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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV119^5 : TPTP v8.1.2. 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 : n009.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 : Sun May  5 09:41:24 EDT 2024

% Result   : Theorem 0.22s 0.55s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  231 (  18 unt;  24 typ;   0 def)
%            Number of atoms       : 2045 ( 206 equ;   0 cnn)
%            Maximal formula atoms :    4 (   9 avg)
%            Number of connectives : 5406 ( 371   ~; 474   |; 221   &;3173   @)
%                                         (   9 <=>; 499  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  859 ( 859   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   35 (  31 usr;  24 con; 0-2 aty)
%                                         ( 659  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  837 ( 752   ^  84   !;   0   ?; 837   :)
%                                         (   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 ) > $o ).

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

thf(func_def_30,type,
    sK11: a > a > $o ).

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 ).

thf(func_def_35,type,
    sK16: a ).

thf(func_def_36,type,
    sK17: a ).

thf(func_def_37,type,
    sK18: a ).

thf(func_def_38,type,
    sK19: a ).

thf(func_def_39,type,
    sK20: a ).

thf(func_def_40,type,
    sK21: a > a > $o ).

thf(func_def_41,type,
    sK22: a > a > $o ).

thf(f802,plain,
    $false,
    inference(avatar_sat_refutation,[],[f29,f36,f65,f106,f203,f207,f298,f382,f500,f558,f801]) ).

thf(f801,plain,
    ( ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(avatar_contradiction_clause,[],[f800]) ).

thf(f800,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(trivial_inequality_removal,[],[f799]) ).

thf(f799,plain,
    ( ( $true = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(forward_demodulation,[],[f790,f681]) ).

thf(f681,plain,
    ( ( ( sK21 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f680]) ).

thf(f680,plain,
    ( ( $false
      = ( $true
       => ( sK21 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(backward_demodulation,[],[f674,f679]) ).

thf(f679,plain,
    ( ( ( ( sK3 @ sK21 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK21 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f674]) ).

thf(f674,plain,
    ( ( ( ( ( sK3 @ sK21 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK21 @ Y1 @ Y0 ) ) ) ) )
       => ( sK21 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f672]) ).

thf(f672,plain,
    ( ( $false
      = ( ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) )
        @ sK21 ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(sigma_clausification,[],[f671]) ).

thf(f671,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f670]) ).

thf(f670,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) )
        | $false )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(backward_demodulation,[],[f663,f666]) ).

thf(f666,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f663]) ).

thf(f663,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK4 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(not_proxy_clausification,[],[f653]) ).

thf(f653,plain,
    ( ( ( ~ ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ sK9 @ sK8 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK4 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ sK9 @ sK8 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f651]) ).

thf(f651,plain,
    ( ( $true
      = ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK4 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(superposition,[],[f631,f580]) ).

thf(f580,plain,
    ( ( ( sK7 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f579]) ).

thf(f579,plain,
    ( ( ( $true
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f578]) ).

thf(f578,plain,
    ( ( ( ( $true
          | ( sK4 @ sK9 @ sK8 ) )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(forward_demodulation,[],[f577,f105]) ).

thf(f105,plain,
    ( ( $true
      = ( sK2 @ sK9 @ sK8 ) )
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f104]) ).

thf(f104,plain,
    ( spl0_8
  <=> ( $true
      = ( sK2 @ sK9 @ sK8 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

thf(f577,plain,
    ( ( ( ( ( sK2 @ sK9 @ sK8 )
          | ( sK4 @ sK9 @ sK8 ) )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f576]) ).

thf(f576,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK8 )
              | ( sK4 @ Y0 @ sK8 ) )
           => ( sK7 @ Y0 @ sK8 ) )
        @ sK9 )
      = $false )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f563]) ).

thf(f563,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK8 )
              | ( sK4 @ Y0 @ sK8 ) )
           => ( sK7 @ Y0 @ sK8 ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f562]) ).

thf(f562,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK8 )
      = $false )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f57]) ).

thf(f57,plain,
    ( spl0_5
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f631,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ X1 @ X2 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK4 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ X1 @ X2 ) ) ) )
         => ( sK7 @ X1 @ X2 ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f630]) ).

thf(f630,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK4 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) ) )
             => ( sK7 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f627]) ).

thf(f627,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK4 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) ) )
             => ( sK7 @ X1 @ Y0 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f626]) ).

thf(f626,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f619]) ).

thf(f619,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK4 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( sK7 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f618]) ).

thf(f618,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) )
        & $true ) )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f606,f616]) ).

thf(f616,plain,
    ( ( ( sK3 @ sK7 )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f606]) ).

thf(f606,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) )
        & ( sK3 @ sK7 ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f594]) ).

thf(f594,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK4 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( sK7 @ Y0 @ Y1 ) ) ) )
          & ( sK3 @ sK7 ) )
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f593]) ).

thf(f593,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK7 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f32]) ).

thf(f32,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
      = $false )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f31]) ).

thf(f31,plain,
    ( spl0_3
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f790,plain,
    ( ( ( sK21 @ sK9 @ sK8 )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f788]) ).

thf(f788,plain,
    ( ( $true
      = ( $true
       => ( sK21 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(superposition,[],[f775,f105]) ).

thf(f775,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( sK2 @ X2 @ X1 )
         => ( sK21 @ X2 @ X1 ) )
        = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f774]) ).

