985)------------------------------
% 0.18/0.34  % (8983)Instruction limit reached!
% 0.18/0.34  % (8983)------------------------------
% 0.18/0.34  % (8983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34  % (8983)Termination reason: Unknown
% 0.18/0.34  % (8983)Termination phase: Saturation
% 0.18/0.34  
% 0.18/0.34  % (8983)Memory used [KB]: 5500
% 0.18/0.34  % (8983)Time elapsed: 0.004 s
% 0.18/0.34  % (8983)Instructions burned: 4 (million)
% 0.18/0.34  % (8983)------------------------------
% 0.18/0.34  % (8983)------------------------------
% 0.18/0.34  % (8989)Instruction limit reached!
% 0.18/0.34  % (8989)------------------------------
% 0.18/0.34  % (8989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34  % (8989)Termination reason: Unknown
% 0.18/0.34  % (8989)Termination phase: Saturation
% 0.18/0.34  
% 0.18/0.34  % (8989)Memory used [KB]: 5500
% 0.18/0.34  % (8989)Time elapsed: 0.004 s
% 0.18/0.34  % (8989)Instructions burned: 4 (million)
% 0.18/0.34  % (8989)------------------------------
% 0.18/0.34  % (8989)------------------------------
% 0.18/0.35  % (8988)Instruction limit reached!
% 0.18/0.35  % (8988)------------------------------
% 0.18/0.35  % (8988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35  % (8988)Termination reason: Unknown
% 0.18/0.35  % (8988)Termination phase: Saturation
% 0.18/0.35  
% 0.18/0.35  % (8988)Memory used [KB]: 5628
% 0.18/0.35  % (8988)Time elapsed: 0.013 s
% 0.18/0.35  % (8988)Instructions burned: 19 (million)
% 0.18/0.35  % (8988)------------------------------
% 0.18/0.35  % (8988)------------------------------
% 0.18/0.35  % (8990)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)
% 0.18/0.35  % (8991)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)
% 0.18/0.35  % (8993)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)
% 0.18/0.35  % (8992)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)
% 0.18/0.35  % (8984)Instruction limit reached!
% 0.18/0.35  % (8984)------------------------------
% 0.18/0.35  % (8984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35  % (8984)Termination reason: Unknown
% 0.18/0.35  % (8984)Termination phase: Saturation
% 0.18/0.35  
% 0.18/0.35  % (8984)Memory used [KB]: 5756
% 0.18/0.35  % (8984)Time elapsed: 0.018 s
% 0.18/0.35  % (8984)Instructions burned: 28 (million)
% 0.18/0.35  % (8984)------------------------------
% 0.18/0.35  % (8984)------------------------------
% 0.18/0.35  % (8992)Instruction limit reached!
% 0.18/0.35  % (8992)------------------------------
% 0.18/0.35  % (8992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35  % (8992)Termination reason: Unknown
% 0.18/0.35  % (8992)Termination phase: Preprocessing 3
% 0.18/0.35  
% 0.18/0.35  % (8992)Memory used [KB]: 1023
% 0.18/0.35  % (8992)Time elapsed: 0.003 s
% 0.18/0.35  % (8992)Instructions burned: 3 (million)
% 0.18/0.35  % (8992)------------------------------
% 0.18/0.35  % (8992)------------------------------
% 0.18/0.36  % (8991)Instruction limit reached!
% 0.18/0.36  % (8991)------------------------------
% 0.18/0.36  % (8991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36  % (8991)Termination reason: Unknown
% 0.18/0.36  % (8991)Termination phase: Saturation
% 0.18/0.36  
% 0.18/0.36  % (8991)Memory used [KB]: 5756
% 0.18/0.36  % (8991)Time elapsed: 0.010 s
% 0.18/0.36  % (8991)Instructions burned: 16 (million)
% 0.18/0.36  % (8991)------------------------------
% 0.18/0.36  % (8991)------------------------------
% 0.18/0.36  % (8994)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.37  % (8994)Instruction limit reached!
% 0.18/0.37  % (8994)------------------------------
% 0.18/0.37  % (8994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (8994)Termination reason: Unknown
% 0.18/0.37  % (8994)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (8994)Memory used [KB]: 1023
% 0.18/0.37  % (8994)Time elapsed: 0.005 s
% 0.18/0.37  % (8994)Instructions burned: 7 (million)
% 0.18/0.37  % (8994)------------------------------
% 0.18/0.37  % (8994)------------------------------
% 0.18/0.37  % (8995)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.37  % (8996)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)
% 0.18/0.37  % (8996)Instruction limit reached!
% 0.18/0.37  % (8996)------------------------------
% 0.18/0.37  % (8996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (8996)Termination reason: Unknown
% 0.18/0.37  % (8996)Termination phase: Preprocessing 3
% 0.18/0.37  
% 0.18/0.37  % (8996)Memory used [KB]: 1023
% 0.18/0.37  % (8996)Time elapsed: 0.003 s
% 0.18/0.37  % (8996)Instructions burned: 3 (million)
% 0.18/0.37  % (8996)------------------------------
% 0.18/0.37  % (8996)------------------------------
% 0.18/0.37  % (8990)Instruction limit reached!
