TSTP Solution File: SEV140^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV140^5 : 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.n3iWP6O8yy true

% Computer : n031.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 19:59:44 EDT 2023

% Result   : Theorem 30.10s 4.60s
% Output   : Refutation 30.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  169 (  10 unt;  18 typ;   0 def)
%            Number of atoms       : 1646 (   0 equ;   1 cnn)
%            Maximal formula atoms :   30 (  10 avg)
%            Number of connectives : 6463 ( 171   ~; 291   |; 357   &;4048   @)
%                                         (   0 <=>; 560  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (  15 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  502 ( 502   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   5 con; 0-2 aty)
%                                         (1036  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 1202 (1036   ^; 166   !;   0   ?;1202   :)

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

thf('#sk3_type',type,
    '#sk3': a ).

thf('#sk806_type',type,
    '#sk806': ( a > a > $o ) > a ).

thf('#sk41_type',type,
    '#sk41': ( a > a > $o ) > a ).

thf('#sk4_type',type,
    '#sk4': a ).

thf('#sk1315_type',type,
    '#sk1315': ( a > a > $o ) > a ).

thf('#sk1275_type',type,
    '#sk1275': ( a > a > $o ) > a ).

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

thf('#form1894_type',type,
    '#form1894': ( a > a > $o ) > $o ).

thf('#form695_type',type,
    '#form695': ( a > a > $o ) > $o ).

thf('#sk54_type',type,
    '#sk54': ( a > a > $o ) > a ).

thf('#sk109_type',type,
    '#sk109': ( a > a > $o ) > a ).

thf('#form646_type',type,
    '#form646': ( a > a > $o ) > $o ).

thf('#sk696_type',type,
    '#sk696': ( a > a > $o ) > a ).

thf('#sk85_type',type,
    '#sk85': ( a > a > $o ) > a ).

thf('#sk30_type',type,
    '#sk30': ( a > a > $o ) > a ).

thf('#sk5_type',type,
    '#sk5': a > a > $o ).

thf('#sk2_type',type,
    '#sk2': a > a > $o ).