thf(f774,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( sK2 @ Y0 @ X1 )
             => ( sK21 @ Y0 @ X1 ) )
          @ X2 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(pi_clausification,[],[f758]) ).

thf(f758,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ Y0 @ X1 )
             => ( sK21 @ Y0 @ X1 ) ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f756]) ).

thf(f756,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK21 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(pi_clausification,[],[f682]) ).

thf(f682,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK21 @ Y1 @ Y0 ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f679]) ).

thf(f558,plain,
    ( ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(avatar_contradiction_clause,[],[f557]) ).

thf(f557,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(trivial_inequality_removal,[],[f556]) ).

thf(f556,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f555]) ).

thf(f555,plain,
    ( ( $true = ~ $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f554]) ).

thf(f554,plain,
    ( ( $true
      = ( ~ ( $true
            | ( sK4 @ sK20 @ sK19 ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(forward_demodulation,[],[f553,f549]) ).

thf(f549,plain,
    ( ( ( sK2 @ sK20 @ sK19 )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(binary_proxy_clausification,[],[f547]) ).

thf(f547,plain,
    ( ( ( ( sK2 @ sK20 @ sK19 )
       => ( sK12 @ sK20 @ sK19 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f546]) ).

thf(f546,plain,
    ( ( ( ^ [Y0: a] :
            ( ( sK2 @ Y0 @ sK19 )
           => ( sK12 @ Y0 @ sK19 ) )
        @ sK20 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f543]) ).

thf(f543,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ Y0 @ sK19 )
           => ( sK12 @ Y0 @ sK19 ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f541]) ).

thf(f541,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK12 @ Y1 @ Y0 ) ) )
        @ sK19 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f528]) ).

thf(f528,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y1 @ Y0 )
               => ( sK12 @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(not_proxy_clausification,[],[f522]) ).

thf(f522,plain,
    ( ( $true
      = ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f521]) ).

thf(f521,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK12 @ Y1 @ Y0 ) ) ) )
       => $false )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(forward_demodulation,[],[f512,f367]) ).

thf(f367,plain,
    ( ( ( sK12 @ sK13 @ sK14 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f366]) ).

thf(f366,plain,
    ( ( ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK13 @ sK14 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK4 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK13 @ sK14 ) ) ) )
       => ( sK12 @ sK13 @ sK14 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f365]) ).

thf(f365,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK3 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ sK13 @ Y0 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK3 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK4 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ sK13 @ Y0 ) ) ) )
           => ( sK12 @ sK13 @ Y0 ) )
        @ sK14 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f364]) ).

thf(f364,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK3 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y3 @ Y2 )
                               => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                   => ( Y1 @ sK13 @ Y0 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( sK3 @ Y1 )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK4 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ sK13 @ Y0 ) ) ) )
           => ( sK12 @ sK13 @ Y0 ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f360]) ).

thf(f360,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK4 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( sK12 @ Y0 @ Y1 ) ) )
        @ sK13 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f351]) ).

thf(f351,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK4 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( sK12 @ Y0 @ Y1 ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(not_proxy_clausification,[],[f319]) ).

thf(f319,plain,
    ( ( ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK4 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( sK12 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f316]) ).

thf(f316,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK4 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) ) )
                     => ( sK12 @ Y0 @ Y1 ) ) ) )
            & $true ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f313,f315]) ).

thf(f315,plain,
    ( ( $true
      = ( sK3 @ sK12 ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f304]) ).

thf(f304,plain,
    ( ( $true
      = ( ( sK3 @ sK12 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK4 @ Y1 @ Y0 ) )
                 => ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f302]) ).

thf(f302,plain,
    ( ( ( ( ( sK3 @ sK12 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK2 @ Y1 @ Y0 )
                      | ( sK4 @ Y1 @ Y0 ) )
                   => ( sK12 @ Y1 @ Y0 ) ) ) ) )
       => ( sK12 @ sK5 @ sK6 ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f301]) ).

thf(f301,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK4 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK12 )
      = $false )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f35]) ).

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

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

thf(f313,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK4 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) ) )
                     => ( sK12 @ Y0 @ Y1 ) ) ) )
            & ( sK3 @ sK12 ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f312]) ).

thf(f312,plain,
    ( ( $true
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK4 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( sK12 @ Y0 @ Y1 ) ) ) )
          & ( sK3 @ sK12 ) )
       => $false ) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(superposition,[],[f310,f303]) ).

thf(f303,plain,
    ( ( ( sK12 @ sK5 @ sK6 )
      = $false )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f302]) ).

thf(f310,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y4 @ Y3 )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( sK3 @ Y2 )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK4 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                             => ( Y2 @ Y0 @ Y1 ) ) ) )
                     => ( X1 @ Y0 @ Y1 ) ) ) )
            & ( sK3 @ X1 ) )
         => ( X1 @ sK5 @ sK6 ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f309]) ).

thf(f309,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( sK3 @ Y3 )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK2 @ Y5 @ Y4 )
                                             => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                                 => ( Y3 @ Y1 @ Y2 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( sK3 @ Y3 )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK4 @ Y4 @ Y5 )
                                             => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                 => ( Y3 @ Y1 @ Y2 ) ) ) )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( sK3 @ Y0 ) )
             => ( Y0 @ sK5 @ sK6 ) )
          @ X1 )
        = $true )
    | ~ 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] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ 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] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f512,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y1 @ Y0 )
                 => ( sK12 @ Y1 @ Y0 ) ) ) )
       => ( sK12 @ sK13 @ sK14 ) )
      = $true )
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f510]) ).

