TSTP Solution File: SEV119^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.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 04:12:02 EDT 2024

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   52
%            Number of leaves      :   40
% Syntax   : Number of formulae    :  232 (  18 unt;  31 typ;   0 def)
%            Number of atoms       : 1897 ( 199 equ;   0 cnn)
%            Maximal formula atoms :    4 (   9 avg)
%            Number of connectives : 5102 ( 284   ~; 375   |; 215   &;3091   @)
%                                         (   8 <=>; 490  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  841 ( 841   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  37 usr;  30 con; 0-2 aty)
%                                         ( 639  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  818 ( 732   ^  85   !;   0   ?; 818   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_20,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_21,type,
    sK2: a > a > $o ).

thf(func_def_22,type,
    sK3: a > a > $o ).

thf(func_def_23,type,
    sK4: ( a > a > $o ) > $o ).

thf(func_def_24,type,
    sK5: a ).

thf(func_def_25,type,
    sK6: a ).

thf(func_def_26,type,
    sK7: a > a > $o ).

thf(func_def_27,type,
    sK8: a ).

thf(func_def_28,type,
    sK9: a ).

thf(func_def_29,type,
    sK10: a ).

thf(func_def_30,type,
    sK11: a ).

thf(func_def_31,type,
    sK12: a > a > $o ).

thf(func_def_32,type,
    sK13: a ).

thf(func_def_33,type,
    sK14: a ).

thf(func_def_34,type,
    sK15: a > a > $o ).

thf(func_def_35,type,
    sK16: a > a > $o ).

thf(func_def_36,type,
    sK17: a > a > $o ).

thf(func_def_37,type,
    sK18: a > a > $o ).

thf(func_def_38,type,
    sK19: a ).

thf(func_def_39,type,
    sK20: a ).

thf(func_def_40,type,
    sK21: a ).

thf(func_def_41,type,
    sK22: a ).

thf(func_def_42,type,
    sK23: a ).

thf(func_def_43,type,
    sK24: a ).

thf(func_def_44,type,
    sK25: a ).

thf(func_def_45,type,
    sK26: a ).

thf(func_def_46,type,
    sK27: a ).

thf(func_def_47,type,
    sK28: a ).

thf(func_def_48,type,
    sK29: a ).

thf(f757,plain,
    $false,
    inference(avatar_sat_refutation,[],[f29,f36,f40,f98,f175,f247,f421,f573,f756]) ).

thf(f756,plain,
    ( ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(avatar_contradiction_clause,[],[f755]) ).

thf(f755,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f754]) ).

thf(f754,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f753]) ).

thf(f753,plain,
    ( ( $true = ~ $true )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f752]) ).

thf(f752,plain,
    ( ( $true
      = ( ~ ( $true
            | ( sK2 @ sK28 @ sK27 ) ) ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f751,f747]) ).

thf(f747,plain,
    ( ( $true
      = ( sK3 @ sK28 @ sK27 ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f743]) ).

thf(f743,plain,
    ( ( $false
      = ( ( sK3 @ sK28 @ sK27 )
       => ( sK7 @ sK28 @ sK27 ) ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f742]) ).

thf(f742,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK27 )
           => ( sK7 @ Y0 @ sK27 ) )
        @ sK28 ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f734]) ).

thf(f734,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ Y0 @ sK27 )
           => ( sK7 @ Y0 @ sK27 ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f730]) ).

thf(f730,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK27 )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f724]) ).

thf(f724,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(not_proxy_clausification,[],[f674]) ).

thf(f674,plain,
    ( ( $true
      = ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y1 @ Y0 )
                   => ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f673]) ).

thf(f673,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK7 @ Y1 @ Y0 ) ) ) )
       => $false ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(backward_demodulation,[],[f642,f672]) ).

thf(f672,plain,
    ( ( ( sK7 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f671]) ).

thf(f671,plain,
    ( ( $false
      = ( $true
       => ( sK7 @ sK9 @ sK8 ) ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f670]) ).

thf(f670,plain,
    ( ( ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) )
                  & ( sK4 @ Y0 ) )
               => ( Y0 @ sK9 @ sK8 ) ) )
          | $true )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f669,f97]) ).

thf(f97,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f96,plain,
    ( spl0_6
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f669,plain,
    ( ( ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) )
                  & ( sK4 @ Y0 ) )
               => ( Y0 @ sK9 @ sK8 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK4 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) ) )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f668]) ).

thf(f668,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) )
                      & ( sK4 @ Y1 ) )
                   => ( Y1 @ Y0 @ sK8 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK4 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK8 ) ) ) )
           => ( sK7 @ Y0 @ sK8 ) )
        @ sK9 ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f665]) ).

thf(f665,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) )
                      & ( sK4 @ Y1 ) )
                   => ( Y1 @ Y0 @ sK8 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK4 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK8 ) ) ) )
           => ( sK7 @ Y0 @ sK8 ) ) ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f661]) ).

thf(f661,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) )
                          & ( sK4 @ Y2 ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK4 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK8 ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f655]) ).

thf(f655,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) )
                          & ( sK4 @ Y2 ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK4 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(not_proxy_clausification,[],[f608]) ).

thf(f608,plain,
    ( ( $true
      = ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) )
                              & ( sK4 @ Y2 ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK4 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f607]) ).

thf(f607,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( sK7 @ Y1 @ Y0 ) ) ) )
            & $true ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f600,f606]) ).

thf(f606,plain,
    ( ( $true
      = ( sK4 @ sK7 ) )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f605]) ).

thf(f605,plain,
    ( ( ( ( sK4 @ sK7 )
        & $true )
      = $true )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f589,f603]) ).

thf(f603,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ Y1 )
                  | ( sK2 @ Y0 @ Y1 ) )
               => ( sK7 @ Y0 @ Y1 ) ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f589]) ).

thf(f589,plain,
    ( ( $true
      = ( ( sK4 @ sK7 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK3 @ Y0 @ Y1 )
                    | ( sK2 @ Y0 @ Y1 ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f587]) ).

thf(f587,plain,
    ( ( $false
      = ( ( ( sK4 @ sK7 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK3 @ Y0 @ Y1 )
                      | ( sK2 @ Y0 @ Y1 ) )
                   => ( sK7 @ Y0 @ Y1 ) ) ) ) )
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f586]) ).

thf(f586,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK7 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f32]) ).

thf(f32,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
      = $false )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f31,plain,
    ( spl0_3
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f600,plain,
    ( ( $true
      = ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( sK7 @ Y1 @ Y0 ) ) ) )
            & ( sK4 @ sK7 ) ) ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f599]) ).

thf(f599,plain,
    ( ( $true
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) )
                              & ( sK4 @ Y2 ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK4 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK7 @ Y1 @ Y0 ) ) ) )
          & ( sK4 @ sK7 ) )
       => $false ) )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(superposition,[],[f595,f588]) ).

thf(f588,plain,
    ( ( ( sK7 @ sK5 @ sK6 )
      = $false )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f587]) ).

thf(f595,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) )
            & ( sK4 @ X1 ) )
         => ( X1 @ sK5 @ sK6 ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f594]) ).

thf(f594,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK2 @ Y5 @ Y4 )
                                             => ( Y3 @ Y5 @ Y4 ) ) ) )
                                    & ( sK4 @ Y3 ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( sK4 @ Y3 )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK3 @ Y5 @ Y4 )
                                             => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK5 @ sK6 ) )
          @ X1 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f24]) ).

thf(f24,plain,
    ( spl0_1
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f642,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK7 @ Y1 @ Y0 ) ) ) )
       => ( sK7 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f641]) ).

thf(f641,plain,
    ( ( $true
      = ( ( $true
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y1 @ Y0 )
                   => ( sK7 @ Y1 @ Y0 ) ) ) ) )
       => ( sK7 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(superposition,[],[f637,f606]) ).

thf(f637,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( sK4 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK3 @ Y1 @ Y0 )
                     => ( X1 @ Y1 @ Y0 ) ) ) ) )
         => ( X1 @ sK9 @ sK8 ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f636]) ).

thf(f636,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( sK4 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) )
          @ X1 ) )
    | ~ spl0_6 ),
    inference(pi_clausification,[],[f97]) ).

thf(f751,plain,
    ( ( $true
      = ( ~ ( ( sK3 @ sK28 @ sK27 )
            | ( sK2 @ sK28 @ sK27 ) ) ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f750]) ).

thf(f750,plain,
    ( ( $true
      = ( ( ( sK3 @ sK28 @ sK27 )
          | ( sK2 @ sK28 @ sK27 ) )
       => $false ) )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(superposition,[],[f620,f749]) ).

thf(f749,plain,
    ( ( ( sK7 @ sK28 @ sK27 )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f748]) ).