% 0.18/0.37  % (8990)------------------------------
% 0.18/0.37  % (8990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (8990)Termination reason: Unknown
% 0.18/0.37  % (8990)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (8990)Memory used [KB]: 5628
% 0.18/0.37  % (8990)Time elapsed: 0.020 s
% 0.18/0.37  % (8990)Instructions burned: 37 (million)
% 0.18/0.37  % (8990)------------------------------
% 0.18/0.37  % (8990)------------------------------
% 0.18/0.37  % (8997)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.38  % (8997)Instruction limit reached!
% 0.18/0.38  % (8997)------------------------------
% 0.18/0.38  % (8997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (8997)Termination reason: Unknown
% 0.18/0.38  % (8997)Termination phase: Preprocessing 3
% 0.18/0.38  
% 0.18/0.38  % (8997)Memory used [KB]: 1023
% 0.18/0.38  % (8997)Time elapsed: 0.003 s
% 0.18/0.38  % (8995)Instruction limit reached!
% 0.18/0.38  % (8995)------------------------------
% 0.18/0.38  % (8995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (8995)Termination reason: Unknown
% 0.18/0.38  % (8995)Termination phase: Saturation
% 0.18/0.38  
% 0.18/0.38  % (8995)Memory used [KB]: 5756
% 0.18/0.38  % (8995)Time elapsed: 0.010 s
% 0.18/0.38  % (8995)Instructions burned: 16 (million)
% 0.18/0.38  % (8995)------------------------------
% 0.18/0.38  % (8995)------------------------------
% 0.18/0.38  % (8997)Instructions burned: 3 (million)
% 0.18/0.38  % (8997)------------------------------
% 0.18/0.38  % (8997)------------------------------
% 0.18/0.38  % (8998)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.38  % (8999)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.38  % (8998)Instruction limit reached!
% 0.18/0.38  % (8998)------------------------------
% 0.18/0.38  % (8998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (8998)Termination reason: Unknown
% 0.18/0.38  % (8998)Termination phase: Saturation
% 0.18/0.38  
% 0.18/0.38  % (8998)Memory used [KB]: 5500
% 0.18/0.38  % (8998)Time elapsed: 0.005 s
% 0.18/0.38  % (8998)Instructions burned: 7 (million)
% 0.18/0.38  % (8998)------------------------------
% 0.18/0.38  % (8998)------------------------------
% 0.18/0.38  % (8999)Instruction limit reached!
% 0.18/0.38  % (8999)------------------------------
% 0.18/0.38  % (8999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (8999)Termination reason: Unknown
% 0.18/0.38  % (8999)Termination phase: Property scanning
% 0.18/0.38  
% 0.18/0.38  % (8999)Memory used [KB]: 1023
% 0.18/0.38  % (8999)Time elapsed: 0.003 s
% 0.18/0.38  % (8999)Instructions burned: 4 (million)
% 0.18/0.38  % (8999)------------------------------
% 0.18/0.38  % (8999)------------------------------
% 0.18/0.38  % (9000)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.39  % (9000)Instruction limit reached!
% 0.18/0.39  % (9000)------------------------------
% 0.18/0.39  % (9000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39  % (9000)Termination reason: Unknown
% 0.18/0.39  % (9000)Termination phase: Saturation
% 0.18/0.39  
% 0.18/0.39  % (9000)Memory used [KB]: 5500
% 0.18/0.39  % (9000)Time elapsed: 0.004 s
% 0.18/0.39  % (9000)Instructions burned: 5 (million)
% 0.18/0.39  % (9000)------------------------------
% 0.18/0.39  % (9000)------------------------------
% 0.18/0.39  % (9001)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.39  % (9002)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.40  % (9003)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.40  % (9004)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.18/0.40  % (9001)Instruction limit reached!
% 0.18/0.40  % (9001)------------------------------
% 0.18/0.40  % (9001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (9001)Termination reason: Unknown
% 0.18/0.40  % (9001)Termination phase: Saturation
% 0.18/0.40  
% 0.18/0.40  % (9001)Memory used [KB]: 5628
% 0.18/0.40  % (9001)Time elapsed: 0.013 s
% 0.18/0.40  % (9003)Instruction limit reached!
% 0.18/0.40  % (9003)------------------------------
% 0.18/0.40  % (9003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (9001)Instructions burned: 19 (million)
% 0.18/0.40  % (9001)------------------------------
% 0.18/0.40  % (9001)------------------------------
% 0.18/0.40  % (9003)Termination reason: Unknown
% 0.18/0.40  % (9003)Termination phase: Saturation
% 0.18/0.40  
% 0.18/0.40  % (9003)Memory used [KB]: 5500
% 0.18/0.40  % (9003)Time elapsed: 0.005 s
% 0.18/0.40  % (9003)Instructions burned: 7 (million)
% 0.18/0.40  % (9003)------------------------------
% 0.18/0.40  % (9003)------------------------------
% 0.18/0.40  % (9005)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.18/0.41  % (9005)Instruction limit reached!