thf(f510,plain,
    ( ( ( ( $true
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y1 @ Y0 )
                   => ( sK12 @ Y1 @ Y0 ) ) ) ) )
       => ( sK12 @ sK13 @ sK14 ) )
      = $true )
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(superposition,[],[f504,f315]) ).

thf(f504,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( sK3 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK2 @ Y1 @ Y0 )
                     => ( X1 @ Y1 @ Y0 ) ) ) ) )
         => ( X1 @ sK13 @ sK14 ) ) )
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f503]) ).

thf(f503,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK13 @ sK14 ) )
          @ X1 )
        = $true )
    | ~ spl0_12 ),
    inference(pi_clausification,[],[f381]) ).

thf(f381,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f380]) ).

thf(f380,plain,
    ( spl0_12
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

thf(f553,plain,
    ( ( ( ~ ( ( sK2 @ sK20 @ sK19 )
            | ( sK4 @ sK20 @ sK19 ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f552]) ).

thf(f552,plain,
    ( ( ( ( ( sK2 @ sK20 @ sK19 )
          | ( sK4 @ sK20 @ sK19 ) )
       => $false )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(superposition,[],[f327,f551]) ).

thf(f551,plain,
    ( ( ( sK12 @ sK20 @ sK19 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f550]) ).

thf(f550,plain,
    ( ( ( $true
       => ( sK12 @ sK20 @ sK19 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(backward_demodulation,[],[f547,f549]) ).

thf(f327,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( ( sK2 @ X2 @ X1 )
            | ( sK4 @ X2 @ X1 ) )
         => ( sK12 @ X2 @ X1 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f326]) ).

thf(f326,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( sK2 @ Y0 @ X1 )
                | ( sK4 @ Y0 @ X1 ) )
             => ( sK12 @ Y0 @ X1 ) )
          @ X2 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f321]) ).

thf(f321,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK2 @ Y0 @ X1 )
                | ( sK4 @ Y0 @ X1 ) )
             => ( sK12 @ Y0 @ X1 ) ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f320]) ).

thf(f320,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK4 @ Y1 @ Y0 ) )
                 => ( sK12 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f318]) ).

thf(f318,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK12 @ Y1 @ Y0 ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f317]) ).

thf(f317,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK4 @ Y1 @ Y0 ) )
                 => ( sK12 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f304,f315]) ).

thf(f500,plain,
    ( ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(avatar_contradiction_clause,[],[f499]) ).

thf(f499,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(trivial_inequality_removal,[],[f498]) ).

thf(f498,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f497]) ).

thf(f497,plain,
    ( ( $true = ~ $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f496]) ).

thf(f496,plain,
    ( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
            | $true ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(forward_demodulation,[],[f495,f491]) ).

thf(f491,plain,
    ( ( ( sK4 @ sK17 @ sK18 )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(binary_proxy_clausification,[],[f489]) ).

thf(f489,plain,
    ( ( ( ( sK4 @ sK17 @ sK18 )
       => ( sK12 @ sK17 @ sK18 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(beta_eta_normalization,[],[f488]) ).

thf(f488,plain,
    ( ( ( ^ [Y0: a] :
            ( ( sK4 @ sK17 @ Y0 )
           => ( sK12 @ sK17 @ Y0 ) )
        @ sK18 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(sigma_clausification,[],[f487]) ).

thf(f487,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ sK17 @ Y0 )
           => ( sK12 @ sK17 @ Y0 ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(beta_eta_normalization,[],[f483]) ).

thf(f483,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK4 @ Y0 @ Y1 )
               => ( sK12 @ Y0 @ Y1 ) ) )
        @ sK17 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(sigma_clausification,[],[f480]) ).

thf(f480,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK4 @ Y0 @ Y1 )
               => ( sK12 @ Y0 @ Y1 ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(not_proxy_clausification,[],[f402]) ).

thf(f402,plain,
    ( ( ( ~ ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK4 @ Y0 @ Y1 )
                   => ( sK12 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f401]) ).

thf(f401,plain,
    ( ( ( ~ ( $true
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK4 @ Y0 @ Y1 )
                     => ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(forward_demodulation,[],[f400,f315]) ).

thf(f400,plain,
    ( ( $true
      = ( ~ ( ( sK3 @ sK12 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK4 @ Y0 @ Y1 )
                     => ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f397]) ).

thf(f397,plain,
    ( ( ( ( ( sK3 @ sK12 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK4 @ Y0 @ Y1 )
                   => ( sK12 @ Y0 @ Y1 ) ) ) ) )
       => $false )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(superposition,[],[f389,f367]) ).

thf(f389,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( sK3 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK4 @ Y0 @ Y1 )
                     => ( X1 @ Y0 @ Y1 ) ) ) ) )
         => ( X1 @ sK13 @ sK14 ) ) )
    | ~ spl0_11 ),
    inference(beta_eta_normalization,[],[f388]) ).

thf(f388,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK4 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK13 @ sK14 ) )
          @ X1 )
        = $true )
    | ~ spl0_11 ),
    inference(pi_clausification,[],[f378]) ).

thf(f378,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f377]) ).

thf(f377,plain,
    ( spl0_11
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

thf(f495,plain,
    ( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
            | ( sK4 @ sK17 @ sK18 ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f494]) ).