thf(f748,plain,
    ( ( ( $true
       => ( sK7 @ sK28 @ sK27 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(backward_demodulation,[],[f743,f747]) ).

thf(f620,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( ( sK3 @ X1 @ X2 )
            | ( sK2 @ X1 @ X2 ) )
         => ( sK7 @ X1 @ X2 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f619]) ).

thf(f619,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( sK3 @ X1 @ Y0 )
                | ( sK2 @ X1 @ Y0 ) )
             => ( sK7 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f614]) ).

thf(f614,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK3 @ X1 @ Y0 )
                | ( sK2 @ X1 @ Y0 ) )
             => ( sK7 @ X1 @ Y0 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f613]) ).

thf(f613,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK3 @ Y0 @ Y1 )
                    | ( sK2 @ Y0 @ Y1 ) )
                 => ( sK7 @ Y0 @ Y1 ) ) )
          @ X1 ) )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f603]) ).

thf(f573,plain,
    ( ~ spl0_4
    | ~ spl0_9 ),
    inference(avatar_contradiction_clause,[],[f572]) ).

thf(f572,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(trivial_inequality_removal,[],[f571]) ).

thf(f571,plain,
    ( ( $true = $false )
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(forward_demodulation,[],[f565,f396]) ).

thf(f396,plain,
    ( ( ( sK18 @ sK13 @ sK14 )
      = $false )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f395]) ).

thf(f395,plain,
    ( ( ( $true
       => ( sK18 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f388,f394]) ).

thf(f394,plain,
    ( ( $true
      = ( ( sK4 @ sK18 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK18 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f388]) ).

thf(f388,plain,
    ( ( ( ( ( sK4 @ sK18 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y1 @ Y0 )
                   => ( sK18 @ Y1 @ Y0 ) ) ) ) )
       => ( sK18 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f385]) ).

thf(f385,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) )
        @ sK18 )
      = $false )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f333]) ).

thf(f333,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f324]) ).

thf(f324,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK13 @ sK14 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK4 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK13 @ sK14 ) ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(not_proxy_clausification,[],[f239]) ).

thf(f239,plain,
    ( ( $true
      = ( ~ ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) )
                    & ( sK4 @ Y0 ) )
                 => ( Y0 @ sK13 @ sK14 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK4 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK3 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ sK13 @ sK14 ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f238]) ).

thf(f238,plain,
    ( ( $true
      = ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) )
                  & ( sK4 @ Y0 ) )
               => ( Y0 @ sK13 @ sK14 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK4 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK13 @ sK14 ) ) ) )
       => $false ) )
    | ~ spl0_4 ),
    inference(superposition,[],[f220,f237]) ).

thf(f237,plain,
    ( ( ( sK12 @ sK13 @ sK14 )
      = $false )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f236]) ).

thf(f236,plain,
    ( ( $false
      = ( $true
       => ( sK12 @ sK13 @ sK14 ) ) )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f233,f235]) ).

thf(f235,plain,
    ( ( $true
      = ( ( sK3 @ sK13 @ sK14 )
        | ( sK2 @ sK13 @ sK14 ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f233]) ).

thf(f233,plain,
    ( ( ( ( ( sK3 @ sK13 @ sK14 )
          | ( sK2 @ sK13 @ sK14 ) )
       => ( sK12 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f232]) ).

thf(f232,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK3 @ sK13 @ Y0 )
              | ( sK2 @ sK13 @ Y0 ) )
           => ( sK12 @ sK13 @ Y0 ) )
        @ sK14 ) )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f231]) ).

thf(f231,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK3 @ sK13 @ Y0 )
              | ( sK2 @ sK13 @ Y0 ) )
           => ( sK12 @ sK13 @ Y0 ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f227]) ).

thf(f227,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ Y1 )
                  | ( sK2 @ Y0 @ Y1 ) )
               => ( sK12 @ Y0 @ Y1 ) ) )
        @ sK13 ) )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f221]) ).

thf(f221,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ Y1 )
                  | ( sK2 @ Y0 @ Y1 ) )
               => ( sK12 @ Y0 @ Y1 ) ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(not_proxy_clausification,[],[f202]) ).

thf(f202,plain,
    ( ( ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK3 @ Y0 @ Y1 )
                      | ( sK2 @ Y0 @ Y1 ) )
                   => ( sK12 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f199]) ).

thf(f199,plain,
    ( ( $true
      = ( ~ ( $true
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK3 @ Y0 @ Y1 )
                        | ( sK2 @ Y0 @ Y1 ) )
                     => ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f196,f197]) ).

thf(f197,plain,
    ( ( $true
      = ( sK4 @ sK12 ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f190]) ).

thf(f190,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) )
                            & ( sK4 @ Y2 ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK4 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK12 @ Y1 @ Y0 ) ) ) )
        & ( sK4 @ sK12 ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f188]) ).

thf(f188,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) )
                              & ( sK4 @ Y2 ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK4 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK12 @ Y1 @ Y0 ) ) ) )
          & ( sK4 @ sK12 ) )
       => ( sK12 @ sK5 @ sK6 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f187]) ).

thf(f187,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK12 )
      = $false )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f35]) ).

thf(f35,plain,
    ( ( $false
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f34]) ).

thf(f34,plain,
    ( spl0_4
  <=> ( $false
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f196,plain,
    ( ( $true
      = ( ~ ( ( sK4 @ sK12 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK3 @ Y0 @ Y1 )
                        | ( sK2 @ Y0 @ Y1 ) )
                     => ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f195]) ).

thf(f195,plain,
    ( ( ( ( ( sK4 @ sK12 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK3 @ Y0 @ Y1 )
                      | ( sK2 @ Y0 @ Y1 ) )
                   => ( sK12 @ Y0 @ Y1 ) ) ) ) )
       => $false )
      = $true )
    | ~ spl0_4 ),
    inference(superposition,[],[f182,f189]) ).

thf(f189,plain,
    ( ( ( sK12 @ sK5 @ sK6 )
      = $false )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f188]) ).

thf(f182,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( sK4 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK3 @ Y0 @ Y1 )
                        | ( sK2 @ Y0 @ Y1 ) )
                     => ( X1 @ Y0 @ Y1 ) ) ) ) )
         => ( X1 @ sK5 @ sK6 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f181]) ).

thf(f181,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( sK4 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK3 @ Y1 @ Y2 )
                            | ( sK2 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK5 @ sK6 ) )
          @ X1 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f180]) ).

thf(f180,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
     != $false )
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f20,f35]) ).

thf(f20,plain,
    ( ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( ( ( sK4 @ Y0 )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK3 @ Y1 @ Y2 )
                        | ( sK2 @ Y1 @ Y2 ) )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ sK5 @ sK6 ) ) )
   != ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y3: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( sK2 @ Y5 @ Y4 )
                                         => ( Y3 @ Y5 @ Y4 ) ) ) )
                                & ( sK4 @ Y3 ) )
                             => ( Y3 @ Y2 @ Y1 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y3: a > a > $o] :
                              ( ( ( sK4 @ Y3 )
                                & ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( sK3 @ Y5 @ Y4 )
                                         => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                             => ( Y3 @ Y2 @ Y1 ) ) ) )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( sK4 @ Y0 ) )
         => ( Y0 @ sK5 @ sK6 ) ) ) ),
    inference(beta_eta_normalization,[],[f19]) ).

thf(f19,plain,
    ( ( ^ [Y0: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( sK4 @ Y1 )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( sK3 @ Y2 @ Y3 )
                            | ( sK2 @ Y2 @ Y3 ) )
                         => ( Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y1 @ sK5 @ Y0 ) ) )
      @ sK6 )
   != ( ^ [Y0: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y4: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( sK2 @ Y6 @ Y5 )
                                             => ( Y4 @ Y6 @ Y5 ) ) ) )
                                    & ( sK4 @ Y4 ) )
                                 => ( Y4 @ Y3 @ Y2 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y4: a > a > $o] :
                                  ( ( ( sK4 @ Y4 )
                                    & ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( sK3 @ Y6 @ Y5 )
                                             => ( Y4 @ Y6 @ Y5 ) ) ) ) )
                                 => ( Y4 @ Y3 @ Y2 ) ) ) )
                         => ( Y1 @ Y3 @ Y2 ) ) ) )
                & ( sK4 @ Y1 ) )
             => ( Y1 @ sK5 @ Y0 ) ) )
      @ sK6 ) ),
    inference(negative_extensionality,[],[f18]) ).

