TSTP Solution File: SEV141^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:12:07 EDT 2024

% Result   : Theorem 1.48s 0.59s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  287 (  16 unt;  46 typ;   0 def)
%            Number of atoms       : 2517 ( 229 equ;   0 cnn)
%            Maximal formula atoms :    4 (  10 avg)
%            Number of connectives : 8081 ( 349   ~; 437   |; 417   &;5074   @)
%                                         (  15 <=>; 652  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  677 ( 677   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   63 (  59 usr;  52 con; 0-2 aty)
%                                         (1137  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 1368 (1233   ^ 134   !;   0   ?;1368   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

thf(func_def_23,type,
    sK4: a ).

thf(func_def_24,type,
    sK5: a ).

thf(func_def_25,type,
    sK6: a > a > $o ).

thf(func_def_26,type,
    sK7: a ).

thf(func_def_27,type,
    sK8: a ).

thf(func_def_28,type,
    sK9: a > a > $o ).

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 ).

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 ).

thf(func_def_41,type,
    sK22: a ).

thf(func_def_42,type,
    sK23: a ).

thf(func_def_43,type,
    sK24: a ).

thf(func_def_44,type,
    sK25: a ).

thf(func_def_45,type,
    sK26: ( a > a > $o ) > a ).

thf(func_def_46,type,
    sK27: a ).

thf(func_def_47,type,
    sK28: a ).

thf(func_def_48,type,
    sK29: a ).

thf(func_def_49,type,
    sK30: a ).

thf(func_def_50,type,
    sK31: a ).

thf(func_def_51,type,
    sK32: a ).

thf(func_def_52,type,
    sK33: a ).

thf(func_def_53,type,
    sK34: a ).

thf(func_def_54,type,
    sK35: a ).

thf(func_def_55,type,
    sK36: a ).

thf(func_def_56,type,
    sK37: a ).

thf(func_def_57,type,
    sK38: a > a > $o ).

thf(func_def_58,type,
    sK39: a > a > $o ).

thf(func_def_59,type,
    sK40: a ).

thf(func_def_60,type,
    sK41: a ).

thf(func_def_61,type,
    sK42: a ).

thf(func_def_62,type,
    sK43: a ).

thf(func_def_63,type,
    sK44: a ).

thf(f1723,plain,
    $false,
    inference(avatar_sat_refutation,[],[f27,f34,f38,f101,f130,f345,f382,f452,f588,f633,f695,f817,f871,f875,f1312,f1356,f1722]) ).

thf(f1722,plain,
    ( ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(avatar_contradiction_clause,[],[f1721]) ).

thf(f1721,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(trivial_inequality_removal,[],[f1720]) ).

thf(f1720,plain,
    ( ( $false = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(forward_demodulation,[],[f1713,f1553]) ).

thf(f1553,plain,
    ( ( $false
      = ( sK10 @ sK8 @ sK7 ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1552]) ).

thf(f1552,plain,
    ( ( ( $true
       => ( sK10 @ sK8 @ sK7 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(backward_demodulation,[],[f1544,f1551]) ).

thf(f1551,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                 => ( sK10 @ Y0 @ Y1 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK10 @ Y2 @ Y0 )
                        & ( sK10 @ Y1 @ Y2 ) )
                     => ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f1544]) ).

thf(f1544,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y0 @ Y1 )
                   => ( sK10 @ Y0 @ Y1 ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK10 @ Y2 @ Y0 )
                          & ( sK10 @ Y1 @ Y2 ) )
                       => ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
       => ( sK10 @ sK8 @ sK7 ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f1542]) ).

thf(f1542,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK8 @ sK7 ) )
        @ sK10 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(sigma_clausification,[],[f1420]) ).

thf(f1420,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK8 @ sK7 ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f1407]) ).

thf(f1407,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y2 )
                                & ( Y0 @ Y1 @ Y3 ) )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK8 @ sK7 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y2 @ Y3 ) )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
             => ( Y0 @ sK8 @ sK7 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(not_proxy_clausification,[],[f1385]) ).

thf(f1385,plain,
    ( ( $true
      = ( ~ ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y2 )
                                    & ( Y0 @ Y1 @ Y3 ) )
                                 => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK3 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ sK8 @ sK7 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y1 )
                                    & ( Y0 @ Y2 @ Y3 ) )
                                 => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
                 => ( Y0 @ sK8 @ sK7 ) ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1376]) ).

thf(f1376,plain,
    ( ( $true
      = ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y2 )
                                  & ( Y0 @ Y1 @ Y3 ) )
                               => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK8 @ sK7 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y1 )
                                  & ( Y0 @ Y2 @ Y3 ) )
                               => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
               => ( Y0 @ sK8 @ sK7 ) ) ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(superposition,[],[f969,f1375]) ).

thf(f1375,plain,
    ( ( ( sK6 @ sK8 @ sK7 )
      = $false )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1374]) ).

thf(f1374,plain,
    ( ( ( $true
       => ( sK6 @ sK8 @ sK7 ) )
      = $false )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1373]) ).

thf(f1373,plain,
    ( ( $false
      = ( ( $true
          | ( sK3 @ sK8 @ sK7 ) )
       => ( sK6 @ sK8 @ sK7 ) ) )
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(forward_demodulation,[],[f1372,f129]) ).

thf(f129,plain,
    ( ( ( sK2 @ sK8 @ sK7 )
      = $true )
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f128]) ).

thf(f128,plain,
    ( spl0_8
  <=> ( ( sK2 @ sK8 @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

thf(f1372,plain,
    ( ( $false
      = ( ( ( sK2 @ sK8 @ sK7 )
          | ( sK3 @ sK8 @ sK7 ) )
       => ( sK6 @ sK8 @ sK7 ) ) )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f1371]) ).

thf(f1371,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK7 )
              | ( sK3 @ Y0 @ sK7 ) )
           => ( sK6 @ Y0 @ sK7 ) )
        @ sK8 ) )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f1366]) ).

thf(f1366,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK7 )
              | ( sK3 @ Y0 @ sK7 ) )
           => ( sK6 @ Y0 @ sK7 ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f1362]) ).

thf(f1362,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK6 @ Y1 @ Y0 ) ) )
        @ sK7 ) )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f97]) ).

thf(f97,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK6 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f96]) ).

thf(f96,plain,
    ( spl0_5
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK6 @ Y1 @ Y0 ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f969,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y2 )
                                    & ( Y0 @ Y1 @ Y3 ) )
                                 => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK3 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ X2 @ X1 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y1 )
                                    & ( Y0 @ Y2 @ Y3 ) )
                                 => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
                 => ( Y0 @ X2 @ X1 ) ) ) )
         => ( sK6 @ X2 @ X1 ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f968]) ).

thf(f968,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y4 @ Y3 )
                                        & ( Y1 @ Y2 @ Y4 ) )
                                     => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK3 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y4 @ Y2 )
                                        & ( Y1 @ Y3 @ Y4 ) )
                                     => ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) ) )
             => ( sK6 @ Y0 @ X1 ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f958]) ).

thf(f958,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y4 @ Y3 )
                                        & ( Y1 @ Y2 @ Y4 ) )
                                     => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK3 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) )
                | ( !! @ ( a > a > $o )
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( sK2 @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) )
                        & ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y4 @ Y2 )
                                        & ( Y1 @ Y3 @ Y4 ) )
                                     => ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
                     => ( Y1 @ Y0 @ X1 ) ) ) )
             => ( sK6 @ Y0 @ X1 ) ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f957]) ).

thf(f957,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y4 )
                                            & ( Y2 @ Y3 @ Y5 ) )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y3 )
                                            & ( Y2 @ Y4 @ Y5 ) )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK6 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f905]) ).

thf(f905,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y4 )
                                          & ( Y2 @ Y3 @ Y5 ) )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y3 )
                                          & ( Y2 @ Y4 @ Y5 ) )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK6 @ Y1 @ Y0 ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f896]) ).

thf(f896,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y4 )
                                            & ( Y2 @ Y3 @ Y5 ) )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y3 )
                                            & ( Y2 @ Y4 @ Y5 ) )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK6 @ Y1 @ Y0 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK6 @ Y2 @ Y0 )
                        & ( sK6 @ Y1 @ Y2 ) )
                     => ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f892]) ).

thf(f892,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y4 )
                                              & ( Y2 @ Y3 @ Y5 ) )
                                           => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y3 )
                                              & ( Y2 @ Y4 @ Y5 ) )
                                           => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK6 @ Y1 @ Y0 ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK6 @ Y2 @ Y0 )
                          & ( sK6 @ Y1 @ Y2 ) )
                       => ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
       => ( sK6 @ sK4 @ sK5 ) )
      = $false )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f891]) ).

thf(f891,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) )
        @ sK6 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f30]) ).

thf(f30,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f29]) ).

thf(f29,plain,
    ( spl0_3
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f1713,plain,
    ( ( ( sK10 @ sK8 @ sK7 )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1709]) ).

thf(f1709,plain,
    ( ( ( $true
       => ( sK10 @ sK8 @ sK7 ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(superposition,[],[f1703,f129]) ).

thf(f1703,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( sK2 @ X1 @ X2 )
         => ( sK10 @ X1 @ X2 ) ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f1702]) ).

thf(f1702,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK2 @ X1 @ Y0 )
             => ( sK10 @ X1 @ Y0 ) )
          @ X2 ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(pi_clausification,[],[f1699]) ).

thf(f1699,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ X1 @ Y0 )
             => ( sK10 @ X1 @ Y0 ) ) )
        = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(beta_eta_normalization,[],[f1698]) ).

