TSTP Solution File: SEV310^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV310^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qWfSiDq9kE true

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:00:23 EDT 2023

% Result   : Theorem 51.58s 7.28s
% Output   : Refutation 51.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  115 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :  851 (   9 equ;   0 cnn)
%            Maximal formula atoms :   26 (   8 avg)
%            Number of connectives : 2702 (  89   ~; 125   |;   0   &;1630   @)
%                                         (   0 <=>; 455  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  13 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  274 ( 274   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   4 con; 0-2 aty)
%                                         ( 403  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  633 ( 501   ^; 132   !;   0   ?; 633   :)

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

thf('#sk1_type',type,
    '#sk1': a ).

thf('#form1076_type',type,
    '#form1076': ( a > $o ) > $o ).

thf('#l_lift30859_type',type,
    '#l_lift30859': a > $o ).

thf('#sk336_type',type,
    '#sk336': ( a > $o ) > a ).

thf('#sk12_type',type,
    '#sk12': ( a > $o ) > ( a > $o ) > a ).

thf(cK_type,type,
    cK: ( a > $o ) > a > $o ).

thf('#sk244_type',type,
    '#sk244': ( a > $o ) > a > $o ).

thf('#form811_type',type,
    '#form811': $o ).

thf('#sk236_type',type,
    '#sk236': ( a > $o ) > a ).

thf(cTHM90A_pme,conjecture,
    ( ! [X: a > $o,Y: a > $o] :
        ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: a] :
            ( ( cK @ X @ Xx )
           => ( cK @ Y @ Xx ) ) )
   => ! [Xx: a] :
        ( ! [S: a > $o] :
            ( ! [Xx0: a] :
                ( ( cK @ S @ Xx0 )
               => ( S @ Xx0 ) )
           => ( S @ Xx ) )
       => ( cK
          @ ^ [Xx0: a] :
            ! [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( cK @ S @ Xx1 )
                 => ( S @ Xx1 ) )
             => ( S @ Xx0 ) )
          @ Xx ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cK @ X @ Xx )
             => ( cK @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ! [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( cK @ S @ Xx0 )
                 => ( S @ Xx0 ) )
             => ( S @ Xx ) )
         => ( cK
            @ ^ [Xx0: a] :
              ! [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( cK @ S @ Xx1 )
                   => ( S @ Xx1 ) )
               => ( S @ Xx0 ) )
            @ Xx ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM90A_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( !!
        @ ^ [Y0: a > $o] :
            ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y0 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
           => ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: a > $o] :
        ( !!
        @ ^ [Y1: a > $o] :
            ( ( !!
              @ ^ [Y2: a] :
                  ( ( Y0 @ Y2 )
                 => ( Y1 @ Y2 ) ) )
           => ( !!
              @ ^ [Y2: a] :
                  ( ( cK @ Y0 @ Y2 )
                 => ( cK @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: a > $o] :
      ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( X2 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: a] :
                ( ( cK @ X2 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl23,plain,
    ( !!
    @ ^ [Y0: a > $o] :
        ( ( !!
          @ ^ [Y1: a] :
              ( ( !!
                @ ^ [Y2: a > $o] :
                    ( ( !!
                      @ ^ [Y3: a] :
                          ( ( cK @ Y2 @ Y3 )
                         => ( Y2 @ Y3 ) ) )
                   => ( Y2 @ Y1 ) ) )
             => ( Y0 @ Y1 ) ) )
       => ( !!
          @ ^ [Y1: a] :
              ( ( cK
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a > $o] :
                        ( ( !!
                          @ ^ [Y4: a] :
                              ( ( cK @ Y3 @ Y4 )
                             => ( Y3 @ Y4 ) ) )
                       => ( Y3 @ Y2 ) ) )
                @ Y1 )
             => ( cK @ Y0 @ Y1 ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl88,plain,
    ! [X2: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
           => ( X2 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl91,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) )
             => ( X2 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl92,plain,
    ! [X2: a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a > $o] :
                ( ( !!
                  @ ^ [Y1: a] :
                      ( ( cK @ Y0 @ Y1 )
                     => ( Y0 @ Y1 ) ) )
               => ( Y0 @ ( '#sk336' @ X2 ) ) ) )
         => ( X2 @ ( '#sk336' @ X2 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl93,plain,
    ! [X2: a > $o] :
      ( ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl95,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X4 @ Y0 )
             => ( X4 @ Y0 ) ) )
       => ( X4 @ ( '#sk336' @ X2 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl97,plain,
    ! [X0: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl95]) ).