thf(f18,plain,
    ( ( ^ [Y0: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( sK4 @ Y1 )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( sK3 @ Y2 @ Y3 )
                            | ( sK2 @ Y2 @ Y3 ) )
                         => ( Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y1 @ sK5 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y4: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( sK2 @ Y6 @ Y5 )
                                             => ( Y4 @ Y6 @ Y5 ) ) ) )
                                    & ( sK4 @ Y4 ) )
                                 => ( Y4 @ Y3 @ Y2 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y4: a > a > $o] :
                                  ( ( ( sK4 @ Y4 )
                                    & ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( !! @ a
                                          @ ^ [Y6: a] :
                                              ( ( sK3 @ Y6 @ Y5 )
                                             => ( Y4 @ Y6 @ Y5 ) ) ) ) )
                                 => ( Y4 @ Y3 @ Y2 ) ) ) )
                         => ( Y1 @ Y3 @ Y2 ) ) ) )
                & ( sK4 @ Y1 ) )
             => ( Y1 @ sK5 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f17]) ).

thf(f17,plain,
    ( ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( sK4 @ Y2 )
                & ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( sK3 @ Y3 @ Y4 )
                            | ( sK2 @ Y3 @ Y4 ) )
                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
             => ( Y2 @ Y0 @ Y1 ) ) )
      @ sK5 )
   != ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK2 @ Y7 @ Y6 )
                                             => ( Y5 @ Y7 @ Y6 ) ) ) )
                                    & ( sK4 @ Y5 ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( sK4 @ Y5 )
                                    & ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK3 @ Y7 @ Y6 )
                                             => ( Y5 @ Y7 @ Y6 ) ) ) ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) ) )
                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                & ( sK4 @ Y2 ) )
             => ( Y2 @ Y0 @ Y1 ) ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f16]) ).

thf(f16,plain,
    ( ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK2 @ Y7 @ Y6 )
                                             => ( Y5 @ Y7 @ Y6 ) ) ) )
                                    & ( sK4 @ Y5 ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( sK4 @ Y5 )
                                    & ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK3 @ Y7 @ Y6 )
                                             => ( Y5 @ Y7 @ Y6 ) ) ) ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) ) )
                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                & ( sK4 @ Y2 ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) )
   != ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( sK4 @ Y2 )
                & ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( sK3 @ Y3 @ Y4 )
                            | ( sK2 @ Y3 @ Y4 ) )
                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) ) ),
    inference(equality_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( ( ^ [Y0: a,Y1: a] :
            ( !! @ ( a > a > $o )
            @ ^ [Y2: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y3: a] :
                        ( !! @ a
                        @ ^ [Y4: a] :
                            ( ( ( !! @ ( a > a > $o )
                                @ ^ [Y5: a > a > $o] :
                                    ( ( ( !! @ a
                                        @ ^ [Y6: a] :
                                            ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( ( sK2 @ Y7 @ Y6 )
                                               => ( Y5 @ Y7 @ Y6 ) ) ) )
                                      & ( sK4 @ Y5 ) )
                                   => ( Y5 @ Y4 @ Y3 ) ) )
                              | ( !! @ ( a > a > $o )
                                @ ^ [Y5: a > a > $o] :
                                    ( ( ( sK4 @ Y5 )
                                      & ( !! @ a
                                        @ ^ [Y6: a] :
                                            ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( ( sK3 @ Y7 @ Y6 )
                                               => ( Y5 @ Y7 @ Y6 ) ) ) ) )
                                   => ( Y5 @ Y4 @ Y3 ) ) ) )
                           => ( Y2 @ Y4 @ Y3 ) ) ) )
                  & ( sK4 @ Y2 ) )
               => ( Y2 @ Y0 @ Y1 ) ) ) )
      = ( ^ [Y0: a,Y1: a] :
            ( !! @ ( a > a > $o )
            @ ^ [Y2: a > a > $o] :
                ( ( ( sK4 @ Y2 )
                  & ( !! @ a
                    @ ^ [Y3: a] :
                        ( !! @ a
                        @ ^ [Y4: a] :
                            ( ( ( sK3 @ Y3 @ Y4 )
                              | ( sK2 @ Y3 @ Y4 ) )
                           => ( Y2 @ Y3 @ Y4 ) ) ) ) )
               => ( Y2 @ Y0 @ Y1 ) ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f14]) ).

thf(f14,plain,
    ( ( ^ [Y0: ( a > a > $o ) > $o] :
          ( ( ^ [Y1: a,Y2: a] :
                ( !! @ ( a > a > $o )
                @ ^ [Y3: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y4: a] :
                            ( !! @ a
                            @ ^ [Y5: a] :
                                ( ( ( !! @ ( a > a > $o )
                                    @ ^ [Y6: a > a > $o] :
                                        ( ( ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( ( sK2 @ Y8 @ Y7 )
                                                   => ( Y6 @ Y8 @ Y7 ) ) ) )
                                          & ( Y0 @ Y6 ) )
                                       => ( Y6 @ Y5 @ Y4 ) ) )
                                  | ( !! @ ( a > a > $o )
                                    @ ^ [Y6: a > a > $o] :
                                        ( ( ( Y0 @ Y6 )
                                          & ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( ( sK3 @ Y8 @ Y7 )
                                                   => ( Y6 @ Y8 @ Y7 ) ) ) ) )
                                       => ( Y6 @ Y5 @ Y4 ) ) ) )
                               => ( Y3 @ Y5 @ Y4 ) ) ) )
                      & ( Y0 @ Y3 ) )
                   => ( Y3 @ Y1 @ Y2 ) ) ) )
          = ( ^ [Y1: a,Y2: a] :
                ( !! @ ( a > a > $o )
                @ ^ [Y3: a > a > $o] :
                    ( ( ( Y0 @ Y3 )
                      & ( !! @ a
                        @ ^ [Y4: a] :
                            ( !! @ a
                            @ ^ [Y5: a] :
                                ( ( ( sK3 @ Y4 @ Y5 )
                                  | ( sK2 @ Y4 @ Y5 ) )
                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                   => ( Y3 @ Y1 @ Y2 ) ) ) ) )
      @ sK4 )
    = $false ),
    inference(sigma_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( !! @ ( ( a > a > $o ) > $o )
      @ ^ [Y0: ( a > a > $o ) > $o] :
          ( ( ^ [Y1: a,Y2: a] :
                ( !! @ ( a > a > $o )
                @ ^ [Y3: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y4: a] :
                            ( !! @ a
                            @ ^ [Y5: a] :
                                ( ( ( !! @ ( a > a > $o )
                                    @ ^ [Y6: a > a > $o] :
                                        ( ( ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( ( sK2 @ Y8 @ Y7 )
                                                   => ( Y6 @ Y8 @ Y7 ) ) ) )
                                          & ( Y0 @ Y6 ) )
                                       => ( Y6 @ Y5 @ Y4 ) ) )
                                  | ( !! @ ( a > a > $o )
                                    @ ^ [Y6: a > a > $o] :
                                        ( ( ( Y0 @ Y6 )
                                          & ( !! @ a
                                            @ ^ [Y7: a] :
                                                ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( ( sK3 @ Y8 @ Y7 )
                                                   => ( Y6 @ Y8 @ Y7 ) ) ) ) )
                                       => ( Y6 @ Y5 @ Y4 ) ) ) )
                               => ( Y3 @ Y5 @ Y4 ) ) ) )
                      & ( Y0 @ Y3 ) )
                   => ( Y3 @ Y1 @ Y2 ) ) ) )
          = ( ^ [Y1: a,Y2: a] :
                ( !! @ ( a > a > $o )
                @ ^ [Y3: a > a > $o] :
                    ( ( ( Y0 @ Y3 )
                      & ( !! @ a
                        @ ^ [Y4: a] :
                            ( !! @ a
                            @ ^ [Y5: a] :
                                ( ( ( sK3 @ Y4 @ Y5 )
                                  | ( sK2 @ Y4 @ Y5 ) )
                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                   => ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f12]) ).