thf(f1698,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                 => ( sK10 @ Y0 @ Y1 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(pi_clausification,[],[f1695]) ).

thf(f1695,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK10 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(boolean_simplification,[],[f1694]) ).

thf(f1694,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                 => ( sK10 @ Y0 @ Y1 ) ) ) )
        & $true ) )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(backward_demodulation,[],[f1551,f1692]) ).

thf(f1692,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK10 @ Y2 @ Y0 )
                      & ( sK10 @ Y1 @ Y2 ) )
                   => ( sK10 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_8 ),
    inference(binary_proxy_clausification,[],[f1551]) ).

thf(f1356,plain,
    ( ~ spl0_3
    | ~ spl0_6 ),
    inference(avatar_contradiction_clause,[],[f1355]) ).

thf(f1355,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f1352]) ).

thf(f1352,plain,
    ( ( $false = $true )
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(superposition,[],[f923,f1345]) ).

thf(f1345,plain,
    ( ( $false
      = ( ( ( sK6 @ sK40 @ sK41 )
          & ( sK6 @ sK42 @ sK40 ) )
       => ( sK6 @ sK42 @ sK41 ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f1344]) ).

thf(f1344,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK6 @ sK40 @ sK41 )
              & ( sK6 @ Y0 @ sK40 ) )
           => ( sK6 @ Y0 @ sK41 ) )
        @ sK42 ) )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f1341]) ).

thf(f1341,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK6 @ sK40 @ sK41 )
              & ( sK6 @ Y0 @ sK40 ) )
           => ( sK6 @ Y0 @ sK41 ) ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f1340]) ).

thf(f1340,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK6 @ sK40 @ Y0 )
                  & ( sK6 @ Y1 @ sK40 ) )
               => ( sK6 @ Y1 @ Y0 ) ) )
        @ sK41 )
      = $false )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f1334]) ).

thf(f1334,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK6 @ sK40 @ Y0 )
                  & ( sK6 @ Y1 @ sK40 ) )
               => ( sK6 @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f1332]) ).

thf(f1332,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK6 @ Y0 @ Y1 )
                      & ( sK6 @ Y2 @ Y0 ) )
                   => ( sK6 @ Y2 @ Y1 ) ) ) )
        @ sK40 ) )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f100]) ).

thf(f100,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK6 @ Y0 @ Y1 )
                      & ( sK6 @ Y2 @ Y0 ) )
                   => ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f99]) ).

thf(f99,plain,
    ( spl0_6
  <=> ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK6 @ Y0 @ Y1 )
                      & ( sK6 @ Y2 @ Y0 ) )
                   => ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f923,plain,
    ( ! [X2: a,X3: a,X1: a] :
        ( ( ( ( sK6 @ X3 @ X1 )
            & ( sK6 @ X2 @ X3 ) )
         => ( sK6 @ X2 @ X1 ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f922]) ).

thf(f922,plain,
    ( ! [X2: a,X3: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( ( sK6 @ Y0 @ X1 )
                & ( sK6 @ X2 @ Y0 ) )
             => ( sK6 @ X2 @ X1 ) )
          @ X3 ) )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f917]) ).

thf(f917,plain,
    ( ! [X2: a,X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK6 @ Y0 @ X1 )
                & ( sK6 @ X2 @ Y0 ) )
             => ( sK6 @ X2 @ X1 ) ) )
        = $true )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f916]) ).

thf(f916,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK6 @ Y1 @ X1 )
                    & ( sK6 @ Y0 @ Y1 ) )
                 => ( sK6 @ Y0 @ X1 ) ) )
          @ X2 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f915]) ).

thf(f915,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK6 @ Y1 @ X1 )
                    & ( sK6 @ Y0 @ Y1 ) )
                 => ( sK6 @ Y0 @ X1 ) ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f914]) ).

thf(f914,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK6 @ Y2 @ Y0 )
                        & ( sK6 @ Y1 @ Y2 ) )
                     => ( sK6 @ Y1 @ Y0 ) ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3 ),
    inference(pi_clausification,[],[f907]) ).

thf(f907,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK6 @ Y2 @ Y0 )
                      & ( sK6 @ Y1 @ Y2 ) )
                   => ( sK6 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f906]) ).

thf(f906,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK6 @ Y2 @ Y0 )
                        & ( sK6 @ Y1 @ Y2 ) )
                     => ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
      = $true )
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f896,f905]) ).

thf(f1312,plain,
    ( ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(avatar_contradiction_clause,[],[f1311]) ).

thf(f1311,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(trivial_inequality_removal,[],[f1310]) ).

thf(f1310,plain,
    ( ( $false = $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(boolean_simplification,[],[f1309]) ).

thf(f1309,plain,
    ( ( $true = ~ $true )
    | ~ spl0_3
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f1304,f126]) ).

thf(f126,plain,
    ( ( ( sK3 @ sK8 @ sK7 )
      = $true )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f125]) ).

thf(f125,plain,
    ( spl0_7
  <=> ( ( sK3 @ sK8 @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

thf(f1304,plain,
    ( ( ( ~ ( sK3 @ sK8 @ sK7 ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f1282]) ).

thf(f1282,plain,
    ( ( ( ( sK3 @ sK8 @ sK7 )
       => $false )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f1272,f1196]) ).

thf(f1196,plain,
    ( ( ( sK38 @ sK8 @ sK7 )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f1195]) ).

thf(f1195,plain,
    ( ( $false
      = ( $true
       => ( sK38 @ sK8 @ sK7 ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f1182,f1194]) ).

thf(f1194,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK38 @ Y2 @ Y1 )
                        & ( sK38 @ Y0 @ Y2 ) )
                     => ( sK38 @ Y0 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK38 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f1182]) ).

thf(f1182,plain,
    ( ( $false
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK38 @ Y2 @ Y1 )
                          & ( sK38 @ Y0 @ Y2 ) )
                       => ( sK38 @ Y0 @ Y1 ) ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y0 @ Y1 )
                   => ( sK38 @ Y0 @ Y1 ) ) ) ) )
       => ( sK38 @ sK8 @ sK7 ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f1179]) ).

thf(f1179,plain,
    ( ( $false
      = ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y2 )
                              & ( Y0 @ Y1 @ Y3 ) )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK8 @ sK7 ) )
        @ sK38 ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f1007]) ).

thf(f1007,plain,
    ( ( $false
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y2 )
                              & ( Y0 @ Y1 @ Y3 ) )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK8 @ sK7 ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f982]) ).

thf(f982,plain,
    ( ( ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y2 )
                                & ( Y0 @ Y1 @ Y3 ) )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK8 @ sK7 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y2 @ Y3 ) )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
             => ( Y0 @ sK8 @ sK7 ) ) ) )
      = $false )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(not_proxy_clausification,[],[f980]) ).

thf(f980,plain,
    ( ( $true
      = ( ~ ( ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y2 )
                                    & ( Y0 @ Y1 @ Y3 ) )
                                 => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK3 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ sK8 @ sK7 ) ) )
            | ( !! @ ( a > a > $o )
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( ( sK2 @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( !! @ a
                          @ ^ [Y2: a] :
                              ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y3 @ Y1 )
                                    & ( Y0 @ Y2 @ Y3 ) )
                                 => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
                 => ( Y0 @ sK8 @ sK7 ) ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f979]) ).

thf(f979,plain,
    ( ( $true
      = ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y2 )
                                  & ( Y0 @ Y1 @ Y3 ) )
                               => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK8 @ sK7 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y1 )
                                  & ( Y0 @ Y2 @ Y3 ) )
                               => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
               => ( Y0 @ sK8 @ sK7 ) ) ) )
       => $false ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f969,f114]) ).

thf(f114,plain,
    ( ( ( sK6 @ sK8 @ sK7 )
      = $false )
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f113]) ).

thf(f113,plain,
    ( ( ( $true
       => ( sK6 @ sK8 @ sK7 ) )
      = $false )
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f110,f112]) ).

thf(f112,plain,
    ( ( ( ( sK2 @ sK8 @ sK7 )
        | ( sK3 @ sK8 @ sK7 ) )
      = $true )
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f110]) ).

thf(f110,plain,
    ( ( $false
      = ( ( ( sK2 @ sK8 @ sK7 )
          | ( sK3 @ sK8 @ sK7 ) )
       => ( sK6 @ sK8 @ sK7 ) ) )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f109]) ).

thf(f109,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK7 )
              | ( sK3 @ Y0 @ sK7 ) )
           => ( sK6 @ Y0 @ sK7 ) )
        @ sK8 ) )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f108]) ).

thf(f108,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ sK7 )
              | ( sK3 @ Y0 @ sK7 ) )
           => ( sK6 @ Y0 @ sK7 ) ) )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f104]) ).

thf(f104,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK6 @ Y1 @ Y0 ) ) )
        @ sK7 ) )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f97]) ).

thf(f1272,plain,
    ( ! [X2: a,X1: a] :
        ( ( ( sK3 @ X1 @ X2 )
         => ( sK38 @ X1 @ X2 ) )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f1271]) ).

thf(f1271,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK38 @ X1 @ Y0 ) )
          @ X2 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(pi_clausification,[],[f1262]) ).

thf(f1262,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK3 @ X1 @ Y0 )
             => ( sK38 @ X1 @ Y0 ) ) )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f1261]) ).

thf(f1261,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK38 @ Y0 @ Y1 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(pi_clausification,[],[f1252]) ).

thf(f1252,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK38 @ Y0 @ Y1 ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(boolean_simplification,[],[f1251]) ).