thf(cTHM250C_pme,conjecture,
    ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
      ( ! [Xp1: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                ( ( ( Xp1 @ Xy0 @ Xz )
                  & ( Xp1 @ Xx0 @ Xy0 ) )
               => ( Xp1 @ Xx0 @ Xz ) )
            & ! [Xx0: a,Xy0: a] :
                ( ( ! [Xp10: a > a > $o] :
                      ( ( ! [Xx1: a,Xy1: a,Xz: a] :
                            ( ( ( Xp10 @ Xy1 @ Xz )
                              & ( Xp10 @ Xx1 @ Xy1 ) )
                           => ( Xp10 @ Xx1 @ Xz ) )
                        & ! [Xx1: a,Xy1: a] :
                            ( ( S @ Xx1 @ Xy1 )
                           => ( Xp10 @ Xx1 @ Xy1 ) ) )
                     => ( Xp10 @ Xx0 @ Xy0 ) )
                  | ! [Xp10: a > a > $o] :
                      ( ( ! [Xx1: a,Xy1: a,Xz: a] :
                            ( ( ( Xp10 @ Xy1 @ Xz )
                              & ( Xp10 @ Xx1 @ Xy1 ) )
                           => ( Xp10 @ Xx1 @ Xz ) )
                        & ! [Xx1: a,Xy1: a] :
                            ( ( R @ Xx1 @ Xy1 )
                           => ( Xp10 @ Xx1 @ Xy1 ) ) )
                     => ( Xp10 @ Xx0 @ Xy0 ) ) )
               => ( Xp1 @ Xx0 @ Xy0 ) ) )
         => ( Xp1 @ Xx @ Xy ) )
     => ! [Xp1: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                ( ( ( Xp1 @ Xy0 @ Xz )
                  & ( Xp1 @ Xx0 @ Xy0 ) )
               => ( Xp1 @ Xx0 @ Xz ) )
            & ! [Xx0: a,Xy0: a] :
                ( ( ( S @ Xx0 @ Xy0 )
                  | ( R @ Xx0 @ Xy0 ) )
               => ( Xp1 @ Xx0 @ Xy0 ) ) )
         => ( Xp1 @ Xx @ Xy ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
        ( ! [Xp1: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                  ( ( ( Xp1 @ Xy0 @ Xz )
                    & ( Xp1 @ Xx0 @ Xy0 ) )
                 => ( Xp1 @ Xx0 @ Xz ) )
              & ! [Xx0: a,Xy0: a] :
                  ( ( ! [Xp10: a > a > $o] :
                        ( ( ! [Xx1: a,Xy1: a,Xz: a] :
                              ( ( ( Xp10 @ Xy1 @ Xz )
                                & ( Xp10 @ Xx1 @ Xy1 ) )
                             => ( Xp10 @ Xx1 @ Xz ) )
                          & ! [Xx1: a,Xy1: a] :
                              ( ( S @ Xx1 @ Xy1 )
                             => ( Xp10 @ Xx1 @ Xy1 ) ) )
                       => ( Xp10 @ Xx0 @ Xy0 ) )
                    | ! [Xp10: a > a > $o] :
                        ( ( ! [Xx1: a,Xy1: a,Xz: a] :
                              ( ( ( Xp10 @ Xy1 @ Xz )
                                & ( Xp10 @ Xx1 @ Xy1 ) )
                             => ( Xp10 @ Xx1 @ Xz ) )
                          & ! [Xx1: a,Xy1: a] :
                              ( ( R @ Xx1 @ Xy1 )
                             => ( Xp10 @ Xx1 @ Xy1 ) ) )
                       => ( Xp10 @ Xx0 @ Xy0 ) ) )
                 => ( Xp1 @ Xx0 @ Xy0 ) ) )
           => ( Xp1 @ Xx @ Xy ) )
       => ! [Xp1: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                  ( ( ( Xp1 @ Xy0 @ Xz )
                    & ( Xp1 @ Xx0 @ Xy0 ) )
                 => ( Xp1 @ Xx0 @ Xz ) )
              & ! [Xx0: a,Xy0: a] :
                  ( ( ( S @ Xx0 @ Xy0 )
                    | ( R @ Xx0 @ Xy0 ) )
                 => ( Xp1 @ Xx0 @ Xy0 ) ) )
           => ( Xp1 @ Xx @ Xy ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM250C_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( !!
          @ ^ [Y1: a > a > $o] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( !!
                        @ ^ [Y4: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( !!
                                        @ ^ [Y7: a] :
                                            ( ( ( Y4 @ Y6 @ Y7 )
                                              & ( Y4 @ Y5 @ Y6 ) )
                                           => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                              & ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( !!
                                            @ ^ [Y7: a > a > $o] :
                                                ( ( ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( !!
                                                            @ ^ [Y10: a] :
                                                                ( ( ( Y7 @ Y9 @ Y10 )
                                                                  & ( Y7 @ Y8 @ Y9 ) )
                                                               => ( Y7 @ Y8 @ Y10 ) ) ) ) )
                                                  & ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( Y1 @ Y8 @ Y9 )
                                                           => ( Y7 @ Y8 @ Y9 ) ) ) ) )
                                               => ( Y7 @ Y5 @ Y6 ) ) )
                                          | ( !!
                                            @ ^ [Y7: a > a > $o] :
                                                ( ( ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( !!
                                                            @ ^ [Y10: a] :
                                                                ( ( ( Y7 @ Y9 @ Y10 )
                                                                  & ( Y7 @ Y8 @ Y9 ) )
                                                               => ( Y7 @ Y8 @ Y10 ) ) ) ) )
                                                  & ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( Y0 @ Y8 @ Y9 )
                                                           => ( Y7 @ Y8 @ Y9 ) ) ) ) )
                                               => ( Y7 @ Y5 @ Y6 ) ) ) )
                                       => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                           => ( Y4 @ Y2 @ Y3 ) ) )
                     => ( !!
                        @ ^ [Y4: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( !!
                                        @ ^ [Y7: a] :
                                            ( ( ( Y4 @ Y6 @ Y7 )
                                              & ( Y4 @ Y5 @ Y6 ) )