thf(zip_derived_cl276,plain,
    ! [X0: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) )
         => ( cK
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a > $o] :
                    ( ( !!
                      @ ^ [Y3: a] :
                          ( ( cK @ Y2 @ Y3 )
                         => ( Y2 @ Y3 ) ) )
                   => ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ~ ( ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ '#sk1' ) ) )
     => ( cK
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) )
        @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ( !!
    @ ^ [Y0: a > $o] :
        ( ( !!
          @ ^ [Y1: a] :
              ( ( cK @ Y0 @ Y1 )
             => ( Y0 @ Y1 ) ) )
       => ( Y0 @ '#sk1' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9,plain,
    ! [X2: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( X2 @ Y0 ) ) )
     => ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl21,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( ( cK
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a > $o] :
                    ( ( !!
                      @ ^ [Y3: a] :
                          ( ( cK @ Y2 @ Y3 )
                         => ( Y2 @ Y3 ) ) )
                   => ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) ) ) )
   => ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl108,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl109,plain,
    ( ~ ( ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ ( '#sk236'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0
                @ ( '#sk236'
                  @ ( cK
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a > $o] :
                            ( ( !!
                              @ ^ [Y3: a] :
                                  ( ( cK @ Y2 @ Y3 )
                                 => ( Y2 @ Y3 ) ) )
                           => ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl110,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl109]) ).

thf(zip_derived_cl112,plain,
    ! [X2: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X2 @ Y0 )
             => ( X2 @ Y0 ) ) )
       => ( X2 @ '#sk1' ) )
      | ( cK
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) )
        @ ( '#sk236'
          @ ( cK
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl110]) ).

thf(zip_derived_cl114,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ '#sk1' ) ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl112]) ).

thf(zip_derived_cl185,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl186,plain,
    ( ~ ( ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ ( '#sk236'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0
                @ ( '#sk236'
                  @ ( cK
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a > $o] :
                            ( ( !!
                              @ ^ [Y3: a] :
                                  ( ( cK @ Y2 @ Y3 )
                                 => ( Y2 @ Y3 ) ) )
                           => ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl185]) ).

thf(zip_derived_cl187,plain,
    ( ~ ( $false
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0
                @ ( '#sk236'
                  @ ( cK
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a > $o] :
                            ( ( !!
                              @ ^ [Y3: a] :
                                  ( ( cK @ Y2 @ Y3 )
                                 => ( Y2 @ Y3 ) ) )
                           => ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl186]) ).

thf(zip_derived_cl188,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl187]) ).

thf(zip_derived_cl189,plain,
    ! [X2: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X2 @ Y0 )
             => ( X2 @ Y0 ) ) )
       => ( X2 @ '#sk1' ) )
      | ( cK
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) )
        @ ( '#sk236'
          @ ( cK
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl188]) ).

thf(zip_derived_cl191,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ '#sk1' ) ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl189]) ).

thf(zip_derived_cl264,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( Y0 @ '#sk1' ) ) )
    | ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ ( '#sk236'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl191]) ).

thf(zip_derived_cl265,plain,
    ( '#form811'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl277,plain,
    ! [X0: a > $o] :
      ( ~ '#form811'
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl276,zip_derived_cl265]) ).

thf(zip_derived_cl278,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X2 )
       => ( cK @ X0 @ X2 ) )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ '#form811' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl277]) ).

thf(zip_derived_cl279,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X2 )
      | ( cK @ X0 @ X2 )
      | ~ '#form811'
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).

thf(zip_derived_cl280,plain,
    ! [X0: a > $o,X2: a,X4: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X4 @ Y0 )
             => ( X4 @ Y0 ) ) )
       => ( X4 @ ( '#sk336' @ X0 ) ) )
      | ~ '#form811'
      | ( cK @ X0 @ X2 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl279]) ).

thf(zip_derived_cl282,plain,
    ! [X0: a > $o,X1: a] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl280]) ).