thf(f1251,plain,
    ( ( $true
      = ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK38 @ Y0 @ Y1 ) ) ) ) ) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(backward_demodulation,[],[f1194,f1250]) ).

thf(f1250,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK38 @ Y2 @ Y1 )
                      & ( sK38 @ Y0 @ Y2 ) )
                   => ( sK38 @ Y0 @ Y1 ) ) ) ) )
      = $true )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f1194]) ).

thf(f875,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f874]) ).

thf(f874,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f873]) ).

thf(f873,plain,
    ( ( $false = $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f23,f33]) ).

thf(f33,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f32]) ).

thf(f32,plain,
    ( spl0_4
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f23,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $true )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f22]) ).

thf(f22,plain,
    ( spl0_1
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f871,plain,
    ( ~ spl0_4
    | ~ spl0_27 ),
    inference(avatar_contradiction_clause,[],[f870]) ).

thf(f870,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(trivial_inequality_removal,[],[f869]) ).

thf(f869,plain,
    ( ( $false = $true )
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(boolean_simplification,[],[f868]) ).

thf(f868,plain,
    ( ( $true = ~ $true )
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(boolean_simplification,[],[f867]) ).

thf(f867,plain,
    ( ( ( ~ ( $true
            | ( sK3 @ sK33 @ sK34 ) ) )
      = $true )
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(forward_demodulation,[],[f865,f844]) ).

thf(f844,plain,
    ( ( ( sK2 @ sK33 @ sK34 )
      = $true )
    | ~ spl0_27 ),
    inference(binary_proxy_clausification,[],[f842]) ).

thf(f842,plain,
    ( ( $false
      = ( ( sK2 @ sK33 @ sK34 )
       => ( sK11 @ sK33 @ sK34 ) ) )
    | ~ spl0_27 ),
    inference(beta_eta_normalization,[],[f841]) ).

thf(f841,plain,
    ( ( ( ^ [Y0: a] :
            ( ( sK2 @ sK33 @ Y0 )
           => ( sK11 @ sK33 @ Y0 ) )
        @ sK34 )
      = $false )
    | ~ spl0_27 ),
    inference(sigma_clausification,[],[f832]) ).

thf(f832,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK33 @ Y0 )
           => ( sK11 @ sK33 @ Y0 ) ) )
      = $false )
    | ~ spl0_27 ),
    inference(beta_eta_normalization,[],[f828]) ).

thf(f828,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) )
        @ sK33 ) )
    | ~ spl0_27 ),
    inference(sigma_clausification,[],[f816]) ).

thf(f816,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) )
      = $false )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f815]) ).

thf(f815,plain,
    ( spl0_27
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

thf(f865,plain,
    ( ( ( ~ ( ( sK2 @ sK33 @ sK34 )
            | ( sK3 @ sK33 @ sK34 ) ) )
      = $true )
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(boolean_simplification,[],[f860]) ).

thf(f860,plain,
    ( ( $true
      = ( ( ( sK2 @ sK33 @ sK34 )
          | ( sK3 @ sK33 @ sK34 ) )
       => $false ) )
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(superposition,[],[f271,f843]) ).

thf(f843,plain,
    ( ( ( sK11 @ sK33 @ sK34 )
      = $false )
    | ~ spl0_27 ),
    inference(binary_proxy_clausification,[],[f842]) ).

thf(f271,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ( ( sK2 @ X2 @ X1 )
            | ( sK3 @ X2 @ X1 ) )
         => ( sK11 @ X2 @ X1 ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f270]) ).

thf(f270,plain,
    ( ! [X2: a,X1: a] :
        ( ( ^ [Y0: a] :
              ( ( ( sK2 @ Y0 @ X1 )
                | ( sK3 @ Y0 @ X1 ) )
             => ( sK11 @ Y0 @ X1 ) )
          @ X2 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f269]) ).

thf(f269,plain,
    ( ! [X1: a] :
        ( $true
        = ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK2 @ Y0 @ X1 )
                | ( sK3 @ Y0 @ X1 ) )
             => ( sK11 @ Y0 @ X1 ) ) ) )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f268]) ).

thf(f268,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK3 @ Y1 @ Y0 ) )
                 => ( sK11 @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f264]) ).

thf(f264,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK11 @ Y1 @ Y0 ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f263]) ).

thf(f263,plain,
    ( ( ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK3 @ Y1 @ Y0 ) )
                 => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f254,f262]) ).

thf(f262,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y0 @ Y1 )
                      & ( sK11 @ Y2 @ Y0 ) )
                   => ( sK11 @ Y2 @ Y1 ) ) ) ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f254]) ).

thf(f254,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK11 @ Y0 @ Y1 )
                        & ( sK11 @ Y2 @ Y0 ) )
                     => ( sK11 @ Y2 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK3 @ Y1 @ Y0 ) )
                 => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $true )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f252]) ).

thf(f252,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK11 @ Y0 @ Y1 )
                          & ( sK11 @ Y2 @ Y0 ) )
                       => ( sK11 @ Y2 @ Y1 ) ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK2 @ Y1 @ Y0 )
                      | ( sK3 @ Y1 @ Y0 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) ) )
       => ( sK11 @ sK4 @ sK5 ) )
      = $false )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f251]) ).

thf(f251,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) )
        @ sK11 )
      = $false )
    | ~ spl0_4 ),
    inference(sigma_clausification,[],[f33]) ).

thf(f817,plain,
    ( spl0_27
    | spl0_12
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f811,f450,f340,f343,f815]) ).

thf(f343,plain,
    ( spl0_12
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y0 )
                      & ( sK11 @ Y1 @ Y2 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

thf(f340,plain,
    ( spl0_11
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y4 )
                                          & ( Y2 @ Y3 @ Y5 ) )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y3 )
                                          & ( Y2 @ Y4 @ Y5 ) )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK11 @ Y1 @ Y0 ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

thf(f450,plain,
    ( spl0_14
  <=> ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

thf(f811,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y0 )
                      & ( sK11 @ Y1 @ Y2 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $false )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) )
      = $false )
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(binary_proxy_clausification,[],[f805]) ).

thf(f805,plain,
    ( ( $false
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                 => ( sK11 @ Y0 @ Y1 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK11 @ Y2 @ Y0 )
                        & ( sK11 @ Y1 @ Y2 ) )
                     => ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(not_proxy_clausification,[],[f781]) ).

thf(f781,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK2 @ Y0 @ Y1 )
                     => ( sK11 @ Y0 @ Y1 ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK11 @ Y2 @ Y0 )
                            & ( sK11 @ Y1 @ Y2 ) )
                         => ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
      = $true )
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(boolean_simplification,[],[f777]) ).

thf(f777,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y0 @ Y1 )
                   => ( sK11 @ Y0 @ Y1 ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK11 @ Y2 @ Y0 )
                          & ( sK11 @ Y1 @ Y2 ) )
                       => ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
       => $false )
      = $true )
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(superposition,[],[f767,f401]) ).

thf(f401,plain,
    ( ( ( sK11 @ sK16 @ sK15 )
      = $false )
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f400]) ).

thf(f400,plain,
    ( ( $false
      = ( $true
       => ( sK11 @ sK16 @ sK15 ) ) )
    | ~ spl0_11 ),
    inference(backward_demodulation,[],[f397,f399]) ).

thf(f399,plain,
    ( ( $true
      = ( ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y2 )
                                & ( Y0 @ Y1 @ Y3 ) )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK16 @ sK15 ) ) )
        | ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y2 @ Y3 ) )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
             => ( Y0 @ sK16 @ sK15 ) ) ) ) )
    | ~ spl0_11 ),
    inference(binary_proxy_clausification,[],[f397]) ).

thf(f397,plain,
    ( ( ( ( ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y2 )
                                  & ( Y0 @ Y1 @ Y3 ) )
                               => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK3 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ sK16 @ sK15 ) ) )
          | ( !! @ ( a > a > $o )
            @ ^ [Y0: a > a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) )
                  & ( !! @ a
                    @ ^ [Y1: a] :
                        ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y3 @ Y1 )
                                  & ( Y0 @ Y2 @ Y3 ) )
                               => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
               => ( Y0 @ sK16 @ sK15 ) ) ) )
       => ( sK11 @ sK16 @ sK15 ) )
      = $false )
    | ~ spl0_11 ),
    inference(beta_eta_normalization,[],[f396]) ).

thf(f396,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y4 @ Y3 )
                                      & ( Y1 @ Y2 @ Y4 ) )
                                   => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK15 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y4 @ Y2 )
                                      & ( Y1 @ Y3 @ Y4 ) )
                                   => ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
                   => ( Y1 @ Y0 @ sK15 ) ) ) )
           => ( sK11 @ Y0 @ sK15 ) )
        @ sK16 )
      = $false )
    | ~ spl0_11 ),
    inference(sigma_clausification,[],[f394]) ).

thf(f394,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y4 @ Y3 )
                                      & ( Y1 @ Y2 @ Y4 ) )
                                   => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK3 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ Y0 @ sK15 ) ) )
              | ( !! @ ( a > a > $o )
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y4 @ Y2 )
                                      & ( Y1 @ Y3 @ Y4 ) )
                                   => ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
                   => ( Y1 @ Y0 @ sK15 ) ) ) )
           => ( sK11 @ Y0 @ sK15 ) ) )
      = $false )
    | ~ spl0_11 ),
    inference(beta_eta_normalization,[],[f389]) ).