thf(f494,plain,
    ( ( $true
      = ( ( ( sK2 @ sK17 @ sK18 )
          | ( sK4 @ sK17 @ sK18 ) )
       => $false ) )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(superposition,[],[f327,f493]) ).

thf(f493,plain,
    ( ( ( sK12 @ sK17 @ sK18 )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f492]) ).

thf(f492,plain,
    ( ( ( $true
       => ( sK12 @ sK17 @ sK18 ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_11 ),
    inference(backward_demodulation,[],[f489,f491]) ).

thf(f382,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f375,f34,f24,f380,f377]) ).

thf(f375,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) )
    | ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK13 @ sK14 ) ) ) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f368]) ).

thf(f368,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK13 @ sK14 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK4 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK13 @ sK14 ) ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f366]) ).

thf(f298,plain,
    ( spl0_5
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f297,f31,f27,f57]) ).

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

thf(f297,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f296]) ).

thf(f296,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ( $true = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f264,f222]) ).

thf(f222,plain,
    ( ( ( sK7 @ sK5 @ sK6 )
      = $false )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f221]) ).

thf(f221,plain,
    ( ( $false
      = ( $true
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f218,f220]) ).

thf(f220,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) )
        & ( sK3 @ sK7 ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f218]) ).

thf(f218,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK4 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( sK7 @ Y0 @ Y1 ) ) ) )
          & ( sK3 @ sK7 ) )
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f217]) ).

thf(f217,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK7 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f32]) ).

thf(f264,plain,
    ( ( ( sK7 @ sK5 @ sK6 )
      = $true )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f262]) ).

thf(f262,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK4 @ Y1 @ Y0 ) )
                 => ( sK7 @ Y1 @ Y0 ) ) ) ) )
      = $false )
    | ( ( sK7 @ sK5 @ sK6 )
      = $true )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(superposition,[],[f211,f231]) ).

thf(f231,plain,
    ( ( ( sK3 @ sK7 )
      = $true )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f230]) ).

thf(f230,plain,
    ( ( $true
      = ( $true
        & ( sK3 @ sK7 ) ) )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f220,f229]) ).

thf(f229,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK4 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( sK7 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f220]) ).

thf(f211,plain,
    ( ! [X1: a > a > $o] :
        ( ( ( ( sK3 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK2 @ Y1 @ Y0 )
                        | ( sK4 @ Y1 @ Y0 ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) ) )
          = $false )
        | ( ( X1 @ sK5 @ sK6 )
          = $true ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f90]) ).

thf(f90,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( sK3 @ X1 )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK2 @ Y1 @ Y0 )
                        | ( sK4 @ Y1 @ Y0 ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) ) )
         => ( X1 @ sK5 @ sK6 ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f88]) ).

thf(f88,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK2 @ Y2 @ Y1 )
                            | ( sK4 @ Y2 @ Y1 ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK5 @ sK6 ) )
          @ X1 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f28]) ).

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

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

thf(f206,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f205]) ).

thf(f205,plain,
    ( ( $true = $false )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f28,f35]) ).

thf(f203,plain,
    ( ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(avatar_contradiction_clause,[],[f202]) ).

thf(f202,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(trivial_inequality_removal,[],[f201]) ).

thf(f201,plain,
    ( ( $true = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f195,f169]) ).

thf(f169,plain,
    ( ( ( sK11 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f168]) ).

thf(f168,plain,
    ( ( ( $true
       => ( sK11 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f161,f167]) ).

thf(f167,plain,
    ( ( $true
      = ( ( sK3 @ sK11 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK4 @ Y0 @ Y1 )
                 => ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f161]) ).

thf(f161,plain,
    ( ( ( ( ( sK3 @ sK11 )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK4 @ Y0 @ Y1 )
                   => ( sK11 @ Y0 @ Y1 ) ) ) ) )
       => ( sK11 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f158]) ).

thf(f158,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) )
        @ sK11 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f153]) ).

thf(f153,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK4 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f152]) ).

thf(f152,plain,
    ( ( ( $false
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK4 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f139,f149]) ).

thf(f149,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( sK3 @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK9 @ sK8 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f139]) ).

thf(f139,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y2 @ Y1 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( sK3 @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK4 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK9 @ sK8 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(not_proxy_clausification,[],[f117]) ).

thf(f117,plain,
    ( ( ( ~ ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ sK9 @ sK8 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK4 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ sK9 @ sK8 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f115]) ).

thf(f115,plain,
    ( ( $true
      = ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y2 @ Y1 )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( sK3 @ Y0 )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK4 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK9 @ sK8 ) ) ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f112,f82]) ).

thf(f82,plain,
    ( ( ( sK7 @ sK9 @ sK8 )
      = $false )
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f72]) ).

thf(f72,plain,
    ( ( ( ( ( sK2 @ sK9 @ sK8 )
          | ( sK4 @ sK9 @ sK8 ) )
       => ( sK7 @ sK9 @ sK8 ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f71]) ).

thf(f71,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK8 )
              | ( sK4 @ Y0 @ sK8 ) )
           => ( sK7 @ Y0 @ sK8 ) )
        @ sK9 )
      = $false )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f68]) ).

thf(f68,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK8 )
              | ( sK4 @ Y0 @ sK8 ) )
           => ( sK7 @ Y0 @ sK8 ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f67]) ).

thf(f67,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK4 @ Y1 @ Y0 ) )
               => ( sK7 @ Y1 @ Y0 ) ) )
        @ sK8 )
      = $false )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f58]) ).