                                           => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                              & ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y1 @ Y5 @ Y6 )
                                          | ( Y0 @ Y5 @ Y6 ) )
                                       => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                           => ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( !!
                    @ ^ [Y3: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y3 @ Y5 @ Y6 )
                                          & ( Y3 @ Y4 @ Y5 ) )
                                       => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( !!
                                        @ ^ [Y6: a > a > $o] :
                                            ( ( ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( ( Y6 @ Y8 @ Y9 )
                                                              & ( Y6 @ Y7 @ Y8 ) )
                                                           => ( Y6 @ Y7 @ Y9 ) ) ) ) )
                                              & ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( Y0 @ Y7 @ Y8 )
                                                       => ( Y6 @ Y7 @ Y8 ) ) ) ) )
                                           => ( Y6 @ Y4 @ Y5 ) ) )
                                      | ( !!
                                        @ ^ [Y6: a > a > $o] :
                                            ( ( ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( ( Y6 @ Y8 @ Y9 )
                                                              & ( Y6 @ Y7 @ Y8 ) )
                                                           => ( Y6 @ Y7 @ Y9 ) ) ) ) )
                                              & ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( '#sk1' @ Y7 @ Y8 )
                                                       => ( Y6 @ Y7 @ Y8 ) ) ) ) )
                                           => ( Y6 @ Y4 @ Y5 ) ) ) )
                                   => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                       => ( Y3 @ Y1 @ Y2 ) ) )
                 => ( !!
                    @ ^ [Y3: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y3 @ Y5 @ Y6 )
                                          & ( Y3 @ Y4 @ Y5 ) )
                                       => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y0 @ Y4 @ Y5 )
                                      | ( '#sk1' @ Y4 @ Y5 ) )
                                   => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                       => ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( !!
                                    @ ^ [Y5: a > a > $o] :
                                        ( ( ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( ( Y5 @ Y7 @ Y8 )
                                                          & ( Y5 @ Y6 @ Y7 ) )
                                                       => ( Y5 @ Y6 @ Y8 ) ) ) ) )
                                          & ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( '#sk2' @ Y6 @ Y7 )
                                                   => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                       => ( Y5 @ Y3 @ Y4 ) ) )
                                  | ( !!
                                    @ ^ [Y5: a > a > $o] :
                                        ( ( ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( ( Y5 @ Y7 @ Y8 )
                                                          & ( Y5 @ Y6 @ Y7 ) )
                                                       => ( Y5 @ Y6 @ Y8 ) ) ) ) )
                                          & ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( '#sk1' @ Y6 @ Y7 )
                                                   => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                       => ( Y5 @ Y3 @ Y4 ) ) ) )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) )
             => ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( '#sk2' @ Y3 @ Y4 )
                                  | ( '#sk1' @ Y3 @ Y4 ) )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( ( !!
            @ ^ [Y1: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( Y1 @ Y3 @ Y4 )
                                  & ( Y1 @ Y2 @ Y3 ) )
                               => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( !!
                                @ ^ [Y4: a > a > $o] :
                                    ( ( ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( ( Y4 @ Y6 @ Y7 )
                                                      & ( Y4 @ Y5 @ Y6 ) )
                                                   => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                                      & ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( '#sk2' @ Y5 @ Y6 )
                                               => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                                   => ( Y4 @ Y2 @ Y3 ) ) )
                              | ( !!
                                @ ^ [Y4: a > a > $o] :
                                    ( ( ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( ( Y4 @ Y6 @ Y7 )
                                                      & ( Y4 @ Y5 @ Y6 ) )
                                                   => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                                      & ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( '#sk1' @ Y5 @ Y6 )
                                               => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                                   => ( Y4 @ Y2 @ Y3 ) ) ) )
                           => ( Y1 @ Y2 @ Y3 ) ) ) ) )
               => ( Y1 @ '#sk3' @ Y0 ) ) )
         => ( !!
            @ ^ [Y1: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( Y1 @ Y3 @ Y4 )
                                  & ( Y1 @ Y2 @ Y3 ) )
                               => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( '#sk2' @ Y2 @ Y3 )
                              | ( '#sk1' @ Y2 @ Y3 ) )
                           => ( Y1 @ Y2 @ Y3 ) ) ) ) )
               => ( Y1 @ '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ~ ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( !!