thf(zip_derived_cl314,plain,
    ! [X0: a > $o,X1: a] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( cK @ X0 @ X1 )
      | ~ '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl282]) ).

thf(zip_derived_cl265_001,plain,
    ( '#form811'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl315,plain,
    ! [X0: a > $o,X1: a] :
      ( ~ '#form811'
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl314,zip_derived_cl265]) ).

thf(zip_derived_cl316,plain,
    ! [X0: a > $o,X1: a] :
      ( ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( cK @ X0 @ X1 )
      | ~ '#form811' ),
    inference(simplify,[status(thm)],[zip_derived_cl315]) ).

thf(zip_derived_cl317,plain,
    ! [X0: a > $o,X1: a,X3: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X3 @ Y0 )
             => ( X3 @ Y0 ) ) )
       => ( X3 @ ( '#sk336' @ X0 ) ) )
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl316]) ).

thf(zip_derived_cl319,plain,
    ! [X0: a > $o,X1: a] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl317]) ).

thf(zip_derived_cl332,plain,
    ! [X0: a > $o,X1: a] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( cK @ X0 @ X1 )
      | ~ '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl319]) ).

thf(zip_derived_cl265_002,plain,
    ( '#form811'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl333,plain,
    ! [X0: a > $o,X1: a] :
      ( ~ '#form811'
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl332,zip_derived_cl265]) ).

thf(zip_derived_cl334,plain,
    ! [X0: a > $o,X1: a] :
      ( ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( cK @ X0 @ X1 )
      | ~ '#form811' ),
    inference(simplify,[status(thm)],[zip_derived_cl333]) ).

thf(zip_derived_cl335,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form1076' @ X0 )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl336,plain,
    ! [X0: a > $o,X2: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X2 @ Y0 )
             => ( X2 @ Y0 ) ) )
       => ( X2 @ ( '#sk336' @ X0 ) ) )
      | ~ ( '#form1076' @ X0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl335]) ).

thf(zip_derived_cl340,plain,
    ! [X0: a > $o,X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X2 @ Y0 )
             => ( X2 @ Y0 ) ) )
      | ( X2 @ ( '#sk336' @ X0 ) )
      | ~ ( '#form1076' @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl341,plain,
    ! [X0: a > $o,X2: a > $o] :
      ( ~ ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
         => ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) ) )
      | ~ ( '#form1076' @ X0 )
      | ( X2 @ ( '#sk336' @ X0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl340]) ).

thf(zip_derived_cl342,plain,
    ! [X0: a > $o,X2: a > $o] :
      ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
      | ( X2 @ ( '#sk336' @ X0 ) )
      | ~ ( '#form1076' @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl341]) ).

thf(zip_derived_cl265_003,plain,
    ( '#form811'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl266,plain,
    ( ~ ( ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ ( '#sk236'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( cK @ Y0 @ Y1 )
                   => ( Y0 @ Y1 ) ) )
             => ( Y0
                @ ( '#sk236'
                  @ ( cK
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a > $o] :
                            ( ( !!
                              @ ^ [Y3: a] :
                                  ( ( cK @ Y2 @ Y3 )
                                 => ( Y2 @ Y3 ) ) )
                           => ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
    | '#form811' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl270,plain,
    ( ~ ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0
              @ ( '#sk236'
                @ ( cK
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a > $o] :
                          ( ( !!
                            @ ^ [Y3: a] :
                                ( ( cK @ Y2 @ Y3 )
                               => ( Y2 @ Y3 ) ) )
                         => ( Y2 @ Y1 ) ) ) ) ) ) ) )
    | '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl266]) ).

thf(zip_derived_cl271,plain,
    ( ~ ( ( !!
          @ ^ [Y0: a] :
              ( ( cK
                @ ( '#sk244'
                  @ ( cK
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a > $o] :
                            ( ( !!
                              @ ^ [Y3: a] :
                                  ( ( cK @ Y2 @ Y3 )
                                 => ( Y2 @ Y3 ) ) )
                           => ( Y2 @ Y1 ) ) ) ) )
                @ Y0 )
             => ( '#sk244'
                @ ( cK
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a > $o] :
                          ( ( !!
                            @ ^ [Y3: a] :
                                ( ( cK @ Y2 @ Y3 )
                               => ( Y2 @ Y3 ) ) )
                         => ( Y2 @ Y1 ) ) ) )
                @ Y0 ) ) )
       => ( '#sk244'
          @ ( cK
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) )
          @ ( '#sk236'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) ) ) )
    | '#form811' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl270]) ).