thf(f112,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y2 @ Y1 )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) )
                 => ( Y0 @ X1 @ X2 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( sK3 @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK4 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ X1 @ X2 ) ) ) )
         => ( sK7 @ X1 @ X2 ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f111]) ).

thf(f111,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK4 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) ) )
             => ( sK7 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f110]) ).

thf(f110,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y3 @ Y2 )
                                 => ( Y1 @ Y3 @ Y2 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( sK3 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK4 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ X1 @ Y0 ) ) ) )
             => ( sK7 @ X1 @ Y0 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f109]) ).

thf(f109,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f92]) ).

thf(f92,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y4 @ Y3 )
                                   => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( sK3 @ Y2 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK4 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( sK7 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y4 @ Y3 )
                                     => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( sK3 @ Y2 )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK4 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( sK7 @ Y0 @ Y1 ) ) ) )
        & ( sK3 @ sK7 ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f43]) ).

thf(f43,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y4 @ Y3 )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( sK3 @ Y2 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK4 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( sK7 @ Y0 @ Y1 ) ) ) )
          & ( sK3 @ sK7 ) )
       => ( sK7 @ sK5 @ sK6 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f42]) ).

thf(f42,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y5 @ Y4 )
                                           => ( Y3 @ Y5 @ Y4 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( sK3 @ Y3 )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK4 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( sK3 @ Y0 ) )
           => ( Y0 @ sK5 @ sK6 ) )
        @ sK7 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f32]) ).

thf(f195,plain,
    ( ( ( sK11 @ sK9 @ sK8 )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(boolean_simplification,[],[f194]) ).

thf(f194,plain,
    ( ( $true
      = ( $true
       => ( sK11 @ sK9 @ sK8 ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(superposition,[],[f187,f102]) ).

thf(f102,plain,
    ( ( ( sK4 @ sK9 @ sK8 )
      = $true )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f101]) ).

thf(f101,plain,
    ( spl0_7
  <=> ( ( sK4 @ sK9 @ sK8 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

thf(f187,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( sK4 @ X1 @ X2 )
         => ( sK11 @ X1 @ X2 ) )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f186]) ).

thf(f186,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
             => ( sK11 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(pi_clausification,[],[f182]) ).

thf(f182,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
             => ( sK11 @ X1 @ Y0 ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f181]) ).

thf(f181,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK4 @ Y0 @ Y1 )
                 => ( sK11 @ Y0 @ Y1 ) ) )
          @ X1 ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(pi_clausification,[],[f178]) ).

thf(f178,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK4 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f177]) ).

thf(f177,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK4 @ Y0 @ Y1 )
                 => ( sK11 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f167,f176]) ).

thf(f176,plain,
    ( ( $true
      = ( sK3 @ sK11 ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f167]) ).

thf(f106,plain,
    ( spl0_7
    | spl0_8
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f99,f57,f104,f101]) ).

thf(f99,plain,
    ( ( $true
      = ( sK2 @ sK9 @ sK8 ) )
    | ( ( sK4 @ sK9 @ sK8 )
      = $true )
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f83]) ).

thf(f83,plain,
    ( ( ( ( sK2 @ sK9 @ sK8 )
        | ( sK4 @ sK9 @ sK8 ) )
      = $true )
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f72]) ).

thf(f65,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f64]) ).

thf(f64,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f63]) ).