thf(f12,plain,
    ( $false
    = ( ^ [Y0: a > a > $o] :
          ( !! @ ( ( a > a > $o ) > $o )
          @ ^ [Y1: ( a > a > $o ) > $o] :
              ( ( ^ [Y2: a,Y3: a] :
                    ( !! @ ( a > a > $o )
                    @ ^ [Y4: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y5: a] :
                                ( !! @ a
                                @ ^ [Y6: a] :
                                    ( ( ( !! @ ( a > a > $o )
                                        @ ^ [Y7: a > a > $o] :
                                            ( ( ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( ( sK2 @ Y9 @ Y8 )
                                                       => ( Y7 @ Y9 @ Y8 ) ) ) )
                                              & ( Y1 @ Y7 ) )
                                           => ( Y7 @ Y6 @ Y5 ) ) )
                                      | ( !! @ ( a > a > $o )
                                        @ ^ [Y7: a > a > $o] :
                                            ( ( ( Y1 @ Y7 )
                                              & ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( ( Y0 @ Y9 @ Y8 )
                                                       => ( Y7 @ Y9 @ Y8 ) ) ) ) )
                                           => ( Y7 @ Y6 @ Y5 ) ) ) )
                                   => ( Y4 @ Y6 @ Y5 ) ) ) )
                          & ( Y1 @ Y4 ) )
                       => ( Y4 @ Y2 @ Y3 ) ) ) )
              = ( ^ [Y2: a,Y3: a] :
                    ( !! @ ( a > a > $o )
                    @ ^ [Y4: a > a > $o] :
                        ( ( ( Y1 @ Y4 )
                          & ( !! @ a
                            @ ^ [Y5: a] :
                                ( !! @ a
                                @ ^ [Y6: a] :
                                    ( ( ( Y0 @ Y5 @ Y6 )
                                      | ( sK2 @ Y5 @ Y6 ) )
                                   => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                       => ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
      @ sK3 ) ),
    inference(sigma_clausification,[],[f11]) ).

thf(f11,plain,
    ( $false
    = ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( !! @ ( ( a > a > $o ) > $o )
          @ ^ [Y1: ( a > a > $o ) > $o] :
              ( ( ^ [Y2: a,Y3: a] :
                    ( !! @ ( a > a > $o )
                    @ ^ [Y4: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y5: a] :
                                ( !! @ a
                                @ ^ [Y6: a] :
                                    ( ( ( !! @ ( a > a > $o )
                                        @ ^ [Y7: a > a > $o] :
                                            ( ( ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( ( sK2 @ Y9 @ Y8 )
                                                       => ( Y7 @ Y9 @ Y8 ) ) ) )
                                              & ( Y1 @ Y7 ) )
                                           => ( Y7 @ Y6 @ Y5 ) ) )
                                      | ( !! @ ( a > a > $o )
                                        @ ^ [Y7: a > a > $o] :
                                            ( ( ( Y1 @ Y7 )
                                              & ( !! @ a
                                                @ ^ [Y8: a] :
                                                    ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( ( Y0 @ Y9 @ Y8 )
                                                       => ( Y7 @ Y9 @ Y8 ) ) ) ) )
                                           => ( Y7 @ Y6 @ Y5 ) ) ) )
                                   => ( Y4 @ Y6 @ Y5 ) ) ) )
                          & ( Y1 @ Y4 ) )
                       => ( Y4 @ Y2 @ Y3 ) ) ) )
              = ( ^ [Y2: a,Y3: a] :
                    ( !! @ ( a > a > $o )
                    @ ^ [Y4: a > a > $o] :
                        ( ( ( Y1 @ Y4 )
                          & ( !! @ a
                            @ ^ [Y5: a] :
                                ( !! @ a
                                @ ^ [Y6: a] :
                                    ( ( ( Y0 @ Y5 @ Y6 )
                                      | ( sK2 @ Y5 @ Y6 ) )
                                   => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                       => ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a > a > $o] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( !! @ ( ( a > a > $o ) > $o )
              @ ^ [Y2: ( a > a > $o ) > $o] :
                  ( ( ^ [Y3: a,Y4: a] :
                        ( !! @ ( a > a > $o )
                        @ ^ [Y5: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y6: a] :
                                    ( !! @ a
                                    @ ^ [Y7: a] :
                                        ( ( ( !! @ ( a > a > $o )
                                            @ ^ [Y8: a > a > $o] :
                                                ( ( ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( !! @ a
                                                        @ ^ [Y10: a] :
                                                            ( ( Y0 @ Y10 @ Y9 )
                                                           => ( Y8 @ Y10 @ Y9 ) ) ) )
                                                  & ( Y2 @ Y8 ) )
                                               => ( Y8 @ Y7 @ Y6 ) ) )
                                          | ( !! @ ( a > a > $o )
                                            @ ^ [Y8: a > a > $o] :
                                                ( ( ( Y2 @ Y8 )
                                                  & ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( !! @ a
                                                        @ ^ [Y10: a] :
                                                            ( ( Y1 @ Y10 @ Y9 )
                                                           => ( Y8 @ Y10 @ Y9 ) ) ) ) )
                                               => ( Y8 @ Y7 @ Y6 ) ) ) )
                                       => ( Y5 @ Y7 @ Y6 ) ) ) )
                              & ( Y2 @ Y5 ) )
                           => ( Y5 @ Y3 @ Y4 ) ) ) )
                  = ( ^ [Y3: a,Y4: a] :
                        ( !! @ ( a > a > $o )
                        @ ^ [Y5: a > a > $o] :
                            ( ( ( Y2 @ Y5 )
                              & ( !! @ a
                                @ ^ [Y6: a] :
                                    ( !! @ a
                                    @ ^ [Y7: a] :
                                        ( ( ( Y1 @ Y6 @ Y7 )
                                          | ( Y0 @ Y6 @ Y7 ) )
                                       => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                           => ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
      @ sK2 )
    = $false ),
    inference(sigma_clausification,[],[f7]) ).

thf(f7,plain,
    ( ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( !! @ ( a > a > $o )
          @ ^ [Y1: a > a > $o] :
              ( !! @ ( ( a > a > $o ) > $o )
              @ ^ [Y2: ( a > a > $o ) > $o] :
                  ( ( ^ [Y3: a,Y4: a] :
                        ( !! @ ( a > a > $o )
                        @ ^ [Y5: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y6: a] :
                                    ( !! @ a
                                    @ ^ [Y7: a] :
                                        ( ( ( !! @ ( a > a > $o )
                                            @ ^ [Y8: a > a > $o] :
                                                ( ( ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( !! @ a
                                                        @ ^ [Y10: a] :
                                                            ( ( Y0 @ Y10 @ Y9 )
                                                           => ( Y8 @ Y10 @ Y9 ) ) ) )
                                                  & ( Y2 @ Y8 ) )
                                               => ( Y8 @ Y7 @ Y6 ) ) )
                                          | ( !! @ ( a > a > $o )
                                            @ ^ [Y8: a > a > $o] :
                                                ( ( ( Y2 @ Y8 )
                                                  & ( !! @ a
                                                    @ ^ [Y9: a] :
                                                        ( !! @ a
                                                        @ ^ [Y10: a] :
                                                            ( ( Y1 @ Y10 @ Y9 )
                                                           => ( Y8 @ Y10 @ Y9 ) ) ) ) )
                                               => ( Y8 @ Y7 @ Y6 ) ) ) )
                                       => ( Y5 @ Y7 @ Y6 ) ) ) )
                              & ( Y2 @ Y5 ) )
                           => ( Y5 @ Y3 @ Y4 ) ) ) )
                  = ( ^ [Y3: a,Y4: a] :
                        ( !! @ ( a > a > $o )
                        @ ^ [Y5: a > a > $o] :
                            ( ( ( Y2 @ Y5 )
                              & ( !! @ a
                                @ ^ [Y6: a] :
                                    ( !! @ a
                                    @ ^ [Y7: a] :
                                        ( ( ( Y1 @ Y6 @ Y7 )
                                          | ( Y0 @ Y6 @ Y7 ) )
                                       => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                           => ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
    = $false ),
    inference(not_proxy_clausification,[],[f6]) ).

