TSTP Solution File: SEV243^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV243^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1Qr8gAllTa true

% Computer : n006.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 20:00:10 EDT 2023

% Result   : Theorem 50.94s 7.20s
% Output   : Refutation 50.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  102 (  18 unt;  10 typ;   0 def)
%            Number of atoms       :  550 (  17 equ;   0 cnn)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives : 1763 (  82   ~;  96   |;  92   &;1091   @)
%                                         (   5 <=>; 170  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  11 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  195 ( 195   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (   9 usr;   5 con; 0-2 aty)
%                                         ( 143  !!;  84  ??;   0 @@+;   0 @@-)
%            Number of variables   :  413 ( 277   ^; 132   !;   4   ?; 413   :)

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

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

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

thf('#l_lift29753_type',type,
    '#l_lift29753': a > $o ).

thf('#sk55_type',type,
    '#sk55': ( a > $o ) > a ).

thf('#sk61_type',type,
    '#sk61': ( a > $o ) > a > $o ).

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

thf('#form1220_type',type,
    '#form1220': $o ).

thf('#sk101_type',type,
    '#sk101': ( a > $o ) > a ).

thf('#sk906_type',type,
    '#sk906': a > $o ).

thf(cTHM116_C_pme,conjecture,
    ( ! [Y: a > $o,X: a > $o] :
        ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: a] :
            ( ( cK @ X @ Xx )
           => ( cK @ Y @ Xx ) ) )
   => ! [Xx: a] :
        ( ( cK
          @ ^ [Xx0: a] :
            ? [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( S @ Xx1 )
                 => ( cK @ S @ Xx1 ) )
              & ( S @ Xx0 ) )
          @ Xx )
      <=> ? [S: a > $o] :
            ( ! [Xx0: a] :
                ( ( S @ Xx0 )
               => ( cK @ S @ Xx0 ) )
            & ( S @ Xx ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ! [Y: a > $o,X: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cK @ X @ Xx )
             => ( cK @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ( cK
            @ ^ [Xx0: a] :
              ? [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( S @ Xx1 )
                   => ( cK @ S @ Xx1 ) )
                & ( S @ Xx0 ) )
            @ Xx )
        <=> ? [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( S @ Xx0 )
                 => ( cK @ S @ Xx0 ) )
              & ( S @ Xx ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM116_C_pme]) ).

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

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

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

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

thf(zip_derived_cl7,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X4 @ Y0 )
             => ( X2 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X4 @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( ( X4 @ ( '#sk12' @ X2 @ X4 ) )
         => ( X2 @ ( '#sk12' @ X2 @ X4 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X4 @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl9,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( X4 @ ( '#sk12' @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X4 @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl11,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X4 @ X6 )
       => ( cK @ X2 @ X6 ) )
      | ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl13,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X4 @ X6 )
      | ( cK @ X2 @ X6 )
      | ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl5_001,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( X4 @ Y0 )
           => ( X2 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X4 @ Y0 )
           => ( cK @ X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl15,plain,
    ! [X0: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
           => ( X0 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl17,plain,
    ! [X0: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ??
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 )
                         => ( cK @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) )
             => ( X0 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl18,plain,
    ! [X0: a > $o] :
      ( ~ ( ( ??
            @ ^ [Y0: a > $o] :
                ( ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( cK @ Y0 @ Y1 ) ) )
                & ( Y0 @ ( '#sk55' @ X0 ) ) ) )
         => ( X0 @ ( '#sk55' @ X0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl20,plain,
    ! [X0: a > $o] :
      ( ~ ( X0 @ ( '#sk55' @ X0 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl22,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
       => ( cK @ X0 @ X2 ) )
      | ~ ( X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl25,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
      | ( cK @ X0 @ X2 )
      | ~ ( X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

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

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

thf(zip_derived_cl6,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7617,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7619,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK @ '#l_lift29753' @ X2 )
      | ( cK @ X0 @ X2 )
      | ~ ( X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl25,zip_derived_cl7617]) ).

thf(zip_derived_cl19,plain,
    ! [X0: a > $o] :
      ( ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ ( '#sk55' @ X0 ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl21,plain,
    ! [X0: a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( ( '#sk61' @ X0 @ Y0 )
             => ( cK @ ( '#sk61' @ X0 ) @ Y0 ) ) )
        & ( '#sk61' @ X0 @ ( '#sk55' @ X0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl24,plain,
    ! [X0: a > $o] :
      ( ( '#sk61' @ X0 @ ( '#sk55' @ X0 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
       => ( cK @ X0 @ X2 ) )
      | ( '#sk61' @ X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl29,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
      | ( cK @ X0 @ X2 )
      | ( '#sk61' @ X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl7617_002,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7620,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( cK @ '#l_lift29753' @ X2 )
      | ( cK @ X0 @ X2 )
      | ( '#sk61' @ X0 @ ( '#sk55' @ X0 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl29,zip_derived_cl7617]) ).