thf(zip_derived_cl273,plain,
    ( ~ ( '#sk244'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) )
        @ ( '#sk236'
          @ ( cK
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    | '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).

thf(zip_derived_cl7,plain,
    ~ ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8258,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8258_004,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8271,plain,
    ( ~ ( '#sk244' @ ( cK @ '#l_lift30859' ) @ ( '#sk236' @ ( cK @ '#l_lift30859' ) ) )
    | '#form811' ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl273,zip_derived_cl8258,zip_derived_cl8258]) ).

thf(zip_derived_cl334_005,plain,
    ! [X0: a > $o,X1: a] :
      ( ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 )
      | ( cK @ X0 @ X1 )
      | ~ '#form811' ),
    inference(simplify,[status(thm)],[zip_derived_cl333]) ).

thf(zip_derived_cl335_006,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form1076' @ X0 )
      | ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl339,plain,
    ! [X0: a > $o,X1: a] :
      ( ( '#form1076' @ X0 )
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X1 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl334,zip_derived_cl335]) ).

thf(zip_derived_cl8258_007,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8273,plain,
    ! [X0: a > $o,X1: a] :
      ( ( '#form1076' @ X0 )
      | ~ '#form811'
      | ( cK @ X0 @ X1 )
      | ~ ( cK @ '#l_lift30859' @ X1 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl339,zip_derived_cl8258]) ).

thf(zip_derived_cl94,plain,
    ! [X2: a > $o] :
      ( ~ ( X2 @ ( '#sk336' @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl98,plain,
    ! [X2: a > $o,X4: a] :
      ( ( ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X4 )
       => ( cK @ X2 @ X4 ) )
      | ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl100,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X4 )
      | ( cK @ X2 @ X4 )
      | ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).

thf(zip_derived_cl8258_008,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8263,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( cK @ '#l_lift30859' @ X4 )
      | ( cK @ X2 @ X4 )
      | ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl100,zip_derived_cl8258]) ).

thf(zip_derived_cl272,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( ( cK
            @ ( '#sk244'
              @ ( cK
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a > $o] :
                        ( ( !!
                          @ ^ [Y3: a] :
                              ( ( cK @ Y2 @ Y3 )
                             => ( Y2 @ Y3 ) ) )
                       => ( Y2 @ Y1 ) ) ) ) )
            @ Y0 )
         => ( '#sk244'
            @ ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) )
    | '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).

thf(zip_derived_cl274,plain,
    ! [X2: a] :
      ( ( ( cK
          @ ( '#sk244'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) )
          @ X2 )
       => ( '#sk244'
          @ ( cK
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) )
          @ X2 ) )
      | '#form811' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl272]) ).

thf(zip_derived_cl275,plain,
    ! [X2: a] :
      ( ~ ( cK
          @ ( '#sk244'
            @ ( cK
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a > $o] :
                      ( ( !!
                        @ ^ [Y2: a] :
                            ( ( cK @ Y1 @ Y2 )
                           => ( Y1 @ Y2 ) ) )
                     => ( Y1 @ Y0 ) ) ) ) )
          @ X2 )
      | ( '#sk244'
        @ ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) )
        @ X2 )
      | '#form811' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl274]) ).

thf(zip_derived_cl8258_009,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8258_010,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8272,plain,
    ! [X2: a] :
      ( ~ ( cK @ ( '#sk244' @ ( cK @ '#l_lift30859' ) ) @ X2 )
      | ( '#sk244' @ ( cK @ '#l_lift30859' ) @ X2 )
      | '#form811' ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl275,zip_derived_cl8258,zip_derived_cl8258]) ).