thf(f6,plain,
    ( $true
    = ( ~ ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( !! @ ( a > a > $o )
              @ ^ [Y1: a > a > $o] :
                  ( !! @ ( ( a > a > $o ) > $o )
                  @ ^ [Y2: ( a > a > $o ) > $o] :
                      ( ( ^ [Y3: a,Y4: a] :
                            ( !! @ ( a > a > $o )
                            @ ^ [Y5: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( !! @ a
                                        @ ^ [Y7: a] :
                                            ( ( ( !! @ ( a > a > $o )
                                                @ ^ [Y8: a > a > $o] :
                                                    ( ( ( !! @ a
                                                        @ ^ [Y9: a] :
                                                            ( !! @ a
                                                            @ ^ [Y10: a] :
                                                                ( ( Y0 @ Y10 @ Y9 )
                                                               => ( Y8 @ Y10 @ Y9 ) ) ) )
                                                      & ( Y2 @ Y8 ) )
                                                   => ( Y8 @ Y7 @ Y6 ) ) )
                                              | ( !! @ ( a > a > $o )
                                                @ ^ [Y8: a > a > $o] :
                                                    ( ( ( Y2 @ Y8 )
                                                      & ( !! @ a
                                                        @ ^ [Y9: a] :
                                                            ( !! @ a
                                                            @ ^ [Y10: a] :
                                                                ( ( Y1 @ Y10 @ Y9 )
                                                               => ( Y8 @ Y10 @ Y9 ) ) ) ) )
                                                   => ( Y8 @ Y7 @ Y6 ) ) ) )
                                           => ( Y5 @ Y7 @ Y6 ) ) ) )
                                  & ( Y2 @ Y5 ) )
                               => ( Y5 @ Y3 @ Y4 ) ) ) )
                      = ( ^ [Y3: a,Y4: a] :
                            ( !! @ ( a > a > $o )
                            @ ^ [Y5: a > a > $o] :
                                ( ( ( Y2 @ Y5 )
                                  & ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( !! @ a
                                        @ ^ [Y7: a] :
                                            ( ( ( Y1 @ Y6 @ Y7 )
                                              | ( Y0 @ Y6 @ Y7 ) )
                                           => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                               => ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,plain,
    ( $true
    = ( ~ ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( !! @ ( a > a > $o )
              @ ^ [Y1: a > a > $o] :
                  ( !! @ ( ( a > a > $o ) > $o )
                  @ ^ [Y2: ( a > a > $o ) > $o] :
                      ( ( ^ [Y3: a,Y4: a] :
                            ( !! @ ( a > a > $o )
                            @ ^ [Y5: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( !! @ a
                                        @ ^ [Y7: a] :
                                            ( ( ( !! @ ( a > a > $o )
                                                @ ^ [Y8: a > a > $o] :
                                                    ( ( ( !! @ a
                                                        @ ^ [Y9: a] :
                                                            ( !! @ a
                                                            @ ^ [Y10: a] :
                                                                ( ( Y0 @ Y10 @ Y9 )
                                                               => ( Y8 @ Y10 @ Y9 ) ) ) )
                                                      & ( Y2 @ Y8 ) )
                                                   => ( Y8 @ Y7 @ Y6 ) ) )
                                              | ( !! @ ( a > a > $o )
                                                @ ^ [Y8: a > a > $o] :
                                                    ( ( ( Y2 @ Y8 )
                                                      & ( !! @ a
                                                        @ ^ [Y9: a] :
                                                            ( !! @ a
                                                            @ ^ [Y10: a] :
                                                                ( ( Y1 @ Y10 @ Y9 )
                                                               => ( Y8 @ Y10 @ Y9 ) ) ) ) )
                                                   => ( Y8 @ Y7 @ Y6 ) ) ) )
                                           => ( Y5 @ Y7 @ Y6 ) ) ) )
                                  & ( Y2 @ Y5 ) )
                               => ( Y5 @ Y3 @ Y4 ) ) ) )
                      = ( ^ [Y3: a,Y4: a] :
                            ( !! @ ( a > a > $o )
                            @ ^ [Y5: a > a > $o] :
                                ( ( ( Y2 @ Y5 )
                                  & ( !! @ a
                                    @ ^ [Y6: a] :
                                        ( !! @ a
                                        @ ^ [Y7: a] :
                                            ( ( ( Y1 @ Y6 @ Y7 )
                                              | ( Y0 @ Y6 @ Y7 ) )
                                           => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                               => ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: ( a > a > $o ) > $o,X1: a > a > $o,X2: a > a > $o] :
        ( ( ^ [X3: a,X4: a] :
            ! [X5: a > a > $o] :
              ( ( ( X0 @ X5 )
                & ! [X6: a,X7: a] :
                    ( ( ! [X8: a > a > $o] :
                          ( ( ! [X9: a,X10: a] :
                                ( ( X1 @ X9 @ X10 )
                               => ( X8 @ X9 @ X10 ) )
                            & ( X0 @ X8 ) )
                         => ( X8 @ X6 @ X7 ) )
                      | ! [X11: a > a > $o] :
                          ( ( ( X0 @ X11 )
                            & ! [X12: a,X13: a] :
                                ( ( X2 @ X12 @ X13 )
                               => ( X11 @ X12 @ X13 ) ) )
                         => ( X11 @ X6 @ X7 ) ) )
                   => ( X5 @ X6 @ X7 ) ) )
             => ( X5 @ X3 @ X4 ) ) )
        = ( ^ [X14: a,X15: a] :
            ! [X16: a > a > $o] :
              ( ( ! [X17: a,X18: a] :
                    ( ( ( X2 @ X18 @ X17 )
                      | ( X1 @ X18 @ X17 ) )
                   => ( X16 @ X18 @ X17 ) )
                & ( X0 @ X16 ) )
             => ( X16 @ X14 @ X15 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
        ( ( ^ [X3: a,X4: a] :
            ! [X5: a > a > $o] :
              ( ( ( X0 @ X5 )
                & ! [X6: a,X7: a] :
                    ( ( ! [X8: a > a > $o] :
                          ( ( ! [X9: a,X10: a] :
                                ( ( X2 @ X9 @ X10 )
                               => ( X8 @ X9 @ X10 ) )
                            & ( X0 @ X8 ) )
                         => ( X8 @ X6 @ X7 ) )
                      | ! [X8: a > a > $o] :
                          ( ( ( X0 @ X8 )
                            & ! [X9: a,X10: a] :
                                ( ( X1 @ X9 @ X10 )
                               => ( X8 @ X9 @ X10 ) ) )
                         => ( X8 @ X6 @ X7 ) ) )
                   => ( X5 @ X6 @ X7 ) ) )
             => ( X5 @ X3 @ X4 ) ) )
        = ( ^ [X3: a,X4: a] :
            ! [X5: a > a > $o] :
              ( ( ! [X7: a,X6: a] :
                    ( ( ( X1 @ X6 @ X7 )
                      | ( X2 @ X6 @ X7 ) )
                   => ( X5 @ X6 @ X7 ) )
                & ( X0 @ X5 ) )
             => ( X5 @ X3 @ X4 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ( ( X0 @ X5 )
              & ! [X6: a,X7: a] :
                  ( ( ! [X8: a > a > $o] :
                        ( ( ! [X9: a,X10: a] :
                              ( ( X2 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) )
                          & ( X0 @ X8 ) )
                       => ( X8 @ X6 @ X7 ) )
                    | ! [X8: a > a > $o] :
                        ( ( ( X0 @ X8 )
                          & ! [X9: a,X10: a] :
                              ( ( X1 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) ) )
                       => ( X8 @ X6 @ X7 ) ) )
                 => ( X5 @ X6 @ X7 ) ) )
           => ( X5 @ X3 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ( ! [X7: a,X6: a] :
                  ( ( ( X1 @ X6 @ X7 )
                    | ( X2 @ X6 @ X7 ) )
                 => ( X5 @ X6 @ X7 ) )
              & ( X0 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM252_pme) ).

thf(f220,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) )
                    & ( sK4 @ Y0 ) )
                 => ( Y0 @ X2 @ X1 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK4 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK3 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ X2 @ X1 ) ) ) )
         => ( sK12 @ X2 @ X1 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f219]) ).

thf(f219,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) )
                        & ( sK4 @ Y1 ) )
                     => ( Y1 @ Y0 @ X1 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK4 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK3 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) ) )
             => ( sK12 @ Y0 @ X1 ) )
          @ X2 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f210]) ).

thf(f210,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) )
                        & ( sK4 @ Y1 ) )
                     => ( Y1 @ Y0 @ X1 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK4 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK3 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) ) )
             => ( sK12 @ Y0 @ X1 ) ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f209]) ).

thf(f209,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) )
                            & ( sK4 @ Y2 ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK4 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK12 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f201]) ).

thf(f201,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) )
                          & ( sK4 @ Y2 ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK4 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK12 @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f200]) ).

thf(f200,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) )
                            & ( sK4 @ Y2 ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK4 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK12 @ Y1 @ Y0 ) ) ) )
        & $true )
      = $true )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f190,f197]) ).

thf(f565,plain,
    ( ( $true
      = ( sK18 @ sK13 @ sK14 ) )
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(boolean_simplification,[],[f557]) ).

thf(f557,plain,
    ( ( $true
      = ( $true
       => ( sK18 @ sK13 @ sK14 ) ) )
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(superposition,[],[f551,f243]) ).

thf(f243,plain,
    ( ( $true
      = ( sK3 @ sK13 @ sK14 ) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f242]) ).

thf(f242,plain,
    ( spl0_9
  <=> ( $true
      = ( sK3 @ sK13 @ sK14 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

thf(f551,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( sK3 @ X2 @ X1 )
         => ( sK18 @ X2 @ X1 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f550]) ).

thf(f550,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK3 @ Y0 @ X1 )
             => ( sK18 @ Y0 @ X1 ) )
          @ X2 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f547]) ).

thf(f547,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ Y0 @ X1 )
             => ( sK18 @ Y0 @ X1 ) ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f546]) ).