thf(f63,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f25,f32]) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(f1,conjecture,
    ! [X2: a > a > $o,X0: ( a > a > $o ) > $o,X1: a > a > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ( ( X0 @ X5 )
              & ! [X7: a,X6: a] :
                  ( ( ! [X8: a > a > $o] :
                        ( ( ! [X10: a,X9: a] :
                              ( ( X2 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) )
                          & ( X0 @ X8 ) )
                       => ( X8 @ X6 @ X7 ) )
                    | ! [X8: a > a > $o] :
                        ( ( ! [X9: a,X10: a] :
                              ( ( X1 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) )
                          & ( X0 @ X8 ) )
                       => ( X8 @ X6 @ X7 ) ) )
                 => ( X5 @ X6 @ X7 ) ) )
           => ( X5 @ X3 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ( ! [X6: a,X7: a] :
                  ( ( ( X2 @ X6 @ X7 )
                    | ( X1 @ X6 @ X7 ) )
                 => ( X5 @ X6 @ X7 ) )
              & ( X0 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.cA17ylHlAt/Vampire---4.8_28674',cTHM252_pme) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : SEV119^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % 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
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 11:51:25 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.cA17ylHlAt/Vampire---4.8_28674
% 0.15/0.38  % (28892)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38  % (28890)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.38  % (28888)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.38  % (28891)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38  % (28894)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38  % (28889)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.39  % (28893)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39  % (28892)Instruction limit reached!
% 0.15/0.39  % (28892)------------------------------
% 0.15/0.39  % (28892)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (28895)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39  % (28892)Termination reason: Unknown
% 0.15/0.39  % (28892)Termination phase: Preprocessing 1
% 0.15/0.39  
% 0.15/0.39  % (28892)Memory used [KB]: 1023
% 0.15/0.39  % (28892)Time elapsed: 0.004 s
% 0.15/0.39  % (28892)Instructions burned: 2 (million)
% 0.15/0.39  % (28892)------------------------------
% 0.15/0.39  % (28892)------------------------------
% 0.15/0.39  % (28891)Instruction limit reached!
% 0.15/0.39  % (28891)------------------------------
% 0.15/0.39  % (28891)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (28891)Termination reason: Unknown
% 0.15/0.39  % (28891)Termination phase: Property scanning
% 0.15/0.39  
% 0.15/0.39  % (28891)Memory used [KB]: 1023
% 0.15/0.39  % (28891)Time elapsed: 0.004 s
% 0.15/0.39  % (28891)Instructions burned: 3 (million)
% 0.15/0.39  % (28891)------------------------------
% 0.15/0.39  % (28891)------------------------------
% 0.15/0.39  % (28895)Instruction limit reached!
% 0.15/0.39  % (28895)------------------------------
% 0.15/0.39  % (28895)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (28895)Termination reason: Unknown
% 0.15/0.39  % (28895)Termination phase: Saturation
% 0.15/0.39  
% 0.15/0.39  % (28895)Memory used [KB]: 1023
% 0.15/0.39  % (28895)Time elapsed: 0.004 s
% 0.15/0.39  % (28895)Instructions burned: 3 (million)
% 0.15/0.39  % (28895)------------------------------
% 0.15/0.39  % (28895)------------------------------
% 0.15/0.39  % (28889)Instruction limit reached!
% 0.15/0.39  % (28889)------------------------------
% 0.15/0.39  % (28889)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (28889)Termination reason: Unknown
% 0.15/0.39  % (28889)Termination phase: Saturation
% 0.15/0.39  
% 0.15/0.39  % (28889)Memory used [KB]: 5500
% 0.15/0.39  % (28889)Time elapsed: 0.005 s
% 0.15/0.39  % (28889)Instructions burned: 4 (million)
% 0.15/0.39  % (28889)------------------------------
% 0.15/0.39  % (28889)------------------------------
% 0.15/0.40  % (28894)Instruction limit reached!
% 0.15/0.40  % (28894)------------------------------
% 0.15/0.40  % (28894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (28894)Termination reason: Unknown
% 0.15/0.40  % (28894)Termination phase: Saturation
% 0.15/0.40  
% 0.15/0.40  % (28894)Memory used [KB]: 5500
% 0.15/0.40  % (28894)Time elapsed: 0.018 s
% 0.15/0.40  % (28894)Instructions burned: 19 (million)
% 0.15/0.40  % (28894)------------------------------
% 0.15/0.40  % (28894)------------------------------
% 0.15/0.41  % (28890)Instruction limit reached!
% 0.15/0.41  % (28890)------------------------------
% 0.15/0.41  % (28890)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41  % (28890)Termination reason: Unknown
% 0.15/0.41  % (28890)Termination phase: Saturation
% 0.15/0.41  
% 0.15/0.41  % (28890)Memory used [KB]: 5756
% 0.15/0.41  % (28890)Time elapsed: 0.024 s
% 0.15/0.41  % (28890)Instructions burned: 28 (million)
% 0.15/0.41  % (28890)------------------------------
% 0.15/0.41  % (28890)------------------------------
% 0.15/0.41  % (28911)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.41  % (28914)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 Vampire---4 for (2999ds/15Mi)
% 0.15/0.41  % (28915)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.41  % (28916)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 Vampire---4 for (2999ds/1041Mi)
% 0.15/0.42  % (28915)Instruction limit reached!
% 0.15/0.42  % (28915)------------------------------
% 0.15/0.42  % (28915)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42  % (28915)Termination reason: Unknown
% 0.15/0.42  % (28915)Termination phase: Saturation