thf(zip_derived_cl23,plain,
    ! [X0: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk61' @ X0 @ Y0 )
           => ( cK @ ( '#sk61' @ X0 ) @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl26,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( '#sk61' @ X0 @ X2 )
       => ( cK @ ( '#sk61' @ X0 ) @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl28,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( '#sk61' @ X0 @ X2 )
      | ( cK @ ( '#sk61' @ X0 ) @ X2 )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( cK @ X0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl30,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 )
       => ( cK @ X0 @ X4 ) )
      | ( cK @ ( '#sk61' @ X0 ) @ X2 )
      | ~ ( '#sk61' @ X0 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl31,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ~ ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 )
      | ( cK @ X0 @ X4 )
      | ~ ( '#sk61' @ X0 @ X2 )
      | ( cK @ ( '#sk61' @ X0 ) @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl7617_003,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7621,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ~ ( cK @ '#l_lift29753' @ X4 )
      | ( cK @ X0 @ X4 )
      | ~ ( '#sk61' @ X0 @ X2 )
      | ( cK @ ( '#sk61' @ X0 ) @ X2 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl31,zip_derived_cl7617]) ).

thf(zip_derived_cl3_004,plain,
    ! [X2: a > $o] :
      ( !!
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( X2 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: a] :
                ( ( cK @ Y0 @ Y1 )
               => ( cK @ X2 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: a > $o] :
        ( ( !!
          @ ^ [Y1: a] :
              ( ( Y0 @ Y1 )
             => ( ??
                @ ^ [Y2: a > $o] :
                    ( ( !!
                      @ ^ [Y3: a] :
                          ( ( Y2 @ Y3 )
                         => ( cK @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) ) ) )
       => ( !!
          @ ^ [Y1: a] :
              ( ( cK @ Y0 @ Y1 )
             => ( cK
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a > $o] :
                        ( ( !!
                          @ ^ [Y4: a] :
                              ( ( Y3 @ Y4 )
                             => ( cK @ Y3 @ Y4 ) ) )
                        & ( Y3 @ Y2 ) ) )
                @ Y1 ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl32,plain,
    ! [X2: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( X2 @ Y0 )
           => ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( ??
                @ ^ [Y1: a > $o] :
                    ( ( !!
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 )
                         => ( cK @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a > $o] :
      ( ~ ( ( X2 @ ( '#sk101' @ X2 ) )
         => ( ??
            @ ^ [Y0: a > $o] :
                ( ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( cK @ Y0 @ Y1 ) ) )
                & ( Y0 @ ( '#sk101' @ X2 ) ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a > $o] :
      ( ~ ( ??
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( cK @ Y0 @ Y1 ) ) )
              & ( Y0 @ ( '#sk101' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( ( X4 @ Y0 )
               => ( cK @ X4 @ Y0 ) ) )
          & ( X4 @ ( '#sk101' @ X2 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl42,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X4 @ Y0 )
             => ( cK @ X4 @ Y0 ) ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( ( X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
         => ( cK @ X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl44,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ( X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X2 @ X6 )
       => ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X6 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) )
      | ( X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl48,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X6 )
      | ( X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl7617_005,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7623,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK @ '#l_lift29753' @ X6 )
      | ( X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl48,zip_derived_cl7617]) ).

thf(zip_derived_cl45,plain,
    ! [X2: a > $o,X4: a > $o] :
      ( ~ ( cK @ X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X2 @ X6 )
       => ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X6 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) )
      | ~ ( cK @ X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl49,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X6 )
      | ~ ( cK @ X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl7617_006,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7624,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X2 @ X6 )
      | ( cK @ '#l_lift29753' @ X6 )
      | ~ ( cK @ X4 @ ( '#sk12' @ ( cK @ X4 ) @ X4 ) )
      | ~ ( X4 @ ( '#sk101' @ X2 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl49,zip_derived_cl7617]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk101' @ X2 ) )
      | ( !!
        @ ^ [Y0: a] :
            ( ( cK @ X2 @ Y0 )
           => ( cK
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( cK @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl38,plain,
    ! [X2: a > $o,X4: a] :
      ( ( ( cK @ X2 @ X4 )
       => ( cK
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 ) )
      | ( X2 @ ( '#sk101' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( cK @ X2 @ X4 )
      | ( cK
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X4 )
      | ( X2 @ ( '#sk101' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl7617_007,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7622,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( cK @ X2 @ X4 )
      | ( cK @ '#l_lift29753' @ X4 )
      | ( X2 @ ( '#sk101' @ X2 ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl41,zip_derived_cl7617]) ).

thf(zip_derived_cl6_008,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl232,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
    | ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl262,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk906' @ Y0 )
           => ( cK @ '#sk906' @ Y0 ) ) )
      & ( '#sk906' @ '#sk1' ) )
    | ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl232]) ).