thf(f546,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y1 @ Y0 )
                 => ( sK18 @ Y1 @ Y0 ) ) )
          @ X1 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f431]) ).

thf(f431,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y1 @ Y0 )
               => ( sK18 @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f394]) ).

thf(f421,plain,
    ( ~ spl0_4
    | ~ spl0_10 ),
    inference(avatar_contradiction_clause,[],[f420]) ).

thf(f420,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_10 ),
    inference(trivial_inequality_removal,[],[f419]) ).

thf(f419,plain,
    ( ( $true = $false )
    | ~ spl0_4
    | ~ spl0_10 ),
    inference(boolean_simplification,[],[f418]) ).

thf(f418,plain,
    ( ( $true = ~ $true )
    | ~ spl0_4
    | ~ spl0_10 ),
    inference(forward_demodulation,[],[f412,f246]) ).

thf(f246,plain,
    ( ( $true
      = ( sK2 @ sK13 @ sK14 ) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f245]) ).

thf(f245,plain,
    ( spl0_10
  <=> ( $true
      = ( sK2 @ sK13 @ sK14 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

thf(f412,plain,
    ( ( ( ~ ( sK2 @ sK13 @ sK14 ) )
      = $true )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f409]) ).

thf(f409,plain,
    ( ( $true
      = ( ( sK2 @ sK13 @ sK14 )
       => $false ) )
    | ~ spl0_4 ),
    inference(superposition,[],[f407,f360]) ).

thf(f360,plain,
    ( ( ( sK17 @ sK13 @ sK14 )
      = $false )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f359]) ).

thf(f359,plain,
    ( ( ( $true
       => ( sK17 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f352,f358]) ).

thf(f358,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK17 @ Y1 @ Y0 ) ) ) )
        & ( sK4 @ sK17 ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f352]) ).

thf(f352,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK17 @ Y1 @ Y0 ) ) ) )
          & ( sK4 @ sK17 ) )
       => ( sK17 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f349]) ).

thf(f349,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK13 @ sK14 ) )
        @ sK17 )
      = $false )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f338]) ).

thf(f338,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK13 @ sK14 ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f337]) ).

thf(f337,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK13 @ sK14 ) ) )
        | $false )
      = $false )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f324,f333]) ).

thf(f407,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( sK2 @ X2 @ X1 )
         => ( sK17 @ X2 @ X1 ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f406]) ).

thf(f406,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK2 @ Y0 @ X1 )
             => ( sK17 @ Y0 @ X1 ) )
          @ X2 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f405]) ).

thf(f405,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ Y0 @ X1 )
             => ( sK17 @ Y0 @ X1 ) ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f404]) ).

thf(f404,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK17 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f369]) ).

thf(f369,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK17 @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f358]) ).

thf(f247,plain,
    ( spl0_9
    | spl0_10
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f240,f34,f245,f242]) ).

thf(f240,plain,
    ( ( $true
      = ( sK2 @ sK13 @ sK14 ) )
    | ( $true
      = ( sK3 @ sK13 @ sK14 ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f235]) ).

thf(f175,plain,
    ( ~ spl0_3
    | ~ spl0_5 ),
    inference(avatar_contradiction_clause,[],[f174]) ).

thf(f174,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f173]) ).

thf(f173,plain,
    ( ( $true = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f172]) ).

thf(f172,plain,
    ( ( $true = ~ $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f171]) ).

thf(f171,plain,
    ( ( $true
      = ( ~ ( ( sK3 @ sK11 @ sK10 )
            | $true ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(forward_demodulation,[],[f170,f166]) ).

thf(f166,plain,
    ( ( $true
      = ( sK2 @ sK11 @ sK10 ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f164]) ).

thf(f164,plain,
    ( ( ( ( sK2 @ sK11 @ sK10 )
       => ( sK7 @ sK11 @ sK10 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f163]) ).

thf(f163,plain,
    ( ( ( ^ [Y0: a] :
            ( ( sK2 @ Y0 @ sK10 )
           => ( sK7 @ Y0 @ sK10 ) )
        @ sK11 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f160]) ).

thf(f160,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ Y0 @ sK10 )
           => ( sK7 @ Y0 @ sK10 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f158]) ).

thf(f158,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK10 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f149]) ).

thf(f149,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(not_proxy_clausification,[],[f118]) ).

thf(f118,plain,
    ( ( ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK7 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f117]) ).

thf(f117,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK7 @ Y1 @ Y0 ) ) ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(forward_demodulation,[],[f116,f83]) ).

thf(f83,plain,
    ( ( ( sK7 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f79]) ).

thf(f79,plain,
    ( ( ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) )
                  & ( sK4 @ Y0 ) )
               => ( Y0 @ sK9 @ sK8 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK4 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) ) )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f78]) ).

thf(f78,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) )
                      & ( sK4 @ Y1 ) )
                   => ( Y1 @ Y0 @ sK8 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK4 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK8 ) ) ) )
           => ( sK7 @ Y0 @ sK8 ) )
        @ sK9 ) )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f73]) ).

thf(f73,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) )
                      & ( sK4 @ Y1 ) )
                   => ( Y1 @ Y0 @ sK8 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK4 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK8 ) ) ) )
           => ( sK7 @ Y0 @ sK8 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f71]) ).

thf(f71,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) )
                          & ( sK4 @ Y2 ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK4 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK8 ) )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) )
                          & ( sK4 @ Y2 ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK4 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_3 ),
    inference(not_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( $true
      = ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) )
                              & ( sK4 @ Y2 ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK4 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f57]) ).

thf(f57,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( sK7 @ Y1 @ Y0 ) ) ) )
            & $true ) )
      = $true )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f52,f56]) ).

thf(f56,plain,
    ( ( $true
      = ( sK4 @ sK7 ) )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f55]) ).

thf(f55,plain,
    ( ( ( ( sK4 @ sK7 )
        & $true )
      = $true )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f48,f53]) ).

thf(f53,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK3 @ Y0 @ Y1 )
                  | ( sK2 @ Y0 @ Y1 ) )
               => ( sK7 @ Y0 @ Y1 ) ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ( ( $true
      = ( ( sK4 @ sK7 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK3 @ Y0 @ Y1 )
                    | ( sK2 @ Y0 @ Y1 ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( $false
      = ( ( ( sK4 @ sK7 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK3 @ Y0 @ Y1 )
                      | ( sK2 @ Y0 @ Y1 ) )
                   => ( sK7 @ Y0 @ Y1 ) ) ) ) )
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f44]) ).

thf(f44,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK7 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f32]) ).

thf(f52,plain,
    ( ( $true
      = ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( sK7 @ Y1 @ Y0 ) ) ) )
            & ( sK4 @ sK7 ) ) ) )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f51]) ).

thf(f51,plain,
    ( ( $true
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) )
                              & ( sK4 @ Y2 ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK4 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK7 @ Y1 @ Y0 ) ) ) )
          & ( sK4 @ sK7 ) )
       => $false ) )
    | ~ spl0_3 ),
    inference(superposition,[],[f43,f50]) ).

thf(f50,plain,
    ( ( ( sK7 @ sK5 @ sK6 )
      = $false )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f49]) ).

thf(f49,plain,
    ( ( $false
      = ( $true
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f45,f48]) ).

thf(f43,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                                & ( sK4 @ Y2 ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK4 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) )
            & ( sK4 @ X1 ) )
         => ( X1 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f42]) ).

thf(f42,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK2 @ Y5 @ Y4 )
                                             => ( Y3 @ Y5 @ Y4 ) ) ) )
                                    & ( sK4 @ Y3 ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( sK4 @ Y3 )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK3 @ Y5 @ Y4 )
                                             => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK5 @ sK6 ) )
          @ X1 ) )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( $false
     != ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) )
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f20,f32]) ).

thf(f116,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK7 @ Y1 @ Y0 ) ) ) )
       => ( sK7 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f114]) ).

thf(f114,plain,
    ( ( $true
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK7 @ Y1 @ Y0 ) ) ) )
          & $true )
       => ( sK7 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f105,f56]) ).

thf(f105,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK2 @ Y1 @ Y0 )
                     => ( X1 @ Y1 @ Y0 ) ) ) )
            & ( sK4 @ X1 ) )
         => ( X1 @ sK9 @ sK8 ) ) )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f104]) ).

thf(f104,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK9 @ sK8 ) )
          @ X1 )
        = $true )
    | ~ spl0_5 ),
    inference(pi_clausification,[],[f94]) ).

thf(f94,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f93]) ).

thf(f93,plain,
    ( spl0_5
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f170,plain,
    ( ( $true
      = ( ~ ( ( sK3 @ sK11 @ sK10 )
            | ( sK2 @ sK11 @ sK10 ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f169]) ).