% 0.15/0.42  
% 0.15/0.42  % (28915)Memory used [KB]: 1023
% 0.15/0.42  % (28915)Time elapsed: 0.005 s
% 0.15/0.42  % (28915)Instructions burned: 3 (million)
% 0.15/0.42  % (28915)------------------------------
% 0.15/0.42  % (28915)------------------------------
% 0.15/0.43  % (28914)Instruction limit reached!
% 0.15/0.43  % (28914)------------------------------
% 0.15/0.43  % (28914)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43  % (28914)Termination reason: Unknown
% 0.15/0.43  % (28914)Termination phase: Saturation
% 0.15/0.43  
% 0.15/0.43  % (28914)Memory used [KB]: 5756
% 0.15/0.43  % (28914)Time elapsed: 0.016 s
% 0.15/0.43  % (28914)Instructions burned: 15 (million)
% 0.15/0.43  % (28914)------------------------------
% 0.15/0.43  % (28914)------------------------------
% 0.15/0.43  % (28917)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.43  % (28918)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.43  % (28917)Instruction limit reached!
% 0.22/0.43  % (28917)------------------------------
% 0.22/0.43  % (28917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43  % (28917)Termination reason: Unknown
% 0.22/0.43  % (28917)Termination phase: Saturation
% 0.22/0.43  
% 0.22/0.43  % (28917)Memory used [KB]: 1023
% 0.22/0.43  % (28917)Time elapsed: 0.009 s
% 0.22/0.43  % (28917)Instructions burned: 7 (million)
% 0.22/0.43  % (28917)------------------------------
% 0.22/0.43  % (28917)------------------------------
% 0.22/0.44  % (28911)Instruction limit reached!
% 0.22/0.44  % (28911)------------------------------
% 0.22/0.44  % (28911)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (28911)Termination reason: Unknown
% 0.22/0.44  % (28911)Termination phase: Saturation
% 0.22/0.44  
% 0.22/0.44  % (28911)Memory used [KB]: 5628
% 0.22/0.44  % (28911)Time elapsed: 0.033 s
% 0.22/0.44  % (28911)Instructions burned: 37 (million)
% 0.22/0.44  % (28911)------------------------------
% 0.22/0.44  % (28911)------------------------------
% 0.22/0.44  % (28919)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 Vampire---4 for (2999ds/3Mi)
% 0.22/0.44  % (28919)Instruction limit reached!
% 0.22/0.44  % (28919)------------------------------
% 0.22/0.44  % (28919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (28919)Termination reason: Unknown
% 0.22/0.44  % (28919)Termination phase: Preprocessing 3
% 0.22/0.44  
% 0.22/0.44  % (28919)Memory used [KB]: 1023
% 0.22/0.44  % (28919)Time elapsed: 0.005 s
% 0.22/0.44  % (28919)Instructions burned: 3 (million)
% 0.22/0.44  % (28919)------------------------------
% 0.22/0.44  % (28919)------------------------------
% 0.22/0.44  % (28918)Instruction limit reached!
% 0.22/0.44  % (28918)------------------------------
% 0.22/0.44  % (28918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (28918)Termination reason: Unknown
% 0.22/0.44  % (28918)Termination phase: Saturation
% 0.22/0.44  
% 0.22/0.44  % (28918)Memory used [KB]: 5756
% 0.22/0.44  % (28918)Time elapsed: 0.017 s
% 0.22/0.44  % (28918)Instructions burned: 16 (million)
% 0.22/0.44  % (28918)------------------------------
% 0.22/0.44  % (28918)------------------------------
% 0.22/0.45  % (28920)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 Vampire---4 for (2999ds/3Mi)
% 0.22/0.45  % (28920)Instruction limit reached!
% 0.22/0.45  % (28920)------------------------------
% 0.22/0.45  % (28920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45  % (28920)Termination reason: Unknown
% 0.22/0.45  % (28920)Termination phase: Preprocessing 3
% 0.22/0.45  
% 0.22/0.45  % (28920)Memory used [KB]: 1023
% 0.22/0.45  % (28920)Time elapsed: 0.005 s
% 0.22/0.45  % (28920)Instructions burned: 3 (million)
% 0.22/0.45  % (28920)------------------------------
% 0.22/0.45  % (28920)------------------------------
% 0.22/0.46  % (28921)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.46  % (28922)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.46  % (28922)Instruction limit reached!
% 0.22/0.46  % (28922)------------------------------
% 0.22/0.46  % (28922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46  % (28922)Termination reason: Unknown
% 0.22/0.46  % (28922)Termination phase: Saturation
% 0.22/0.46  
% 0.22/0.46  % (28922)Memory used [KB]: 5500
% 0.22/0.46  % (28922)Time elapsed: 0.005 s
% 0.22/0.46  % (28922)Instructions burned: 3 (million)
% 0.22/0.46  % (28922)------------------------------
% 0.22/0.46  % (28922)------------------------------
% 0.22/0.46  % (28921)Instruction limit reached!
% 0.22/0.46  % (28921)------------------------------
% 0.22/0.46  % (28921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46  % (28921)Termination reason: Unknown
% 0.22/0.46  % (28921)Termination phase: Saturation
% 0.22/0.46  
% 0.22/0.46  % (28921)Memory used [KB]: 5500
% 0.22/0.46  % (28921)Time elapsed: 0.009 s
% 0.22/0.46  % (28921)Instructions burned: 7 (million)
% 0.22/0.46  % (28921)------------------------------
% 0.22/0.46  % (28921)------------------------------
% 0.22/0.47  % (28924)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.47  % (28923)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.47  % (28923)Instruction limit reached!
% 0.22/0.47  % (28923)------------------------------
% 0.22/0.47  % (28923)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47  % (28923)Termination reason: Unknown
% 0.22/0.47  % (28923)Termination phase: Saturation
% 0.22/0.47  
% 0.22/0.47  % (28923)Memory used [KB]: 5500
% 0.22/0.47  % (28923)Time elapsed: 0.005 s
% 0.22/0.47  % (28923)Instructions burned: 4 (million)
% 0.22/0.47  % (28923)------------------------------
% 0.22/0.47  % (28923)------------------------------
% 0.22/0.47  % (28925)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.48  % (28924)Instruction limit reached!
% 0.22/0.48  % (28924)------------------------------