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y5 @ Y6 )
                                                  & ( Y3 @ Y4 @ Y5 ) )
                                               => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                  & ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( '#sk2' @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !!
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y5 @ Y6 )
                                                  & ( Y3 @ Y4 @ Y5 ) )
                                               => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                  & ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( '#sk1' @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ '#sk3' @ '#sk4' ) ) )
     => ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( '#sk2' @ Y1 @ Y2 )
                          | ( '#sk1' @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: a > a > $o] :
        ( ( ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( ( Y0 @ Y2 @ Y3 )
                          & ( Y0 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y3 ) ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( !!
                        @ ^ [Y3: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( !!
                                        @ ^ [Y6: a] :
                                            ( ( ( Y3 @ Y5 @ Y6 )
                                              & ( Y3 @ Y4 @ Y5 ) )
                                           => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                              & ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( '#sk2' @ Y4 @ Y5 )
                                       => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                           => ( Y3 @ Y1 @ Y2 ) ) )
                      | ( !!
                        @ ^ [Y3: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( !!
                                        @ ^ [Y6: a] :
                                            ( ( ( Y3 @ Y5 @ Y6 )
                                              & ( Y3 @ Y4 @ Y5 ) )
                                           => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                              & ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( '#sk1' @ Y4 @ Y5 )
                                       => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                           => ( Y3 @ Y1 @ Y2 ) ) ) )
                   => ( Y0 @ Y1 @ Y2 ) ) ) ) )
       => ( Y0 @ '#sk3' @ '#sk4' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ! [X2: a > a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X2 @ Y1 @ Y2 )
                          & ( X2 @ Y0 @ Y1 ) )
                       => ( X2 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( ( !!
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y3: a] :
                                    ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y4 @ Y5 )
                                              & ( Y2 @ Y3 @ Y4 ) )
                                           => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                              & ( !!
                                @ ^ [Y3: a] :
                                    ( !!
                                    @ ^ [Y4: a] :
                                        ( ( '#sk2' @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) )
                      | ( !!
                        @ ^ [Y2: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y3: a] :
                                    ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( ( Y2 @ Y4 @ Y5 )
                                              & ( Y2 @ Y3 @ Y4 ) )
                                           => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                              & ( !!
                                @ ^ [Y3: a] :
                                    ( !!
                                    @ ^ [Y4: a] :
                                        ( ( '#sk1' @ Y3 @ Y4 )
                                       => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                           => ( Y2 @ Y0 @ Y1 ) ) ) )
                   => ( X2 @ Y0 @ Y1 ) ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( X2 @ Y0 @ Y1 )
                    & ( X2 @ ( '#sk30' @ X2 ) @ Y0 ) )
                 => ( X2 @ ( '#sk30' @ X2 ) @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl21,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( X2 @ ( '#sk41' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
             => ( X2 @ ( '#sk30' @ X2 ) @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl24,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
            & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
         => ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    ! [X2: a > a > $o] :
      ( ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
        & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl33,plain,
    ! [X2: a > a > $o] :
      ( ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk2' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
                | ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk1' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) ) )
             => ( X2 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl40,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk2' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
            | ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk1' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) )
         => ( X2 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a > a > $o] :
      ( ~ ( X2 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl7_001,plain,
    ! [X2: a > a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl9,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
   => ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl205,plain,
    ( ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl206,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl205]) ).