thf(f389,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y4 )
                                          & ( Y2 @ Y3 @ Y5 ) )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y3 )
                                          & ( Y2 @ Y4 @ Y5 ) )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK11 @ Y1 @ Y0 ) ) )
        @ sK15 ) )
    | ~ spl0_11 ),
    inference(sigma_clausification,[],[f341]) ).

thf(f341,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y4 )
                                          & ( Y2 @ Y3 @ Y5 ) )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y3 )
                                          & ( Y2 @ Y4 @ Y5 ) )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK11 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f340]) ).

thf(f767,plain,
    ( ! [X1: a > a > $o] :
        ( ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK2 @ Y0 @ Y1 )
                     => ( X1 @ Y0 @ Y1 ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( X1 @ Y2 @ Y0 )
                            & ( X1 @ Y1 @ Y2 ) )
                         => ( X1 @ Y1 @ Y0 ) ) ) ) ) )
         => ( X1 @ sK16 @ sK15 ) )
        = $true )
    | ~ spl0_14 ),
    inference(beta_eta_normalization,[],[f766]) ).

thf(f766,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y2 @ Y3 ) )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
             => ( Y0 @ sK16 @ sK15 ) )
          @ X1 )
        = $true )
    | ~ spl0_14 ),
    inference(pi_clausification,[],[f451]) ).

thf(f451,plain,
    ( ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) ) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f450]) ).

thf(f695,plain,
    ( ~ spl0_4
    | ~ spl0_21 ),
    inference(avatar_contradiction_clause,[],[f694]) ).

thf(f694,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(trivial_inequality_removal,[],[f693]) ).

thf(f693,plain,
    ( ( $false = $true )
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(boolean_simplification,[],[f692]) ).

thf(f692,plain,
    ( ( $true = ~ $true )
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(boolean_simplification,[],[f691]) ).

thf(f691,plain,
    ( ( ( ~ ( ( sK2 @ sK27 @ sK28 )
            | $true ) )
      = $true )
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f690,f666]) ).

thf(f666,plain,
    ( ( ( sK3 @ sK27 @ sK28 )
      = $true )
    | ~ spl0_21 ),
    inference(binary_proxy_clausification,[],[f664]) ).

thf(f664,plain,
    ( ( $false
      = ( ( sK3 @ sK27 @ sK28 )
       => ( sK11 @ sK27 @ sK28 ) ) )
    | ~ spl0_21 ),
    inference(beta_eta_normalization,[],[f663]) ).

thf(f663,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( sK3 @ sK27 @ Y0 )
           => ( sK11 @ sK27 @ Y0 ) )
        @ sK28 ) )
    | ~ spl0_21 ),
    inference(sigma_clausification,[],[f654]) ).

thf(f654,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK3 @ sK27 @ Y0 )
           => ( sK11 @ sK27 @ Y0 ) ) ) )
    | ~ spl0_21 ),
    inference(beta_eta_normalization,[],[f650]) ).

thf(f650,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) )
        @ sK27 ) )
    | ~ spl0_21 ),
    inference(sigma_clausification,[],[f584]) ).

thf(f584,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) ) )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f583]) ).

thf(f583,plain,
    ( spl0_21
  <=> ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

thf(f690,plain,
    ( ( $true
      = ( ~ ( ( sK2 @ sK27 @ sK28 )
            | ( sK3 @ sK27 @ sK28 ) ) ) )
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(boolean_simplification,[],[f684]) ).

thf(f684,plain,
    ( ( ( ( ( sK2 @ sK27 @ sK28 )
          | ( sK3 @ sK27 @ sK28 ) )
       => $false )
      = $true )
    | ~ spl0_4
    | ~ spl0_21 ),
    inference(superposition,[],[f271,f665]) ).

thf(f665,plain,
    ( ( ( sK11 @ sK27 @ sK28 )
      = $false )
    | ~ spl0_21 ),
    inference(binary_proxy_clausification,[],[f664]) ).

thf(f633,plain,
    ( ~ spl0_4
    | ~ spl0_22 ),
    inference(avatar_contradiction_clause,[],[f632]) ).

thf(f632,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_22 ),
    inference(trivial_inequality_removal,[],[f629]) ).

thf(f629,plain,
    ( ( $false = $true )
    | ~ spl0_4
    | ~ spl0_22 ),
    inference(superposition,[],[f309,f614]) ).

thf(f614,plain,
    ( ( ( ( ( sK11 @ sK25 @ sK24 )
          & ( sK11 @ sK23 @ sK25 ) )
       => ( sK11 @ sK23 @ sK24 ) )
      = $false )
    | ~ spl0_22 ),
    inference(beta_eta_normalization,[],[f613]) ).

thf(f613,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( sK11 @ Y0 @ sK24 )
              & ( sK11 @ sK23 @ Y0 ) )
           => ( sK11 @ sK23 @ sK24 ) )
        @ sK25 )
      = $false )
    | ~ spl0_22 ),
    inference(sigma_clausification,[],[f609]) ).

thf(f609,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK11 @ Y0 @ sK24 )
              & ( sK11 @ sK23 @ Y0 ) )
           => ( sK11 @ sK23 @ sK24 ) ) ) )
    | ~ spl0_22 ),
    inference(beta_eta_normalization,[],[f608]) ).

thf(f608,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK11 @ Y1 @ Y0 )
                  & ( sK11 @ sK23 @ Y1 ) )
               => ( sK11 @ sK23 @ Y0 ) ) )
        @ sK24 )
      = $false )
    | ~ spl0_22 ),
    inference(sigma_clausification,[],[f603]) ).

thf(f603,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK11 @ Y1 @ Y0 )
                  & ( sK11 @ sK23 @ Y1 ) )
               => ( sK11 @ sK23 @ Y0 ) ) ) ) )
    | ~ spl0_22 ),
    inference(beta_eta_normalization,[],[f599]) ).

thf(f599,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y1 )
                      & ( sK11 @ Y0 @ Y2 ) )
                   => ( sK11 @ Y0 @ Y1 ) ) ) )
        @ sK23 )
      = $false )
    | ~ spl0_22 ),
    inference(sigma_clausification,[],[f587]) ).

thf(f587,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y1 )
                      & ( sK11 @ Y0 @ Y2 ) )
                   => ( sK11 @ Y0 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f586]) ).

thf(f586,plain,
    ( spl0_22
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y1 )
                      & ( sK11 @ Y0 @ Y2 ) )
                   => ( sK11 @ Y0 @ Y1 ) ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

thf(f309,plain,
    ( ! [X2: a,X3: a,X1: a] :
        ( ( ( ( sK11 @ X1 @ X2 )
            & ( sK11 @ X3 @ X1 ) )
         => ( sK11 @ X3 @ X2 ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f308]) ).

thf(f308,plain,
    ( ! [X2: a,X3: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( ( sK11 @ X1 @ X2 )
                & ( sK11 @ Y0 @ X1 ) )
             => ( sK11 @ Y0 @ X2 ) )
          @ X3 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f307]) ).

thf(f307,plain,
    ( ! [X2: a,X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( ( sK11 @ X1 @ X2 )
                & ( sK11 @ Y0 @ X1 ) )
             => ( sK11 @ Y0 @ X2 ) ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f306]) ).

thf(f306,plain,
    ( ! [X2: a,X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK11 @ X1 @ Y0 )
                    & ( sK11 @ Y1 @ X1 ) )
                 => ( sK11 @ Y1 @ Y0 ) ) )
          @ X2 ) )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f299]) ).

thf(f299,plain,
    ( ! [X1: a] :
        ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK11 @ X1 @ Y0 )
                    & ( sK11 @ Y1 @ X1 ) )
                 => ( sK11 @ Y1 @ Y0 ) ) ) )
        = $true )
    | ~ spl0_4 ),
    inference(beta_eta_normalization,[],[f298]) ).

thf(f298,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK11 @ Y0 @ Y1 )
                        & ( sK11 @ Y2 @ Y0 ) )
                     => ( sK11 @ Y2 @ Y1 ) ) ) )
          @ X1 )
        = $true )
    | ~ spl0_4 ),
    inference(pi_clausification,[],[f262]) ).

thf(f588,plain,
    ( spl0_21
    | spl0_22
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f579,f447,f340,f586,f583]) ).

thf(f447,plain,
    ( spl0_13
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y2 )
                              & ( Y0 @ Y1 @ Y3 ) )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

thf(f579,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK3 @ Y0 @ Y1 )
               => ( sK11 @ Y0 @ Y1 ) ) ) ) )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y1 )
                      & ( sK11 @ Y0 @ Y2 ) )
                   => ( sK11 @ Y0 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(binary_proxy_clausification,[],[f568]) ).

thf(f568,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK11 @ Y2 @ Y1 )
                        & ( sK11 @ Y0 @ Y2 ) )
                     => ( sK11 @ Y0 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK3 @ Y0 @ Y1 )
                 => ( sK11 @ Y0 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(not_proxy_clausification,[],[f463]) ).

thf(f463,plain,
    ( ( $true
      = ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK11 @ Y2 @ Y1 )
                            & ( sK11 @ Y0 @ Y2 ) )
                         => ( sK11 @ Y0 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK3 @ Y0 @ Y1 )
                     => ( sK11 @ Y0 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(boolean_simplification,[],[f458]) ).

thf(f458,plain,
    ( ( $true
      = ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK11 @ Y2 @ Y1 )
                          & ( sK11 @ Y0 @ Y2 ) )
                       => ( sK11 @ Y0 @ Y1 ) ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK3 @ Y0 @ Y1 )
                   => ( sK11 @ Y0 @ Y1 ) ) ) ) )
       => $false ) )
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(superposition,[],[f456,f401]) ).