% 0.18/0.41  % (9005)------------------------------
% 0.18/0.41  % (9005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41  % (9005)Termination reason: Unknown
% 0.18/0.41  % (9005)Termination phase: Saturation
% 0.18/0.41  
% 0.18/0.41  % (9005)Memory used [KB]: 5756
% 0.18/0.41  % (9005)Time elapsed: 0.014 s
% 0.18/0.41  % (9005)Instructions burned: 22 (million)
% 0.18/0.41  % (9005)------------------------------
% 0.18/0.41  % (9005)------------------------------
% 0.18/0.41  % (9006)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.18/0.41  % (9007)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.41  % (9006)Instruction limit reached!
% 0.18/0.41  % (9006)------------------------------
% 0.18/0.41  % (9006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41  % (9006)Termination reason: Unknown
% 0.18/0.41  % (9006)Termination phase: Saturation
% 0.18/0.41  
% 0.18/0.41  % (9006)Memory used [KB]: 5500
% 0.18/0.41  % (9006)Time elapsed: 0.004 s
% 0.18/0.41  % (9006)Instructions burned: 5 (million)
% 0.18/0.41  % (9006)------------------------------
% 0.18/0.41  % (9006)------------------------------
% 0.18/0.42  % (9007)Instruction limit reached!
% 0.18/0.42  % (9007)------------------------------
% 0.18/0.42  % (9007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42  % (9007)Termination reason: Unknown
% 0.18/0.42  % (9007)Termination phase: Saturation
% 0.18/0.42  
% 0.18/0.42  % (9007)Memory used [KB]: 5500
% 0.18/0.42  % (9007)Time elapsed: 0.005 s
% 0.18/0.42  % (9007)Instructions burned: 7 (million)
% 0.18/0.42  % (9007)------------------------------
% 0.18/0.42  % (9007)------------------------------
% 0.18/0.42  % (8982)Instruction limit reached!
% 0.18/0.42  % (8982)------------------------------
% 0.18/0.42  % (8982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42  % (8982)Termination reason: Unknown
% 0.18/0.42  % (8982)Termination phase: Saturation
% 0.18/0.42  
% 0.18/0.42  % (8982)Memory used [KB]: 5884
% 0.18/0.42  % (8982)Time elapsed: 0.083 s
% 0.18/0.42  % (8982)Instructions burned: 184 (million)
% 0.18/0.42  % (8982)------------------------------
% 0.18/0.42  % (8982)------------------------------
% 0.18/0.43  % (9008)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.18/0.43  % (9009)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.18/0.43  % (9010)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.18/0.43  % (9011)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.18/0.44  % (9010)Instruction limit reached!
% 0.18/0.44  % (9010)------------------------------
% 0.18/0.44  % (9010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.44  % (9010)Termination reason: Unknown
% 0.18/0.44  % (9010)Termination phase: Saturation
% 0.18/0.44  
% 0.18/0.44  % (9010)Memory used [KB]: 5628
% 0.18/0.44  % (9010)Time elapsed: 0.010 s
% 0.18/0.44  % (9010)Instructions burned: 19 (million)
% 0.18/0.44  % (9010)------------------------------
% 0.18/0.44  % (9010)------------------------------
% 0.18/0.45  % (8993)First to succeed.
% 0.18/0.45  % (9012)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.18/0.45  % (8987)Instruction limit reached!
% 0.18/0.45  % (8987)------------------------------
% 0.18/0.45  % (8987)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.45  % (8987)Termination reason: Unknown
% 0.18/0.45  % (8987)Termination phase: Saturation
% 0.18/0.45  
% 0.18/0.45  % (8987)Memory used [KB]: 5756
% 0.18/0.45  % (8987)Time elapsed: 0.119 s
% 0.18/0.45  % (8987)Instructions burned: 275 (million)
% 0.18/0.46  % (8987)------------------------------
% 0.18/0.46  % (8987)------------------------------
% 0.18/0.46  % (8993)Refutation found. Thanks to Tanya!
% 0.18/0.46  % SZS status Theorem for theBenchmark
% 0.18/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46  % (8993)------------------------------
% 0.18/0.46  % (8993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.46  % (8993)Termination reason: Refutation
% 0.18/0.46  
% 0.18/0.46  % (8993)Memory used [KB]: 6396
% 0.18/0.46  % (8993)Time elapsed: 0.103 s
% 0.18/0.46  % (8993)Instructions burned: 173 (million)
% 0.18/0.46  % (8993)------------------------------
% 0.18/0.46  % (8993)------------------------------
% 0.18/0.46  % (8981)Success in time 0.118 s
% 0.18/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------