thf(zip_derived_cl207,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  & ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ Y0 ) )
               => ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ Y1 ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl208,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( '#sk1' @ ( '#sk41' @ '#sk1' ) @ Y0 )
              & ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk41' @ '#sk1' ) ) )
           => ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl207]) ).

thf(zip_derived_cl209,plain,
    ( ~ ( ( ( '#sk1' @ ( '#sk41' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
          & ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk41' @ '#sk1' ) ) )
       => ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl208]) ).

thf(zip_derived_cl211,plain,
    ( ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl209]) ).

thf(zip_derived_cl214,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( !!
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y3 @ Y4 )
                                      & ( Y1 @ Y2 @ Y3 ) )
                                   => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( '#sk2' @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ ( '#sk85' @ '#sk1' ) @ Y0 ) ) )
              | ( !!
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y3 @ Y4 )
                                      & ( Y1 @ Y2 @ Y3 ) )
                                   => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( '#sk1' @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ ( '#sk85' @ '#sk1' ) @ Y0 ) ) ) )
           => ( '#sk1' @ ( '#sk85' @ '#sk1' ) @ Y0 ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' )
    | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl211]) ).

thf(zip_derived_cl217,plain,
    ( ~ ( ( ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk2' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) )
          | ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk1' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) ) )
       => ( '#sk1' @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) )
    | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl214]) ).

thf(zip_derived_cl220,plain,
    ( ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' )
    | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl217]) ).

thf(zip_derived_cl226,plain,
    ( ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) )
    | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
    | ( '#sk1' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl220]) ).

thf(zip_derived_cl32,plain,
    ! [X2: a > a > $o] :
      ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk2' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
                | ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk1' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) ) )
             => ( X2 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk2' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
            | ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk1' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) )
         => ( X2 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a > a > $o] :
      ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl48,plain,
    ! [X2: a > a > $o] :
      ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl54,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X4 @ Y1 @ Y2 )
                          & ( X4 @ Y0 @ Y1 ) )
                       => ( X4 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X4 @ Y0 @ Y1 ) ) ) ) )
       => ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl63,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X4 @ Y1 @ Y2 )
                          & ( X4 @ Y0 @ Y1 ) )
                       => ( X4 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X4 @ Y0 @ Y1 ) ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl66,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X4 @ Y1 @ Y2 )
                        & ( X4 @ Y0 @ Y1 ) )
                     => ( X4 @ Y0 @ Y2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl69,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( X4 @ Y0 @ Y1 )
                    & ( X4 @ ( '#sk30' @ X4 ) @ Y0 ) )
                 => ( X4 @ ( '#sk30' @ X4 ) @ Y1 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl72,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( X4 @ ( '#sk41' @ X4 ) @ Y0 )
                & ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk41' @ X4 ) ) )
             => ( X4 @ ( '#sk30' @ X4 ) @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl75,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( ( ( X4 @ ( '#sk41' @ X4 ) @ ( '#sk54' @ X4 ) )
            & ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk41' @ X4 ) ) )
         => ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk54' @ X4 ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl79,plain,
    ! [X2: a > a > $o] :
      ( ~ ( '#form646' @ X2 )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl229,plain,
    ( ( '#form646' @ '#sk1' )
    | ( '#sk1' @ '#sk3' @ '#sk4' )
    | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl226,zip_derived_cl79]) ).

thf(zip_derived_cl232,plain,
    ! [X2: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X2 @ Y1 @ Y2 )
                          & ( X2 @ Y0 @ Y1 ) )
                       => ( X2 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X2 @ Y0 @ Y1 ) ) ) ) )
       => ( X2 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) )
      | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
      | ( '#sk1' @ '#sk3' @ '#sk4' )
      | ( '#form646' @ '#sk1' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl229]) ).

thf(zip_derived_cl244,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X2 @ Y1 @ Y2 )
                          & ( X2 @ Y0 @ Y1 ) )
                       => ( X2 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X2 @ Y0 @ Y1 ) ) ) ) )
      | ( X2 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) )
      | ( '#form646' @ '#sk1' )
      | ( '#sk1' @ '#sk3' @ '#sk4' )
      | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl232]) ).

thf(zip_derived_cl247,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ~ ( '#sk1' @ ( '#sk30' @ '#sk1' ) @ ( '#sk54' @ '#sk1' ) )
      | ( '#sk1' @ '#sk3' @ '#sk4' )
      | ( '#form646' @ '#sk1' )
      | ( X2 @ ( '#sk85' @ '#sk1' ) @ ( '#sk109' @ '#sk1' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl244]) ).

thf(zip_derived_cl250,plain,
    ! [X2: a > a > $o] :
      ( ( '#form1894' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl251,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( X2 @ Y0 @ Y1 )
                    & ( X2 @ ( '#sk30' @ X2 ) @ Y0 ) )
                 => ( X2 @ ( '#sk30' @ X2 ) @ Y1 ) ) ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl250]) ).

thf(zip_derived_cl256,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( X2 @ ( '#sk41' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
             => ( X2 @ ( '#sk30' @ X2 ) @ Y0 ) ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl251]) ).

thf(zip_derived_cl262,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
            & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
         => ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl256]) ).

thf(zip_derived_cl265,plain,
    ! [X2: a > a > $o] :
      ( ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
        & ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl262]) ).