thf(f456,plain,
    ( ! [X1: a > a > $o] :
        ( ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( X1 @ Y2 @ Y1 )
                            & ( X1 @ Y0 @ Y2 ) )
                         => ( X1 @ Y0 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK3 @ Y0 @ Y1 )
                     => ( X1 @ Y0 @ Y1 ) ) ) ) )
         => ( X1 @ sK16 @ sK15 ) )
        = $true )
    | ~ spl0_13 ),
    inference(beta_eta_normalization,[],[f455]) ).

thf(f455,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y2 )
                                & ( Y0 @ Y1 @ Y3 ) )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK3 @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ sK16 @ sK15 ) )
          @ X1 ) )
    | ~ spl0_13 ),
    inference(pi_clausification,[],[f448]) ).

thf(f448,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y2 )
                              & ( Y0 @ Y1 @ Y3 ) )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) )
      = $true )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f447]) ).

thf(f452,plain,
    ( spl0_13
    | spl0_14
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f445,f340,f450,f447]) ).

thf(f445,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y2 )
                              & ( Y0 @ Y1 @ Y3 ) )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK3 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) )
      = $true )
    | ( $true
      = ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK16 @ sK15 ) ) ) )
    | ~ spl0_11 ),
    inference(binary_proxy_clausification,[],[f399]) ).

thf(f382,plain,
    ( ~ spl0_4
    | ~ spl0_12 ),
    inference(avatar_contradiction_clause,[],[f381]) ).

thf(f381,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(trivial_inequality_removal,[],[f377]) ).

thf(f377,plain,
    ( ( $false = $true )
    | ~ spl0_4
    | ~ spl0_12 ),
    inference(superposition,[],[f374,f309]) ).

thf(f374,plain,
    ( ( $false
      = ( ( ( sK11 @ sK14 @ sK12 )
          & ( sK11 @ sK13 @ sK14 ) )
       => ( sK11 @ sK13 @ sK12 ) ) )
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f373]) ).

thf(f373,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( sK11 @ Y0 @ sK12 )
              & ( sK11 @ sK13 @ Y0 ) )
           => ( sK11 @ sK13 @ sK12 ) )
        @ sK14 )
      = $false )
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f372]) ).

thf(f372,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK11 @ Y0 @ sK12 )
              & ( sK11 @ sK13 @ Y0 ) )
           => ( sK11 @ sK13 @ sK12 ) ) ) )
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f371]) ).

thf(f371,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK11 @ Y1 @ sK12 )
                  & ( sK11 @ Y0 @ Y1 ) )
               => ( sK11 @ Y0 @ sK12 ) ) )
        @ sK13 ) )
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f361]) ).

thf(f361,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK11 @ Y1 @ sK12 )
                  & ( sK11 @ Y0 @ Y1 ) )
               => ( sK11 @ Y0 @ sK12 ) ) ) )
      = $false )
    | ~ spl0_12 ),
    inference(beta_eta_normalization,[],[f357]) ).

thf(f357,plain,
    ( ( ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y0 )
                      & ( sK11 @ Y1 @ Y2 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) )
        @ sK12 )
      = $false )
    | ~ spl0_12 ),
    inference(sigma_clausification,[],[f344]) ).

thf(f344,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y0 )
                      & ( sK11 @ Y1 @ Y2 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $false )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f343]) ).

thf(f345,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f336,f32,f25,f343,f340]) ).

thf(f25,plain,
    ( spl0_2
  <=> ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f336,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK11 @ Y2 @ Y0 )
                      & ( sK11 @ Y1 @ Y2 ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) ) )
      = $false )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y4 )
                                          & ( Y2 @ Y3 @ Y5 ) )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK3 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                  | ( !! @ ( a > a > $o )
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( !! @ a
                                @ ^ [Y4: a] :
                                    ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y5 @ Y3 )
                                          & ( Y2 @ Y4 @ Y5 ) )
                                       => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                       => ( Y2 @ Y1 @ Y0 ) ) ) )
               => ( sK11 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f328]) ).

thf(f328,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y4 )
                                            & ( Y2 @ Y3 @ Y5 ) )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK3 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                    | ( !! @ ( a > a > $o )
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( sK2 @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) )
                            & ( !! @ a
                              @ ^ [Y3: a] :
                                  ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( !! @ a
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y5 @ Y3 )
                                            & ( Y2 @ Y4 @ Y5 ) )
                                         => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                         => ( Y2 @ Y1 @ Y0 ) ) ) )
                 => ( sK11 @ Y1 @ Y0 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK11 @ Y2 @ Y0 )
                        & ( sK11 @ Y1 @ Y2 ) )
                     => ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
      = $false )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(not_proxy_clausification,[],[f267]) ).

thf(f267,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( ( Y2 @ Y5 @ Y4 )
                                                & ( Y2 @ Y3 @ Y5 ) )
                                             => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( ( Y2 @ Y5 @ Y3 )
                                                & ( Y2 @ Y4 @ Y5 ) )
                                             => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( sK11 @ Y1 @ Y0 ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK11 @ Y2 @ Y0 )
                            & ( sK11 @ Y1 @ Y2 ) )
                         => ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
      = $true )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(boolean_simplification,[],[f266]) ).

thf(f266,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y4 )
                                              & ( Y2 @ Y3 @ Y5 ) )
                                           => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y3 )
                                              & ( Y2 @ Y4 @ Y5 ) )
                                           => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK11 @ Y1 @ Y0 ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK11 @ Y2 @ Y0 )
                          & ( sK11 @ Y1 @ Y2 ) )
                       => ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
       => $false )
      = $true )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f260,f253]) ).

thf(f253,plain,
    ( ( ( sK11 @ sK4 @ sK5 )
      = $false )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f252]) ).

thf(f260,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( ( Y2 @ Y5 @ Y4 )
                                                & ( Y2 @ Y3 @ Y5 ) )
                                             => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK3 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) )
                        | ( !! @ ( a > a > $o )
                          @ ^ [Y2: a > a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( sK2 @ Y3 @ Y4 )
                                         => ( Y2 @ Y3 @ Y4 ) ) ) )
                                & ( !! @ a
                                  @ ^ [Y3: a] :
                                      ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( ( Y2 @ Y5 @ Y3 )
                                                & ( Y2 @ Y4 @ Y5 ) )
                                             => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                             => ( Y2 @ Y1 @ Y0 ) ) ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( X1 @ Y2 @ Y0 )
                            & ( X1 @ Y1 @ Y2 ) )
                         => ( X1 @ Y1 @ Y0 ) ) ) ) ) )
         => ( X1 @ sK4 @ sK5 ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f259]) ).

thf(f259,plain,
    ( ! [X1: a > a > $o] :
        ( ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( !! @ a
                                              @ ^ [Y6: a] :
                                                  ( ( ( Y3 @ Y6 @ Y5 )
                                                    & ( Y3 @ Y4 @ Y6 ) )
                                                 => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK3 @ Y4 @ Y5 )
                                             => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y3: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( ( sK2 @ Y4 @ Y5 )
                                             => ( Y3 @ Y4 @ Y5 ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( !! @ a
                                          @ ^ [Y5: a] :
                                              ( !! @ a
                                              @ ^ [Y6: a] :
                                                  ( ( ( Y3 @ Y6 @ Y4 )
                                                    & ( Y3 @ Y5 @ Y6 ) )
                                                 => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                                 => ( Y3 @ Y2 @ Y1 ) ) ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y2 @ Y3 ) )
                             => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
             => ( Y0 @ sK4 @ sK5 ) )
          @ X1 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f26]) ).

thf(f26,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f25]) ).

thf(f130,plain,
    ( spl0_7
    | spl0_8
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f123,f96,f128,f125]) ).

thf(f123,plain,
    ( ( ( sK3 @ sK8 @ sK7 )
      = $true )
    | ( ( sK2 @ sK8 @ sK7 )
      = $true )
    | ~ spl0_5 ),
    inference(binary_proxy_clausification,[],[f112]) ).

thf(f101,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f92,f29,f22,f99,f96]) ).

thf(f92,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK6 @ Y0 @ Y1 )
                      & ( sK6 @ Y2 @ Y0 ) )
                   => ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ Y0 )
                  | ( sK3 @ Y1 @ Y0 ) )
               => ( sK6 @ Y1 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f89]) ).

thf(f89,plain,
    ( ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK6 @ Y0 @ Y1 )
                        & ( sK6 @ Y2 @ Y0 ) )
                     => ( sK6 @ Y2 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( ( sK2 @ Y1 @ Y0 )
                    | ( sK3 @ Y1 @ Y0 ) )
                 => ( sK6 @ Y1 @ Y0 ) ) ) ) )
      = $false )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(not_proxy_clausification,[],[f53]) ).

thf(f53,plain,
    ( ( ( ~ ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK6 @ Y0 @ Y1 )
                            & ( sK6 @ Y2 @ Y0 ) )
                         => ( sK6 @ Y2 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK2 @ Y1 @ Y0 )
                        | ( sK3 @ Y1 @ Y0 ) )
                     => ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
      = $true )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(boolean_simplification,[],[f52]) ).

thf(f52,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK6 @ Y0 @ Y1 )
                          & ( sK6 @ Y2 @ Y0 ) )
                       => ( sK6 @ Y2 @ Y1 ) ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( sK2 @ Y1 @ Y0 )
                      | ( sK3 @ Y1 @ Y0 ) )
                   => ( sK6 @ Y1 @ Y0 ) ) ) ) )
       => $false )
      = $true )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(superposition,[],[f42,f46]) ).