thf(zip_derived_cl264,plain,
    ( ( '#sk906' @ '#sk1' )
    | ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl262]) ).

thf(zip_derived_cl6_009,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl267,plain,
    ( ~ ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk1' ) ) )
    | ( '#sk906' @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl264,zip_derived_cl6]) ).

thf(zip_derived_cl412,plain,
    ( '#form1220'
    | ~ ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk1' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl413,plain,
    ! [X2: a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( ( X2 @ Y0 )
               => ( cK @ X2 @ Y0 ) ) )
          & ( X2 @ '#sk1' ) )
      | '#form1220' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl412]) ).

thf(zip_derived_cl417,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( cK @ X2 @ Y0 ) ) )
      | ~ ( X2 @ '#sk1' )
      | '#form1220' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl413]) ).

thf(zip_derived_cl418,plain,
    ! [X2: a > $o] :
      ( ~ ( ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
         => ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) ) )
      | '#form1220'
      | ~ ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl417]) ).

thf(zip_derived_cl419,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
      | ~ ( X2 @ '#sk1' )
      | '#form1220' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl418]) ).

thf(zip_derived_cl7617_010,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

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

thf(zip_derived_cl12,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ( ( cK @ X4 @ X6 )
       => ( cK @ X2 @ X6 ) )
      | ~ ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X4 @ X6 )
      | ( cK @ X2 @ X6 )
      | ~ ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl420,plain,
    ! [X2: a > $o] :
      ( ~ ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
      | ~ ( X2 @ '#sk1' )
      | '#form1220' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl418]) ).

thf(zip_derived_cl6_011,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl233,plain,
    ( ~ ( cK
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk1' )
    | ~ ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk1' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl412_012,plain,
    ( '#form1220'
    | ~ ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk1' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl612,plain,
    ( ~ '#form1220'
    | ~ ( cK
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a > $o] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( cK @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk1' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl233,zip_derived_cl412]) ).

thf(zip_derived_cl7617_013,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7637,plain,
    ( ~ '#form1220'
    | ~ ( cK @ '#l_lift29753' @ '#sk1' ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl612,zip_derived_cl7617]) ).

thf(zip_derived_cl13_014,plain,
    ! [X2: a > $o,X4: a > $o,X6: a] :
      ( ~ ( cK @ X4 @ X6 )
      | ( cK @ X2 @ X6 )
      | ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl6_015,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl231,plain,
    ! [X0: a > $o] :
      ( ~ ( ??
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( cK @ Y0 @ Y1 ) ) )
              & ( Y0 @ '#sk1' ) ) )
      | ( X0
        @ ( '#sk12'
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a > $o] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( cK @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X0 ) )
      | ~ ( cK @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl6]) ).

thf(zip_derived_cl7617_016,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7638,plain,
    ! [X0: a > $o] :
      ( ~ ( ??
          @ ^ [Y0: a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( cK @ Y0 @ Y1 ) ) )
              & ( Y0 @ '#sk1' ) ) )
      | ( X0 @ ( '#sk12' @ '#l_lift29753' @ X0 ) )
      | ~ ( cK @ X0 @ '#sk1' ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl231,zip_derived_cl7617]) ).

thf(zip_derived_cl6_017,plain,
    ( ( cK
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( cK @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7617_018,plain,
    ! [X1: a] :
      ( ( '#l_lift29753' @ X1 )
      = ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( cK @ Y0 @ Y1 ) ) )
            & ( Y0 @ X1 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl7618,plain,
    ( ( cK @ '#l_lift29753' @ '#sk1' )
   != ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( cK @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk1' ) ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl6,zip_derived_cl7617]) ).

thf(zip_derived_cl7642,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl13,zip_derived_cl7619,zip_derived_cl7620,zip_derived_cl7621,zip_derived_cl7623,zip_derived_cl7624,zip_derived_cl7622,zip_derived_cl419,zip_derived_cl7617,zip_derived_cl14,zip_derived_cl420,zip_derived_cl7637,zip_derived_cl7638,zip_derived_cl7618]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEV243^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1Qr8gAllTa true
% 0.13/0.35  % Computer : n006.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 02:47:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.36  % Python version: Python 3.6.8
% 0.13/0.36  % Running in HO mode
% 0.21/0.67  % Total configuration time : 828
% 0.21/0.67  % Estimated wc time : 1656
% 0.21/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 50.94/7.20  % Solved by lams/20_acsne_simpl.sh.
% 50.94/7.20  % done 470 iterations in 6.336s
% 50.94/7.20  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 50.94/7.20  % SZS output start Refutation
% See solution above
% 50.94/7.20  
% 50.94/7.20  
% 50.94/7.20  % Terminating...
% 51.68/7.28  % Runner terminated.
% 51.68/7.30  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------