thf(zip_derived_cl8258_011,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl3_012,plain,
    ! [X2: a > $o] :
      ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( X2 @ Y1 )
               => ( Y0 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: a] :
                ( ( cK @ X2 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl5,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( X2 @ Y0 )
           => ( X4 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl8,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( X4 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( ( X2 @ ( '#sk12' @ X2 @ X4 ) )
         => ( X4 @ ( '#sk12' @ X2 @ X4 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( X2 @ ( '#sk12' @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X2 @ X6 )
       => ( cK @ X4 @ X6 ) )
      | ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK @ X4 @ X6 )
      | ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl7_013,plain,
    ~ ( cK
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( cK @ Y1 @ Y2 )
                   => ( Y1 @ Y2 ) ) )
             => ( Y1 @ Y0 ) ) )
      @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8258_014,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8259,plain,
    ~ ( cK @ '#l_lift30859' @ '#sk1' ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl7,zip_derived_cl8258]) ).

thf(zip_derived_cl13,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl16,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X2 @ X6 )
       => ( cK @ X4 @ X6 ) )
      | ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK @ X4 @ X6 )
      | ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl9_015,plain,
    ! [X2: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( X2 @ Y0 ) ) )
     => ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl11,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( cK @ X2 @ Y0 )
             => ( X2 @ Y0 ) ) )
      | ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a > $o] :
      ( ~ ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
         => ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) ) )
      | ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl17,plain,
    ! [X2: a > $o] :
      ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
      | ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a > $o] :
      ( ~ ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
      | ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl5_016,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( X2 @ Y0 )
           => ( X4 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl22,plain,
    ! [X0: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( X0 @ Y0 )
           => ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X0 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl58,plain,
    ! [X0: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X0 @ Y0 )
             => ( !!
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( cK @ Y1 @ Y2 )
                         => ( Y1 @ Y2 ) ) )
                   => ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X0 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl59,plain,
    ! [X0: a > $o] :
      ( ~ ( ( X0 @ ( '#sk236' @ X0 ) )
         => ( !!
            @ ^ [Y0: a > $o] :
                ( ( !!
                  @ ^ [Y1: a] :
                      ( ( cK @ Y0 @ Y1 )
                     => ( Y0 @ Y1 ) ) )
               => ( Y0 @ ( '#sk236' @ X0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X0 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl60,plain,
    ! [X0: a > $o] :
      ( ( X0 @ ( '#sk236' @ X0 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X0 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( cK @ Y2 @ Y3 )
                           => ( Y2 @ Y3 ) ) )
                     => ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl62,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( cK @ X0 @ X2 )
       => ( cK
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( cK @ Y1 @ Y2 )
                       => ( Y1 @ Y2 ) ) )
                 => ( Y1 @ Y0 ) ) )
          @ X2 ) )
      | ( X0 @ ( '#sk236' @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl64,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK @ X0 @ X2 )
      | ( cK
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( cK @ Y1 @ Y2 )
                     => ( Y1 @ Y2 ) ) )
               => ( Y1 @ Y0 ) ) )
        @ X2 )
      | ( X0 @ ( '#sk236' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl8258_017,plain,
    ! [X1: a] :
      ( ( '#l_lift30859' @ X1 )
      = ( !!
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( cK @ Y0 @ Y1 )
                 => ( Y0 @ Y1 ) ) )
           => ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8260,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK @ X0 @ X2 )
      | ( cK @ '#l_lift30859' @ X2 )
      | ( X0 @ ( '#sk236' @ X0 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl64,zip_derived_cl8258]) ).

thf(zip_derived_cl8282,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl342,zip_derived_cl8271,zip_derived_cl8273,zip_derived_cl8263,zip_derived_cl8272,zip_derived_cl8258,zip_derived_cl19,zip_derived_cl8259,zip_derived_cl20,zip_derived_cl17,zip_derived_cl18,zip_derived_cl8260]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV310^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qWfSiDq9kE true
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 04:23:32 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.21/0.65  % Total configuration time : 828
% 0.21/0.65  % Estimated wc time : 1656
% 0.21/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 51.58/7.28  % Solved by lams/20_acsne_simpl.sh.
% 51.58/7.28  % done 288 iterations in 6.414s
% 51.58/7.28  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 51.58/7.28  % SZS output start Refutation
% See solution above
% 51.58/7.28  
% 51.58/7.28  
% 51.58/7.28  % Terminating...
% 52.20/7.40  % Runner terminated.
% 52.20/7.40  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------