thf(f46,plain,
    ( ( ( sK6 @ sK4 @ sK5 )
      = $false )
    | ~ spl0_3 ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( ( ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y4 )
                                              & ( Y2 @ Y3 @ Y5 ) )
                                           => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK3 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) )
                      | ( !! @ ( a > a > $o )
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( ( sK2 @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y5 @ Y3 )
                                              & ( Y2 @ Y4 @ Y5 ) )
                                           => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
                           => ( Y2 @ Y1 @ Y0 ) ) ) )
                   => ( sK6 @ Y1 @ Y0 ) ) ) )
          & ( !! @ a
            @ ^ [Y0: a] :
                ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK6 @ Y2 @ Y0 )
                          & ( sK6 @ Y1 @ Y2 ) )
                       => ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
       => ( sK6 @ sK4 @ sK5 ) )
      = $false )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f44]) ).

thf(f44,plain,
    ( ( ( ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) )
        @ sK6 )
      = $false )
    | ~ spl0_3 ),
    inference(sigma_clausification,[],[f30]) ).

thf(f42,plain,
    ( ! [X1: a > a > $o] :
        ( ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( X1 @ Y0 @ Y1 )
                            & ( X1 @ Y2 @ Y0 ) )
                         => ( X1 @ Y2 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( ( sK2 @ Y1 @ Y0 )
                        | ( sK3 @ Y1 @ Y0 ) )
                     => ( X1 @ Y1 @ Y0 ) ) ) ) )
         => ( X1 @ sK4 @ sK5 ) )
        = $true )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f41]) ).

thf(f41,plain,
    ( ! [X1: a > a > $o] :
        ( $true
        = ( ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y1 @ Y2 )
                                & ( Y0 @ Y3 @ Y1 ) )
                             => ( Y0 @ Y3 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( sK2 @ Y2 @ Y1 )
                            | ( sK3 @ Y2 @ Y1 ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) )
             => ( Y0 @ sK4 @ sK5 ) )
          @ X1 ) )
    | ~ spl0_1 ),
    inference(pi_clausification,[],[f23]) ).

thf(f38,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f37]) ).

thf(f37,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f36]) ).

thf(f36,plain,
    ( ( $false = $true )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f26,f30]) ).

thf(f34,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f20,f32,f29]) ).

thf(f20,plain,
    ( ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y5 )
                                                  & ( Y3 @ Y4 @ Y6 ) )
                                               => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK3 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                          | ( !! @ ( a > a > $o )
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( sK2 @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) )
                                  & ( !! @ a
                                    @ ^ [Y4: a] :
                                        ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( !! @ a
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y6 @ Y4 )
                                                  & ( Y3 @ Y5 @ Y6 ) )
                                               => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
                               => ( Y3 @ Y2 @ Y1 ) ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y3 @ Y1 )
                              & ( Y0 @ Y2 @ Y3 ) )
                           => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false )
    | ( ( !! @ ( a > a > $o )
        @ ^ [Y0: a > a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y1 @ Y2 )
                              & ( Y0 @ Y3 @ Y1 ) )
                           => ( Y0 @ Y3 @ Y2 ) ) ) ) )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( ( sK2 @ Y2 @ Y1 )
                          | ( sK3 @ Y2 @ Y1 ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) )
           => ( Y0 @ sK4 @ sK5 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f18]) ).

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

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

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

thf(f15,plain,
    ( ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( !! @ a
                          @ ^ [Y5: a] :
                              ( ( ( Y2 @ Y3 @ Y4 )
                                & ( Y2 @ Y5 @ Y3 ) )
                             => ( Y2 @ Y5 @ Y4 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( sK2 @ Y4 @ Y3 )
                            | ( sK3 @ Y4 @ Y3 ) )
                         => ( Y2 @ Y4 @ Y3 ) ) ) ) )
             => ( Y2 @ Y0 @ Y1 ) ) )
      @ sK4 )
   != ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > a > $o )
          @ ^ [Y2: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( ( ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( !! @ a
                                              @ ^ [Y8: a] :
                                                  ( ( ( Y5 @ Y8 @ Y7 )
                                                    & ( Y5 @ Y6 @ Y8 ) )
                                                 => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK3 @ Y6 @ Y7 )
                                             => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) )
                            | ( !! @ ( a > a > $o )
                              @ ^ [Y5: a > a > $o] :
                                  ( ( ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( ( sK2 @ Y6 @ Y7 )
                                             => ( Y5 @ Y6 @ Y7 ) ) ) )
                                    & ( !! @ a
                                      @ ^ [Y6: a] :
                                          ( !! @ a
                                          @ ^ [Y7: a] :
                                              ( !! @ a
                                              @ ^ [Y8: a] :
                                                  ( ( ( Y5 @ Y8 @ Y6 )
                                                    & ( Y5 @ Y7 @ Y8 ) )
                                                 => ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
                                 => ( Y5 @ Y4 @ Y3 ) ) ) )
                         => ( Y2 @ Y4 @ Y3 ) ) ) )
                & ( !! @ a
                  @ ^ [Y3: a] :
                      ( !! @ a
                      @ ^ [Y4: a] :
                          ( !! @ a
                          @ ^ [Y5: a] :
                              ( ( ( Y2 @ Y5 @ Y3 )
                                & ( Y2 @ Y4 @ Y5 ) )
                             => ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
             => ( Y2 @ Y0 @ Y1 ) ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f14]) ).

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

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

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

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

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

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

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

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

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

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

thf(f1,conjecture,
    ! [X0: a > a > $o,X1: a > a > $o] :
      ( ( ^ [X2: a,X3: a] :
          ! [X4: a > a > $o] :
            ( ( ! [X6: a,X5: a,X7: a] :
                  ( ( ( X4 @ X5 @ X6 )
                    & ( X4 @ X6 @ X7 ) )
                 => ( X4 @ X5 @ X7 ) )
              & ! [X5: a,X6: a] :
                  ( ( ! [X8: a > a > $o] :
                        ( ( ! [X10: a,X9: a,X7: a] :
                              ( ( ( X8 @ X9 @ X10 )
                                & ( X8 @ X10 @ X7 ) )
                             => ( X8 @ X9 @ X7 ) )
                          & ! [X10: a,X9: a] :
                              ( ( X1 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) ) )
                       => ( X8 @ X5 @ X6 ) )
                    | ! [X8: a > a > $o] :
                        ( ( ! [X10: a,X9: a] :
                              ( ( X0 @ X9 @ X10 )
                             => ( X8 @ X9 @ X10 ) )
                          & ! [X10: a,X7: a,X9: a] :
                              ( ( ( X8 @ X9 @ X10 )
                                & ( X8 @ X10 @ X7 ) )
                             => ( X8 @ X9 @ X7 ) ) )
                       => ( X8 @ X5 @ X6 ) ) )
                 => ( X4 @ X5 @ X6 ) ) )
           => ( X4 @ X2 @ X3 ) ) )
      = ( ^ [X2: a,X3: a] :
          ! [X4: a > a > $o] :
            ( ( ! [X5: a,X6: a] :
                  ( ( ( X0 @ X5 @ X6 )
                    | ( X1 @ X5 @ X6 ) )
                 => ( X4 @ X5 @ X6 ) )
              & ! [X5: a,X7: a,X6: a] :
                  ( ( ( X4 @ X5 @ X6 )
                    & ( X4 @ X6 @ X7 ) )
                 => ( X4 @ X5 @ X7 ) ) )
           => ( X4 @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250_pme) ).