thf(f169,plain,
    ( ( $true
      = ( ( ( sK3 @ sK11 @ sK10 )
          | ( sK2 @ sK11 @ sK10 ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f77,f168]) ).

thf(f168,plain,
    ( ( ( sK7 @ sK11 @ sK10 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f167]) ).

thf(f167,plain,
    ( ( ( $true
       => ( sK7 @ sK11 @ sK10 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f164,f166]) ).

thf(f77,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( ( sK3 @ X1 @ X2 )
            | ( sK2 @ X1 @ X2 ) )
         => ( sK7 @ X1 @ X2 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f76]) ).

thf(f76,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( sK3 @ X1 @ Y0 )
                | ( sK2 @ X1 @ Y0 ) )
             => ( sK7 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f70]) ).

thf(f70,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK3 @ X1 @ Y0 )
                | ( sK2 @ X1 @ Y0 ) )
             => ( sK7 @ X1 @ Y0 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f69]) ).

thf(f69,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK3 @ Y0 @ Y1 )
                    | ( sK2 @ Y0 @ Y1 ) )
                 => ( sK7 @ Y0 @ Y1 ) ) )
          @ X1 ) )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f53]) ).

thf(f98,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f91,f31,f96,f93]) ).

thf(f91,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) )
    | ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f84]) ).

thf(f84,plain,
    ( ( $true
      = ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( sK4 @ Y0 ) )
             => ( Y0 @ sK9 @ sK8 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK4 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) ) ) )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f79]) ).

thf(f40,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f39]) ).

thf(f39,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f38]) ).

thf(f38,plain,
    ( ( $true = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f28,f32]) ).

thf(f28,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f27]) ).

thf(f27,plain,
    ( spl0_2
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f36,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f22,f34,f31]) ).

thf(f22,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
      = $false )
    | ( $false
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f29,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f21,f27,f24]) ).