thf(zip_derived_cl267,plain,
    ! [X2: a > a > $o] :
      ( ( X2 @ ( '#sk41' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl6,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk2' @ Y1 @ Y2 )
                        | ( '#sk1' @ Y1 @ Y2 ) )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ '#sk3' @ '#sk4' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl11,plain,
    ~ ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( '#sk2' @ Y0 @ Y1 )
                    | ( '#sk1' @ Y0 @ Y1 ) )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
     => ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl13,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( ( '#sk5' @ Y1 @ Y2 )
                    & ( '#sk5' @ Y0 @ Y1 ) )
                 => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( '#sk2' @ Y0 @ Y1 )
                | ( '#sk1' @ Y0 @ Y1 ) )
             => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( !!
            @ ^ [Y2: a] :
                ( ( ( '#sk5' @ Y1 @ Y2 )
                  & ( '#sk5' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( '#sk5' @ Y0 @ Y1 )
                & ( '#sk5' @ X2 @ Y0 ) )
             => ( '#sk5' @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: a,X4: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( '#sk5' @ X4 @ Y0 )
            & ( '#sk5' @ X2 @ X4 ) )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( ( '#sk5' @ X4 @ X6 )
        & ( '#sk5' @ X2 @ X4 ) )
     => ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( '#sk5' @ X4 @ X6 )
          & ( '#sk5' @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk5' @ X4 @ X6 )
      | ~ ( '#sk5' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl495,plain,
    ! [X0: a] :
      ( ( '#form1894' @ '#sk5' )
      | ( '#sk5' @ X0 @ ( '#sk54' @ '#sk5' ) )
      | ~ ( '#sk5' @ X0 @ ( '#sk41' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl267,zip_derived_cl35]) ).

thf(zip_derived_cl671,plain,
    ( ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ( '#form1894' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl495]) ).

thf(zip_derived_cl14,plain,
    ~ ( '#sk5' @ '#sk3' @ '#sk4' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl780,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ( '#form1894' @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl671,zip_derived_cl14]) ).

thf(zip_derived_cl266,plain,
    ! [X2: a > a > $o] :
      ( ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl262]) ).

thf(zip_derived_cl801,plain,
    ( ( '#form1894' @ '#sk5' )
    | ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl780,zip_derived_cl266]) ).

thf(zip_derived_cl7_002,plain,
    ! [X2: a > a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
   => ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl14_003,plain,
    ~ ( '#sk5' @ '#sk3' @ '#sk4' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl289,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
   => $false ),
    inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl14]) ).

thf(zip_derived_cl290,plain,
    ( (~)
    @ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl289]) ).

thf(zip_derived_cl291,plain,
    ~ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl290]) ).

thf(zip_derived_cl292,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl291]) ).

thf(zip_derived_cl250_004,plain,
    ! [X2: a > a > $o] :
      ( ( '#form1894' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl293,plain,
    ( ~ ( '#form1894' @ '#sk5' )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk2' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) )
                  | ( !!
                    @ ^ [Y2: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( !!
                                    @ ^ [Y5: a] :
                                        ( ( ( Y2 @ Y4 @ Y5 )
                                          & ( Y2 @ Y3 @ Y4 ) )
                                       => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                          & ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( '#sk1' @ Y3 @ Y4 )
                                   => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                       => ( Y2 @ Y0 @ Y1 ) ) ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl292,zip_derived_cl250]) ).

thf(zip_derived_cl294,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( !!
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y3 @ Y4 )
                                      & ( Y1 @ Y2 @ Y3 ) )
                                   => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( '#sk2' @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) )
              | ( !!
                @ ^ [Y1: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( !!
                                @ ^ [Y4: a] :
                                    ( ( ( Y1 @ Y3 @ Y4 )
                                      & ( Y1 @ Y2 @ Y3 ) )
                                   => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( '#sk1' @ Y2 @ Y3 )
                               => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                   => ( Y1 @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) ) )
           => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl293]) ).

thf(zip_derived_cl295,plain,
    ( ~ ( ( ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk2' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) )
          | ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk1' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) ) )
       => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl294]) ).

thf(zip_derived_cl297,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl295]) ).