thf(f27,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f19,f25,f22]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n004.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 18:31:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TH0_THM_EQU_NAR problem
% 0.14/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38  % (24368)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38  % (24370)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38  % (24371)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38  % (24372)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38  % (24373)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.38  % (24374)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38  % (24371)Instruction limit reached!
% 0.14/0.38  % (24371)------------------------------
% 0.14/0.38  % (24371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (24371)Termination reason: Unknown
% 0.14/0.38  % (24371)Termination phase: Property scanning
% 0.14/0.38  % (24372)Instruction limit reached!
% 0.14/0.38  % (24372)------------------------------
% 0.14/0.38  % (24372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  
% 0.14/0.38  % (24371)Memory used [KB]: 1023
% 0.14/0.38  % (24371)Time elapsed: 0.003 s
% 0.14/0.38  % (24371)Instructions burned: 2 (million)
% 0.14/0.38  % (24371)------------------------------
% 0.14/0.38  % (24371)------------------------------
% 0.14/0.38  % (24372)Termination reason: Unknown
% 0.14/0.38  % (24372)Termination phase: shuffling
% 0.14/0.38  
% 0.14/0.38  % (24372)Memory used [KB]: 1023
% 0.14/0.38  % (24372)Time elapsed: 0.003 s
% 0.14/0.38  % (24372)Instructions burned: 2 (million)
% 0.14/0.38  % (24372)------------------------------
% 0.14/0.38  % (24372)------------------------------
% 0.14/0.38  % (24375)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38  % (24375)Instruction limit reached!
% 0.21/0.38  % (24375)------------------------------
% 0.21/0.38  % (24375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38  % (24375)Termination reason: Unknown
% 0.21/0.38  % (24375)Termination phase: Preprocessing 3
% 0.21/0.38  
% 0.21/0.38  % (24375)Memory used [KB]: 1023
% 0.21/0.38  % (24375)Time elapsed: 0.004 s
% 0.21/0.38  % (24375)Instructions burned: 4 (million)
% 0.21/0.38  % (24375)------------------------------
% 0.21/0.38  % (24375)------------------------------
% 0.21/0.39  % (24374)Instruction limit reached!
% 0.21/0.39  % (24374)------------------------------
% 0.21/0.39  % (24374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (24374)Termination reason: Unknown
% 0.21/0.39  % (24374)Termination phase: Saturation
% 0.21/0.39  
% 0.21/0.39  % (24374)Memory used [KB]: 5500
% 0.21/0.39  % (24374)Time elapsed: 0.012 s
% 0.21/0.39  % (24374)Instructions burned: 19 (million)
% 0.21/0.39  % (24374)------------------------------
% 0.21/0.39  % (24374)------------------------------
% 0.21/0.39  % (24369)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.39  % (24370)Instruction limit reached!
% 0.21/0.39  % (24370)------------------------------
% 0.21/0.39  % (24370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (24370)Termination reason: Unknown
% 0.21/0.39  % (24370)Termination phase: Saturation
% 0.21/0.39  
% 0.21/0.39  % (24370)Memory used [KB]: 5628
% 0.21/0.39  % (24370)Time elapsed: 0.016 s
% 0.21/0.39  % (24370)Instructions burned: 28 (million)
% 0.21/0.39  % (24370)------------------------------
% 0.21/0.39  % (24370)------------------------------
% 0.21/0.39  % (24369)Instruction limit reached!
% 0.21/0.39  % (24369)------------------------------
% 0.21/0.39  % (24369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (24369)Termination reason: Unknown
% 0.21/0.39  % (24369)Termination phase: Saturation
% 0.21/0.39  
% 0.21/0.39  % (24369)Memory used [KB]: 5500
% 0.21/0.39  % (24369)Time elapsed: 0.005 s
% 0.21/0.39  % (24369)Instructions burned: 5 (million)
% 0.21/0.39  % (24369)------------------------------
% 0.21/0.39  % (24369)------------------------------
% 0.21/0.39  % (24376)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.40  % (24377)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.40  % (24379)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.41  % (24377)Instruction limit reached!
% 0.21/0.41  % (24377)------------------------------
% 0.21/0.41  % (24377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (24377)Termination reason: Unknown
% 0.21/0.41  % (24377)Termination phase: Saturation
% 0.21/0.41  
% 0.21/0.41  % (24377)Memory used [KB]: 5628
% 0.21/0.41  % (24377)Time elapsed: 0.010 s
% 0.21/0.41  % (24377)Instructions burned: 16 (million)
% 0.21/0.41  % (24377)------------------------------
% 0.21/0.41  % (24377)------------------------------
% 0.21/0.41  % (24378)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41  % (24378)Instruction limit reached!
% 0.21/0.41  % (24378)------------------------------
% 0.21/0.41  % (24378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (24378)Termination reason: Unknown
% 0.21/0.41  % (24378)Termination phase: Property scanning
% 0.21/0.41  
% 0.21/0.41  % (24378)Memory used [KB]: 1023
% 0.21/0.41  % (24378)Time elapsed: 0.003 s
% 0.21/0.41  % (24378)Instructions burned: 3 (million)
% 0.21/0.41  % (24378)------------------------------
% 0.21/0.41  % (24378)------------------------------
% 0.21/0.41  % (24381)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41  % (24376)Instruction limit reached!
% 0.21/0.41  % (24376)------------------------------
% 0.21/0.41  % (24376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (24376)Termination reason: Unknown
% 0.21/0.41  % (24376)Termination phase: Saturation
% 0.21/0.41  
% 0.21/0.41  % (24376)Memory used [KB]: 5628
% 0.21/0.41  % (24376)Time elapsed: 0.021 s
% 0.21/0.41  % (24376)Instructions burned: 38 (million)
% 0.21/0.41  % (24376)------------------------------
% 0.21/0.41  % (24376)------------------------------
% 0.21/0.42  % (24381)Instruction limit reached!
% 0.21/0.42  % (24381)------------------------------
% 0.21/0.42  % (24381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (24381)Termination reason: Unknown
% 0.21/0.42  % (24381)Termination phase: Saturation
% 0.21/0.42  
% 0.21/0.42  % (24381)Memory used [KB]: 5756
% 0.21/0.42  % (24381)Time elapsed: 0.036 s
% 0.21/0.42  % (24381)Instructions burned: 17 (million)
% 0.21/0.42  % (24381)------------------------------
% 0.21/0.42  % (24381)------------------------------
% 0.21/0.42  % (24380)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.42  % (24383)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42  % (24382)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42  % (24383)Instruction limit reached!
% 0.21/0.42  % (24383)------------------------------
% 0.21/0.42  % (24383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (24383)Termination reason: Unknown
% 0.21/0.42  % (24383)Termination phase: Property scanning
% 0.21/0.42  
% 0.21/0.42  % (24383)Memory used [KB]: 1023
% 0.21/0.42  % (24383)Time elapsed: 0.003 s
% 0.21/0.42  % (24383)Instructions burned: 3 (million)
% 0.21/0.42  % (24383)------------------------------
% 0.21/0.42  % (24383)------------------------------
% 0.21/0.42  % (24382)Instruction limit reached!
% 0.21/0.42  % (24382)------------------------------
% 0.21/0.42  % (24382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (24382)Termination reason: Unknown
% 0.21/0.42  % (24382)Termination phase: Property scanning
% 0.21/0.42  
% 0.21/0.42  % (24382)Memory used [KB]: 1023
% 0.21/0.42  % (24382)Time elapsed: 0.003 s
% 0.21/0.42  % (24382)Instructions burned: 3 (million)
% 0.21/0.42  % (24382)------------------------------
% 0.21/0.42  % (24382)------------------------------
% 0.21/0.42  % (24380)Instruction limit reached!
% 0.21/0.42  % (24380)------------------------------
% 0.21/0.42  % (24380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (24380)Termination reason: Unknown
% 0.21/0.42  % (24380)Termination phase: Saturation
% 0.21/0.42  
% 0.21/0.42  % (24380)Memory used [KB]: 1023
% 0.21/0.42  % (24380)Time elapsed: 0.035 s
% 0.21/0.42  % (24380)Instructions burned: 8 (million)
% 0.21/0.42  % (24380)------------------------------
% 0.21/0.42  % (24380)------------------------------
% 0.21/0.43  % (24384)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43  % (24384)Instruction limit reached!
% 0.21/0.43  % (24384)------------------------------
% 0.21/0.43  % (24384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (24384)Termination reason: Unknown
% 0.21/0.43  % (24384)Termination phase: Saturation
% 0.21/0.43  
% 0.21/0.43  % (24384)Memory used [KB]: 5500
% 0.21/0.43  % (24384)Time elapsed: 0.006 s
% 0.21/0.43  % (24384)Instructions burned: 8 (million)
% 0.21/0.43  % (24384)------------------------------
% 0.21/0.43  % (24384)------------------------------
% 0.21/0.43  % (24385)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43  % (24385)Instruction limit reached!
% 0.21/0.43  % (24385)------------------------------
% 0.21/0.43  % (24385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (24385)Termination reason: Unknown
% 0.21/0.43  % (24385)Termination phase: Property scanning
% 0.21/0.43  
% 0.21/0.43  % (24385)Memory used [KB]: 1023
% 0.21/0.43  % (24385)Time elapsed: 0.003 s
% 0.21/0.43  % (24385)Instructions burned: 3 (million)
% 0.21/0.43  % (24385)------------------------------
% 0.21/0.43  % (24385)------------------------------
% 0.21/0.44  % (24386)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44  % (24387)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.44  % (24386)Instruction limit reached!
% 0.21/0.44  % (24386)------------------------------
% 0.21/0.44  % (24386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44  % (24386)Termination reason: Unknown
% 0.21/0.44  % (24386)Termination phase: Saturation
% 0.21/0.44  
% 0.21/0.44  % (24386)Memory used [KB]: 5500
% 0.21/0.44  % (24386)Time elapsed: 0.004 s
% 0.21/0.44  % (24386)Instructions burned: 5 (million)
% 0.21/0.44  % (24386)------------------------------
% 0.21/0.44  % (24386)------------------------------
% 0.21/0.44  % (24388)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45  % (24389)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45  % (24387)Instruction limit reached!
% 0.21/0.45  % (24387)------------------------------
% 0.21/0.45  % (24387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (24387)Termination reason: Unknown