thf(f21,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) )
                                  & ( sK4 @ Y3 ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK4 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( sK4 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) )
    | ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK4 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK3 @ Y1 @ Y2 )
                          | ( sK2 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 18:42:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_EQU_NAR problem
% 0.14/0.35  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37  % (13393)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.14/0.37  % (13386)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.37  % (13393)Instruction limit reached!
% 0.14/0.37  % (13393)------------------------------
% 0.14/0.37  % (13393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (13393)Termination reason: Unknown
% 0.14/0.37  % (13388)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.14/0.37  % (13393)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (13393)Memory used [KB]: 1023
% 0.14/0.37  % (13393)Time elapsed: 0.003 s
% 0.14/0.37  % (13393)Instructions burned: 3 (million)
% 0.14/0.37  % (13389)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37  % (13393)------------------------------
% 0.14/0.37  % (13393)------------------------------
% 0.14/0.37  % (13387)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.14/0.37  % (13391)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.14/0.37  % (13390)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37  % (13389)Instruction limit reached!
% 0.14/0.37  % (13389)------------------------------
% 0.14/0.37  % (13389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (13389)Termination reason: Unknown
% 0.14/0.37  % (13389)Termination phase: shuffling
% 0.14/0.37  
% 0.14/0.37  % (13389)Memory used [KB]: 895
% 0.14/0.37  % (13389)Time elapsed: 0.003 s
% 0.14/0.37  % (13389)Instructions burned: 2 (million)
% 0.14/0.37  % (13389)------------------------------
% 0.14/0.37  % (13389)------------------------------
% 0.14/0.37  % (13390)Instruction limit reached!
% 0.14/0.37  % (13390)------------------------------
% 0.14/0.37  % (13390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (13390)Termination reason: Unknown
% 0.14/0.37  % (13390)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (13390)Memory used [KB]: 1023
% 0.14/0.37  % (13390)Time elapsed: 0.003 s
% 0.14/0.37  % (13390)Instructions burned: 3 (million)
% 0.14/0.37  % (13390)------------------------------
% 0.14/0.37  % (13390)------------------------------
% 0.14/0.37  % (13387)Instruction limit reached!
% 0.14/0.37  % (13387)------------------------------
% 0.14/0.37  % (13387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (13387)Termination reason: Unknown
% 0.14/0.37  % (13387)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (13387)Memory used [KB]: 5500
% 0.14/0.37  % (13387)Time elapsed: 0.004 s
% 0.14/0.37  % (13387)Instructions burned: 4 (million)
% 0.14/0.37  % (13387)------------------------------
% 0.14/0.37  % (13387)------------------------------
% 0.14/0.37  % (13392)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.38  % (13395)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38  % (13388)Instruction limit reached!
% 0.14/0.38  % (13388)------------------------------
% 0.14/0.38  % (13388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (13388)Termination reason: Unknown
% 0.14/0.38  % (13388)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (13388)Memory used [KB]: 5756
% 0.14/0.38  % (13388)Time elapsed: 0.018 s
% 0.14/0.38  % (13388)Instructions burned: 28 (million)
% 0.14/0.38  % (13388)------------------------------
% 0.14/0.38  % (13388)------------------------------
% 0.14/0.38  % (13392)Instruction limit reached!
% 0.14/0.38  % (13392)------------------------------
% 0.14/0.38  % (13392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (13392)Termination reason: Unknown
% 0.14/0.38  % (13392)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (13392)Memory used [KB]: 5500
% 0.14/0.38  % (13392)Time elapsed: 0.012 s
% 0.14/0.38  % (13392)Instructions burned: 18 (million)
% 0.14/0.38  % (13392)------------------------------
% 0.14/0.38  % (13392)------------------------------
% 0.14/0.38  % (13396)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.38  % (13398)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39  % (13398)Instruction limit reached!
% 0.14/0.39  % (13398)------------------------------
% 0.14/0.39  % (13398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (13398)Termination reason: Unknown
% 0.14/0.39  % (13398)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (13398)Memory used [KB]: 5500
% 0.14/0.39  % (13398)Time elapsed: 0.004 s
% 0.14/0.39  % (13398)Instructions burned: 3 (million)
% 0.14/0.39  % (13398)------------------------------
% 0.14/0.39  % (13398)------------------------------
% 0.14/0.39  % (13399)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.14/0.39  % (13396)Instruction limit reached!
% 0.14/0.39  % (13396)------------------------------
% 0.14/0.39  % (13396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (13396)Termination reason: Unknown
% 0.14/0.39  % (13396)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (13396)Memory used [KB]: 5756
% 0.14/0.39  % (13396)Time elapsed: 0.011 s
% 0.14/0.39  % (13396)Instructions burned: 16 (million)
% 0.14/0.39  % (13396)------------------------------
% 0.14/0.39  % (13396)------------------------------
% 0.14/0.40  % (13405)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40  % (13406)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40  % (13395)Instruction limit reached!
% 0.14/0.40  % (13395)------------------------------
% 0.14/0.40  % (13395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (13395)Termination reason: Unknown
% 0.14/0.40  % (13395)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (13395)Memory used [KB]: 5628
% 0.14/0.40  % (13395)Time elapsed: 0.021 s
% 0.14/0.40  % (13395)Instructions burned: 37 (million)
% 0.14/0.40  % (13395)------------------------------
% 0.14/0.40  % (13395)------------------------------
% 0.14/0.40  % (13408)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.40  % (13405)Instruction limit reached!
% 0.14/0.40  % (13405)------------------------------
% 0.14/0.40  % (13405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (13405)Termination reason: Unknown
% 0.14/0.40  % (13405)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (13405)Memory used [KB]: 1023
% 0.14/0.40  % (13405)Time elapsed: 0.006 s
% 0.14/0.40  % (13405)Instructions burned: 7 (million)
% 0.14/0.40  % (13405)------------------------------
% 0.14/0.40  % (13405)------------------------------
% 0.14/0.40  % (13408)Instruction limit reached!
% 0.14/0.40  % (13408)------------------------------
% 0.14/0.40  % (13408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (13408)Termination reason: Unknown
% 0.14/0.40  % (13408)Termination phase: Preprocessing 3
% 0.14/0.40  
% 0.14/0.40  % (13408)Memory used [KB]: 1023
% 0.14/0.40  % (13408)Time elapsed: 0.003 s
% 0.14/0.40  % (13408)Instructions burned: 3 (million)
% 0.14/0.40  % (13408)------------------------------
% 0.14/0.40  % (13408)------------------------------
% 0.14/0.41  % (13412)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)
% 0.14/0.41  % (13406)Instruction limit reached!
% 0.14/0.41  % (13406)------------------------------
% 0.14/0.41  % (13406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (13406)Termination reason: Unknown
% 0.14/0.41  % (13406)Termination phase: Saturation
% 0.14/0.41  
% 0.14/0.41  % (13406)Memory used [KB]: 5756
% 0.14/0.41  % (13406)Time elapsed: 0.013 s
% 0.14/0.41  % (13406)Instructions burned: 17 (million)
% 0.14/0.41  % (13406)------------------------------
% 0.14/0.41  % (13406)------------------------------
% 0.14/0.41  % (13412)Instruction limit reached!
% 0.14/0.41  % (13412)------------------------------
% 0.14/0.41  % (13412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (13412)Termination reason: Unknown
% 0.14/0.41  % (13412)Termination phase: Property scanning
% 0.14/0.41  
% 0.14/0.41  % (13412)Memory used [KB]: 1023
% 0.14/0.41  % (13412)Time elapsed: 0.004 s
% 0.14/0.41  % (13412)Instructions burned: 3 (million)
% 0.14/0.41  % (13412)------------------------------
% 0.14/0.41  % (13412)------------------------------
% 0.14/0.41  % (13413)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)
% 0.14/0.42  % (13414)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)
% 0.14/0.42  % (13415)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.42  % (13413)Instruction limit reached!
% 0.14/0.42  % (13413)------------------------------
% 0.14/0.42  % (13413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (13413)Termination reason: Unknown
% 0.14/0.42  % (13413)Termination phase: Saturation
% 0.14/0.42  
% 0.14/0.42  % (13413)Memory used [KB]: 5500
% 0.14/0.42  % (13413)Time elapsed: 0.006 s
% 0.14/0.42  % (13413)Instructions burned: 8 (million)
% 0.14/0.42  % (13413)------------------------------
% 0.14/0.42  % (13413)------------------------------
% 0.20/0.42  % (13414)Instruction limit reached!
% 0.20/0.42  % (13414)------------------------------
% 0.20/0.42  % (13414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42  % (13414)Termination reason: Unknown
% 0.20/0.42  % (13414)Termination phase: Saturation
% 0.20/0.42  
% 0.20/0.42  % (13414)Memory used [KB]: 5500
% 0.20/0.42  % (13414)Time elapsed: 0.004 s
% 0.20/0.42  % (13414)Instructions burned: 4 (million)
% 0.20/0.42  % (13414)------------------------------
% 0.20/0.42  % (13414)------------------------------
% 0.20/0.42  % (13415)Instruction limit reached!
% 0.20/0.42  % (13415)------------------------------
% 0.20/0.42  % (13415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42  % (13415)Termination reason: Unknown
% 0.20/0.42  % (13415)Termination phase: Saturation
% 0.20/0.42  
% 0.20/0.42  % (13415)Memory used [KB]: 5500
% 0.20/0.42  % (13415)Time elapsed: 0.005 s
% 0.20/0.42  % (13415)Instructions burned: 4 (million)
% 0.20/0.42  % (13415)------------------------------
% 0.20/0.42  % (13415)------------------------------
% 0.20/0.42  % (13416)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)
% 0.20/0.42  % (13417)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43  % (13418)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.43  % (13416)Instruction limit reached!
% 0.20/0.43  % (13416)------------------------------
% 0.20/0.43  % (13416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43  % (13418)Instruction limit reached!
% 0.20/0.43  % (13418)------------------------------
% 0.20/0.43  % (13418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43  % (13418)Termination reason: Unknown
% 0.20/0.43  % (13418)Termination phase: Saturation
% 0.20/0.43  
% 0.20/0.43  % (13418)Memory used [KB]: 5500
% 0.20/0.43  % (13418)Time elapsed: 0.005 s
% 0.20/0.43  % (13418)Instructions burned: 6 (million)
% 0.20/0.43  % (13418)------------------------------
% 0.20/0.43  % (13418)------------------------------
% 0.20/0.43  % (13416)Termination reason: Unknown
% 0.20/0.43  % (13416)Termination phase: Saturation
% 0.20/0.43  
% 0.20/0.43  % (13416)Memory used [KB]: 5500
% 0.20/0.43  % (13416)Time elapsed: 0.011 s
% 0.20/0.43  % (13416)Instructions burned: 18 (million)
% 0.20/0.43  % (13416)------------------------------
% 0.20/0.43  % (13416)------------------------------
% 0.20/0.43  % (13419)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)
% 0.20/0.43  % (13420)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)
% 0.20/0.44  % (13421)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.45  % (13422)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)
% 0.20/0.45  % (13421)Instruction limit reached!
% 0.20/0.45  % (13421)------------------------------
% 0.20/0.45  % (13421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45  % (13421)Termination reason: Unknown
% 0.20/0.45  % (13421)Termination phase: Saturation
% 0.20/0.45  
% 0.20/0.45  % (13421)Memory used [KB]: 5500
% 0.20/0.45  % (13421)Time elapsed: 0.005 s
% 0.20/0.45  % (13421)Instructions burned: 6 (million)
% 0.20/0.45  % (13421)------------------------------
% 0.20/0.45  % (13421)------------------------------
% 0.20/0.45  % (13420)Instruction limit reached!
% 0.20/0.45  % (13420)------------------------------
% 0.20/0.45  % (13420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45  % (13420)Termination reason: Unknown
% 0.20/0.45  % (13420)Termination phase: Saturation
% 0.20/0.45  
% 0.20/0.45  % (13420)Memory used [KB]: 5628
% 0.20/0.45  % (13420)Time elapsed: 0.016 s
% 0.20/0.45  % (13420)Instructions burned: 22 (million)
% 0.20/0.45  % (13420)------------------------------
% 0.20/0.45  % (13420)------------------------------
% 0.20/0.45  % (13422)Instruction limit reached!
% 0.20/0.45  % (13422)------------------------------
% 0.20/0.45  % (13422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45  % (13422)Termination reason: Unknown
% 0.20/0.45  % (13422)Termination phase: Saturation
% 0.20/0.45  
% 0.20/0.45  % (13422)Memory used [KB]: 5500
% 0.20/0.45  % (13422)Time elapsed: 0.005 s
% 0.20/0.45  % (13422)Instructions burned: 6 (million)
% 0.20/0.45  % (13422)------------------------------
% 0.20/0.45  % (13422)------------------------------
% 0.20/0.46  % (13424)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)
% 0.20/0.46  % (13386)Instruction limit reached!
% 0.20/0.46  % (13386)------------------------------
% 0.20/0.46  % (13386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46  % (13386)Termination reason: Unknown
% 0.20/0.46  % (13386)Termination phase: Saturation
% 0.20/0.46  
% 0.20/0.46  % (13386)Memory used [KB]: 7675
% 0.20/0.46  % (13386)Time elapsed: 0.096 s
% 0.20/0.46  % (13386)Instructions burned: 183 (million)
% 0.20/0.46  % (13386)------------------------------
% 0.20/0.46  % (13386)------------------------------
% 0.20/0.46  % (13423)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.46  % (13425)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)
% 0.20/0.47  % (13425)Instruction limit reached!
% 0.20/0.47  % (13425)------------------------------
% 0.20/0.47  % (13425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47  % (13425)Termination reason: Unknown
% 0.20/0.47  % (13425)Termination phase: Saturation
% 0.20/0.47  
% 0.20/0.47  % (13425)Memory used [KB]: 5628
% 0.20/0.47  % (13425)Time elapsed: 0.009 s
% 0.20/0.47  % (13425)Instructions burned: 19 (million)
% 0.20/0.47  % (13425)------------------------------
% 0.20/0.47  % (13425)------------------------------
% 0.20/0.47  % (13428)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)
% 0.20/0.48  % (13432)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.48  % (13399)First to succeed.
% 0.20/0.48  % (13432)Instruction limit reached!
% 0.20/0.48  % (13432)------------------------------
% 0.20/0.48  % (13432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48  % (13432)Termination reason: Unknown
% 0.20/0.48  % (13432)Termination phase: Saturation
% 0.20/0.48  
% 0.20/0.48  % (13432)Memory used [KB]: 5756
% 0.20/0.48  % (13432)Time elapsed: 0.007 s
% 0.20/0.48  % (13432)Instructions burned: 19 (million)
% 0.20/0.48  % (13432)------------------------------
% 0.20/0.48  % (13432)------------------------------
% 0.20/0.49  % (13399)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (13399)------------------------------
% 0.20/0.49  % (13399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.49  % (13399)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (13399)Memory used [KB]: 6140
% 0.20/0.49  % (13399)Time elapsed: 0.100 s
% 0.20/0.49  % (13399)Instructions burned: 144 (million)
% 0.20/0.49  % (13399)------------------------------
% 0.20/0.49  % (13399)------------------------------
% 0.20/0.49  % (13383)Success in time 0.121 s
% 0.20/0.49  % Vampire---4.8 exiting
%------------------------------------------------------------------------------