% 0.22/0.48  % (28924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48  % (28924)Termination reason: Unknown
% 0.22/0.48  % (28924)Termination phase: Saturation
% 0.22/0.48  
% 0.22/0.48  % (28924)Memory used [KB]: 5500
% 0.22/0.48  % (28924)Time elapsed: 0.015 s
% 0.22/0.48  % (28924)Instructions burned: 19 (million)
% 0.22/0.48  % (28924)------------------------------
% 0.22/0.48  % (28924)------------------------------
% 0.22/0.48  % (28926)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.49  % (28926)Instruction limit reached!
% 0.22/0.49  % (28926)------------------------------
% 0.22/0.49  % (28926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49  % (28926)Termination reason: Unknown
% 0.22/0.49  % (28926)Termination phase: Saturation
% 0.22/0.49  
% 0.22/0.49  % (28926)Memory used [KB]: 5500
% 0.22/0.49  % (28926)Time elapsed: 0.006 s
% 0.22/0.49  % (28926)Instructions burned: 7 (million)
% 0.22/0.49  % (28926)------------------------------
% 0.22/0.49  % (28926)------------------------------
% 0.22/0.49  % (28928)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 Vampire---4 for (2999ds/21Mi)
% 0.22/0.49  % (28927)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 Vampire---4 for (2999ds/902Mi)
% 0.22/0.50  % (28929)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2998ds/5Mi)
% 0.22/0.50  % (28929)Instruction limit reached!
% 0.22/0.50  % (28929)------------------------------
% 0.22/0.50  % (28929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50  % (28929)Termination reason: Unknown
% 0.22/0.50  % (28929)Termination phase: Saturation
% 0.22/0.50  
% 0.22/0.50  % (28929)Memory used [KB]: 5500
% 0.22/0.50  % (28929)Time elapsed: 0.005 s
% 0.22/0.50  % (28929)Instructions burned: 6 (million)
% 0.22/0.50  % (28929)------------------------------
% 0.22/0.50  % (28929)------------------------------
% 0.22/0.50  % (28928)Instruction limit reached!
% 0.22/0.50  % (28928)------------------------------
% 0.22/0.50  % (28928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50  % (28928)Termination reason: Unknown
% 0.22/0.50  % (28928)Termination phase: Saturation
% 0.22/0.50  
% 0.22/0.50  % (28928)Memory used [KB]: 5628
% 0.22/0.50  % (28928)Time elapsed: 0.015 s
% 0.22/0.50  % (28928)Instructions burned: 21 (million)
% 0.22/0.50  % (28928)------------------------------
% 0.22/0.50  % (28928)------------------------------
% 0.22/0.50  % (28930)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 Vampire---4 for (2998ds/6Mi)
% 0.22/0.51  % (28930)Instruction limit reached!
% 0.22/0.51  % (28930)------------------------------
% 0.22/0.51  % (28930)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51  % (28930)Termination reason: Unknown
% 0.22/0.51  % (28930)Termination phase: Saturation
% 0.22/0.51  
% 0.22/0.51  % (28930)Memory used [KB]: 5500
% 0.22/0.51  % (28930)Time elapsed: 0.005 s
% 0.22/0.51  % (28930)Instructions burned: 7 (million)
% 0.22/0.51  % (28930)------------------------------
% 0.22/0.51  % (28930)------------------------------
% 0.22/0.51  % (28888)Instruction limit reached!
% 0.22/0.51  % (28888)------------------------------
% 0.22/0.51  % (28888)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51  % (28888)Termination reason: Unknown
% 0.22/0.51  % (28888)Termination phase: Saturation
% 0.22/0.51  
% 0.22/0.51  % (28888)Memory used [KB]: 7675
% 0.22/0.51  % (28888)Time elapsed: 0.125 s
% 0.22/0.51  % (28888)Instructions burned: 184 (million)
% 0.22/0.51  % (28888)------------------------------
% 0.22/0.51  % (28888)------------------------------
% 0.22/0.51  % (28931)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2998ds/377Mi)
% 0.22/0.52  % (28932)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 Vampire---4 for (2998ds/779Mi)
% 0.22/0.52  % (28933)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 Vampire---4 for (2998ds/19Mi)
% 0.22/0.52  % (28934)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.22/0.53  % (28933)Instruction limit reached!
% 0.22/0.53  % (28933)------------------------------
% 0.22/0.53  % (28933)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53  % (28933)Termination reason: Unknown
% 0.22/0.53  % (28933)Termination phase: Saturation
% 0.22/0.53  
% 0.22/0.53  % (28933)Memory used [KB]: 5500
% 0.22/0.53  % (28933)Time elapsed: 0.010 s
% 0.22/0.53  % (28933)Instructions burned: 19 (million)
% 0.22/0.53  % (28933)------------------------------
% 0.22/0.53  % (28933)------------------------------
% 0.22/0.54  % (28916)First to succeed.
% 0.22/0.54  % (28935)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.22/0.55  % (28935)Instruction limit reached!
% 0.22/0.55  % (28935)------------------------------
% 0.22/0.55  % (28935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55  % (28935)Termination reason: Unknown
% 0.22/0.55  % (28935)Termination phase: Saturation
% 0.22/0.55  
% 0.22/0.55  % (28935)Memory used [KB]: 5756
% 0.22/0.55  % (28935)Time elapsed: 0.010 s
% 0.22/0.55  % (28935)Instructions burned: 19 (million)
% 0.22/0.55  % (28935)------------------------------
% 0.22/0.55  % (28935)------------------------------
% 0.22/0.55  % (28916)Refutation found. Thanks to Tanya!
% 0.22/0.55  % SZS status Theorem for Vampire---4
% 0.22/0.55  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.55  % (28916)------------------------------
% 0.22/0.55  % (28916)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55  % (28916)Termination reason: Refutation
% 0.22/0.55  
% 0.22/0.55  % (28916)Memory used [KB]: 6140
% 0.22/0.55  % (28916)Time elapsed: 0.138 s
% 0.22/0.55  % (28916)Instructions burned: 165 (million)
% 0.22/0.55  % (28916)------------------------------
% 0.22/0.55  % (28916)------------------------------
% 0.22/0.55  % (28885)Success in time 0.168 s
% 0.22/0.55  % Vampire---4.8 exiting
%------------------------------------------------------------------------------