thf(zip_derived_cl802,plain,
    ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ),
    inference(clc,[status(thm)],[zip_derived_cl801,zip_derived_cl297]) ).

thf(zip_derived_cl79_005,plain,
    ! [X2: a > a > $o] :
      ( ~ ( '#form646' @ X2 )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl80,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X4 @ Y1 @ Y2 )
                          & ( X4 @ Y0 @ Y1 ) )
                       => ( X4 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( X4 @ Y0 @ Y1 ) ) ) ) )
       => ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ~ ( '#form646' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl81,plain,
    ! [X0: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( '#sk5' @ Y1 @ Y2 )
                          & ( '#sk5' @ Y0 @ Y1 ) )
                       => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
       => ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) )
      | ~ ( '#form646' @ X0 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl1987,plain,
    ! [X0: a > a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( '#sk5' @ Y1 @ Y2 )
                          & ( '#sk5' @ Y0 @ Y1 ) )
                       => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) )
      | ~ ( '#form646' @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl1988,plain,
    ! [X0: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) )
      | ~ ( '#form646' @ X0 )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1987]) ).

thf(zip_derived_cl250_006,plain,
    ! [X2: a > a > $o] :
      ( ( '#form1894' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1989,plain,
    ! [X0: a > a > $o] :
      ( ~ ( '#form1894' @ '#sk5' )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) )
      | ~ ( '#form646' @ X0 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl1988,zip_derived_cl250]) ).

thf(zip_derived_cl268,plain,
    ! [X2: a > a > $o] :
      ( ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk41' @ X2 ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl495_007,plain,
    ! [X0: a] :
      ( ( '#form1894' @ '#sk5' )
      | ( '#sk5' @ X0 @ ( '#sk54' @ '#sk5' ) )
      | ~ ( '#sk5' @ X0 @ ( '#sk41' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl267,zip_derived_cl35]) ).

thf(zip_derived_cl810,plain,
    ( ( '#form1894' @ '#sk5' )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ( '#form1894' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl268,zip_derived_cl495]) ).

thf(zip_derived_cl846,plain,
    ( ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ( '#form1894' @ '#sk5' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl810]) ).

thf(zip_derived_cl266_008,plain,
    ! [X2: a > a > $o] :
      ( ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( '#form1894' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl262]) ).

thf(zip_derived_cl938,plain,
    '#form1894' @ '#sk5',
    inference(clc,[status(thm)],[zip_derived_cl846,zip_derived_cl266]) ).

thf(zip_derived_cl1990,plain,
    ! [X0: a > a > $o] :
      ( ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) )
      | ~ ( '#form646' @ X0 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1989,zip_derived_cl938]) ).

thf(zip_derived_cl1991,plain,
    ! [X0: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk1' @ ( '#sk1275' @ '#sk5' ) @ Y0 )
             => ( '#sk5' @ ( '#sk1275' @ '#sk5' ) @ Y0 ) ) )
      | ~ ( '#form646' @ X0 )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1990]) ).

thf(zip_derived_cl1992,plain,
    ! [X0: a > a > $o] :
      ( ~ ( ( '#sk1' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ) )
         => ( '#sk5' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ) ) )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) )
      | ~ ( '#form646' @ X0 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1991]) ).

thf(zip_derived_cl1994,plain,
    ! [X0: a > a > $o] :
      ( ~ ( '#sk5' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ) )
      | ~ ( '#form646' @ X0 )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1992]) ).

thf(zip_derived_cl802_009,plain,
    ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ),
    inference(clc,[status(thm)],[zip_derived_cl801,zip_derived_cl297]) ).

thf(zip_derived_cl1993,plain,
    ! [X0: a > a > $o] :
      ( ( '#sk1' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ) )
      | ~ ( '#form646' @ X0 )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1992]) ).

thf(zip_derived_cl2001,plain,
    ( ~ ( '#form646' @ '#sk5' )
    | ( '#sk1' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl802,zip_derived_cl1993]) ).

thf(zip_derived_cl296,plain,
    ( ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl295]) ).

thf(zip_derived_cl298,plain,
    ( ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl296]) ).

thf(zip_derived_cl79_010,plain,
    ! [X2: a > a > $o] :
      ( ~ ( '#form646' @ X2 )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl299,plain,
    ( ( '#form646' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' )
    | ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl298,zip_derived_cl79]) ).