% 0.21/0.45  % (24387)Termination phase: Saturation
% 0.21/0.45  
% 0.21/0.45  % (24387)Memory used [KB]: 5500
% 0.21/0.45  % (24387)Time elapsed: 0.011 s
% 0.21/0.45  % (24387)Instructions burned: 19 (million)
% 0.21/0.45  % (24387)------------------------------
% 0.21/0.45  % (24387)------------------------------
% 0.21/0.45  % (24390)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.45  % (24389)Instruction limit reached!
% 0.21/0.45  % (24389)------------------------------
% 0.21/0.45  % (24389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (24389)Termination reason: Unknown
% 0.21/0.45  % (24389)Termination phase: Saturation
% 0.21/0.45  
% 0.21/0.45  % (24389)Memory used [KB]: 5500
% 0.21/0.45  % (24389)Time elapsed: 0.005 s
% 0.21/0.45  % (24389)Instructions burned: 6 (million)
% 0.21/0.45  % (24389)------------------------------
% 0.21/0.45  % (24389)------------------------------
% 0.21/0.45  % (24391)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.46  % (24392)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.46  % (24391)Instruction limit reached!
% 0.21/0.46  % (24391)------------------------------
% 0.21/0.46  % (24391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46  % (24391)Termination reason: Unknown
% 0.21/0.46  % (24391)Termination phase: Saturation
% 0.21/0.46  
% 0.21/0.46  % (24391)Memory used [KB]: 5628
% 0.21/0.46  % (24391)Time elapsed: 0.013 s
% 0.21/0.46  % (24391)Instructions burned: 23 (million)
% 0.21/0.46  % (24391)------------------------------
% 0.21/0.46  % (24391)------------------------------
% 0.21/0.46  % (24392)Instruction limit reached!
% 0.21/0.46  % (24392)------------------------------
% 0.21/0.46  % (24392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46  % (24392)Termination reason: Unknown
% 0.21/0.46  % (24392)Termination phase: Saturation
% 0.21/0.46  
% 0.21/0.46  % (24392)Memory used [KB]: 5500
% 0.21/0.46  % (24392)Time elapsed: 0.005 s
% 0.21/0.46  % (24392)Instructions burned: 5 (million)
% 0.21/0.46  % (24392)------------------------------
% 0.21/0.46  % (24392)------------------------------
% 0.21/0.46  % (24393)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.47  % (24393)Instruction limit reached!
% 0.21/0.47  % (24393)------------------------------
% 0.21/0.47  % (24393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47  % (24393)Termination reason: Unknown
% 0.21/0.47  % (24393)Termination phase: Saturation
% 0.21/0.47  
% 0.21/0.47  % (24393)Memory used [KB]: 5500
% 0.21/0.47  % (24393)Time elapsed: 0.005 s
% 0.21/0.47  % (24393)Instructions burned: 6 (million)
% 0.21/0.47  % (24393)------------------------------
% 0.21/0.47  % (24393)------------------------------
% 0.21/0.47  % (24394)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.21/0.48  % (24368)Instruction limit reached!
% 0.21/0.48  % (24368)------------------------------
% 0.21/0.48  % (24368)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48  % (24368)Termination reason: Unknown
% 0.21/0.48  % (24368)Termination phase: Saturation
% 0.21/0.48  
% 0.21/0.48  % (24368)Memory used [KB]: 6524
% 0.21/0.48  % (24368)Time elapsed: 0.101 s
% 0.21/0.48  % (24368)Instructions burned: 184 (million)
% 0.21/0.48  % (24368)------------------------------
% 0.21/0.48  % (24368)------------------------------
% 0.21/0.48  % (24395)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.21/0.48  % (24396)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.21/0.49  % (24397)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.49  % (24396)Instruction limit reached!
% 0.21/0.49  % (24396)------------------------------
% 0.21/0.49  % (24396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49  % (24396)Termination reason: Unknown
% 0.21/0.49  % (24396)Termination phase: Saturation
% 0.21/0.49  
% 0.21/0.49  % (24396)Memory used [KB]: 5500
% 0.21/0.49  % (24396)Time elapsed: 0.010 s
% 0.21/0.49  % (24396)Instructions burned: 20 (million)
% 0.21/0.49  % (24396)------------------------------
% 0.21/0.49  % (24396)------------------------------
% 0.21/0.50  % (24398)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.51  % (24398)Instruction limit reached!
% 0.21/0.51  % (24398)------------------------------
% 0.21/0.51  % (24398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51  % (24398)Termination reason: Unknown
% 0.21/0.51  % (24398)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (24398)Memory used [KB]: 5756
% 0.21/0.51  % (24398)Time elapsed: 0.007 s
% 0.21/0.51  % (24398)Instructions burned: 18 (million)
% 0.21/0.51  % (24398)------------------------------
% 0.21/0.51  % (24398)------------------------------
% 0.21/0.51  % (24373)Instruction limit reached!
% 0.21/0.51  % (24373)------------------------------
% 0.21/0.51  % (24373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51  % (24373)Termination reason: Unknown
% 0.21/0.51  % (24373)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (24373)Memory used [KB]: 7164
% 0.21/0.51  % (24373)Time elapsed: 0.135 s
% 0.21/0.51  % (24373)Instructions burned: 277 (million)
% 0.21/0.51  % (24373)------------------------------
% 0.21/0.51  % (24373)------------------------------
% 0.21/0.51  % (24399)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.52  % (24399)Instruction limit reached!
% 0.21/0.52  % (24399)------------------------------
% 0.21/0.52  % (24399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52  % (24399)Termination reason: Unknown
% 0.21/0.52  % (24399)Termination phase: Preprocessing 3
% 0.21/0.52  
% 0.21/0.52  % (24399)Memory used [KB]: 1023
% 0.21/0.52  % (24399)Time elapsed: 0.002 s
% 0.21/0.52  % (24399)Instructions burned: 3 (million)
% 0.21/0.52  % (24399)------------------------------
% 0.21/0.52  % (24399)------------------------------
% 0.21/0.52  % (24400)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.32/0.52  % (24401)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 1.32/0.52  % (24400)Refutation not found, incomplete strategy
% 1.32/0.52  % (24400)------------------------------
% 1.32/0.52  % (24400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.32/0.52  % (24400)Termination reason: Refutation not found, incomplete strategy
% 1.32/0.52  
% 1.32/0.52  
% 1.32/0.52  % (24400)Memory used [KB]: 5500
% 1.32/0.52  % (24400)Time elapsed: 0.005 s
% 1.32/0.52  % (24400)Instructions burned: 13 (million)
% 1.32/0.52  % (24400)------------------------------
% 1.32/0.52  % (24400)------------------------------
% 1.32/0.53  % (24402)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 1.48/0.56  % (24401)Instruction limit reached!
% 1.48/0.56  % (24401)------------------------------
% 1.48/0.56  % (24401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.56  % (24401)Termination reason: Unknown
% 1.48/0.56  % (24401)Termination phase: Saturation
% 1.48/0.56  
% 1.48/0.56  % (24401)Memory used [KB]: 6140
% 1.48/0.56  % (24401)Time elapsed: 0.039 s
% 1.48/0.56  % (24401)Instructions burned: 129 (million)
% 1.48/0.56  % (24401)------------------------------
% 1.48/0.56  % (24401)------------------------------
% 1.48/0.56  % (24402)Instruction limit reached!
% 1.48/0.56  % (24402)------------------------------
% 1.48/0.56  % (24402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.56  % (24402)Termination reason: Unknown
% 1.48/0.56  % (24402)Termination phase: Saturation
% 1.48/0.56  
% 1.48/0.56  % (24402)Memory used [KB]: 5884
% 1.48/0.56  % (24402)Time elapsed: 0.032 s
% 1.48/0.56  % (24402)Instructions burned: 102 (million)
% 1.48/0.56  % (24402)------------------------------
% 1.48/0.56  % (24402)------------------------------
% 1.48/0.57  % (24403)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 1.48/0.57  % (24403)Instruction limit reached!
% 1.48/0.57  % (24403)------------------------------
% 1.48/0.57  % (24403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.57  % (24403)Termination reason: Unknown
% 1.48/0.57  % (24403)Termination phase: Property scanning
% 1.48/0.57  
% 1.48/0.57  % (24403)Memory used [KB]: 1023
% 1.48/0.57  % (24403)Time elapsed: 0.002 s
% 1.48/0.57  % (24403)Instructions burned: 4 (million)
% 1.48/0.57  % (24403)------------------------------
% 1.48/0.57  % (24403)------------------------------
% 1.48/0.57  % (24404)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 1.48/0.57  % (24404)Refutation not found, incomplete strategy
% 1.48/0.57  % (24404)------------------------------
% 1.48/0.57  % (24404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.57  % (24404)Termination reason: Refutation not found, incomplete strategy
% 1.48/0.57  
% 1.48/0.57  
% 1.48/0.57  % (24404)Memory used [KB]: 5500
% 1.48/0.57  % (24404)Time elapsed: 0.003 s
% 1.48/0.57  % (24404)Instructions burned: 6 (million)
% 1.48/0.57  % (24404)------------------------------
% 1.48/0.57  % (24404)------------------------------
% 1.48/0.58  % (24394)Instruction limit reached!
% 1.48/0.58  % (24394)------------------------------
% 1.48/0.58  % (24394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.58  % (24394)Termination reason: Unknown
% 1.48/0.58  % (24394)Termination phase: Saturation
% 1.48/0.58  
% 1.48/0.58  % (24394)Memory used [KB]: 7547
% 1.48/0.58  % (24394)Time elapsed: 0.104 s
% 1.48/0.58  % (24394)Instructions burned: 378 (million)
% 1.48/0.58  % (24394)------------------------------
% 1.48/0.58  % (24394)------------------------------
% 1.48/0.58  % (24405)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.48/0.58  % (24379)First to succeed.
% 1.48/0.58  % (24407)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.48/0.58  % (24406)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 1.48/0.59  % (24379)Refutation found. Thanks to Tanya!
% 1.48/0.59  % SZS status Theorem for theBenchmark
% 1.48/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.59  % (24379)------------------------------
% 1.48/0.59  % (24379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.59  % (24379)Termination reason: Refutation
% 1.48/0.59  
% 1.48/0.59  % (24379)Memory used [KB]: 6908
% 1.48/0.59  % (24379)Time elapsed: 0.212 s
% 1.48/0.59  % (24379)Instructions burned: 394 (million)
% 1.48/0.59  % (24379)------------------------------
% 1.48/0.59  % (24379)------------------------------
% 1.48/0.59  % (24367)Success in time 0.224 s
% 1.48/0.59  % Vampire---4.8 exiting
%------------------------------------------------------------------------------