thf(zip_derived_cl300,plain,
    ! [X2: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X2 @ Y1 @ Y2 )
                          & ( X2 @ Y0 @ Y1 ) )
                       => ( X2 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X2 @ Y0 @ Y1 ) ) ) ) )
       => ( X2 @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) )
      | ~ ( '#form1894' @ '#sk5' )
      | ( '#form646' @ '#sk5' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl299]) ).

thf(zip_derived_cl301,plain,
    ( ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
     => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) ) )
    | ~ ( '#form1894' @ '#sk5' )
    | ( '#form646' @ '#sk5' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl300]) ).

thf(zip_derived_cl316,plain,
    ( ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
    | ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) )
    | ( '#form646' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl301]) ).

thf(zip_derived_cl297_011,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk109' @ '#sk5' ) )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl295]) ).

thf(zip_derived_cl317,plain,
    ( ~ ( '#form1894' @ '#sk5' )
    | ( '#form646' @ '#sk5' )
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl316,zip_derived_cl297]) ).

thf(zip_derived_cl318,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
    | ( '#form646' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl317]) ).

thf(zip_derived_cl250_012,plain,
    ! [X2: a > a > $o] :
      ( ( '#form1894' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl319,plain,
    ( ~ ( '#form1894' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' )
    | ( '#form646' @ '#sk5' )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl318,zip_derived_cl250]) ).

thf(zip_derived_cl320,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
    | ( '#form646' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl319]) ).

thf(zip_derived_cl28,plain,
    ! [X2: a > a > $o] :
      ( ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk2' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
                | ( !!
                  @ ^ [Y1: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( ( Y1 @ Y3 @ Y4 )
                                        & ( Y1 @ Y2 @ Y3 ) )
                                     => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( '#sk1' @ Y2 @ Y3 )
                                 => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                     => ( Y1 @ ( '#sk85' @ X2 ) @ Y0 ) ) ) )
             => ( X2 @ ( '#sk85' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl38,plain,
    ! [X2: a > a > $o] :
      ( ~ ( ( ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk2' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
            | ( !!
              @ ^ [Y0: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( !!
                              @ ^ [Y3: a] :
                                  ( ( ( Y0 @ Y2 @ Y3 )
                                    & ( Y0 @ Y1 @ Y2 ) )
                                 => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                    & ( !!
                      @ ^ [Y1: a] :
                          ( !!
                          @ ^ [Y2: a] :
                              ( ( '#sk1' @ Y1 @ Y2 )
                             => ( Y0 @ Y1 @ Y2 ) ) ) ) )
                 => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) )
         => ( X2 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a > a > $o] :
      ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a > a > $o] :
      ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl50,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X4 @ Y1 @ Y2 )
                          & ( X4 @ Y0 @ Y1 ) )
                       => ( X4 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X4 @ Y0 @ Y1 ) ) ) ) )
       => ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl62,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( X4 @ Y1 @ Y2 )
                          & ( X4 @ Y0 @ Y1 ) )
                       => ( X4 @ Y0 @ Y2 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y0 @ Y1 )
                   => ( X4 @ Y0 @ Y1 ) ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl65,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X4 @ Y1 @ Y2 )
                        & ( X4 @ Y0 @ Y1 ) )
                     => ( X4 @ Y0 @ Y2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl68,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( X4 @ Y0 @ Y1 )
                    & ( X4 @ ( '#sk30' @ X4 ) @ Y0 ) )
                 => ( X4 @ ( '#sk30' @ X4 ) @ Y1 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl71,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( X4 @ ( '#sk41' @ X4 ) @ Y0 )
                & ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk41' @ X4 ) ) )
             => ( X4 @ ( '#sk30' @ X4 ) @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl74,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ~ ( ( ( X4 @ ( '#sk41' @ X4 ) @ ( '#sk54' @ X4 ) )
            & ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk41' @ X4 ) ) )
         => ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk54' @ X4 ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl77,plain,
    ! [X2: a > a > $o,X4: a > a > $o] :
      ( ( ( X4 @ ( '#sk41' @ X4 ) @ ( '#sk54' @ X4 ) )
        & ( X4 @ ( '#sk30' @ X4 ) @ ( '#sk41' @ X4 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk54' @ X2 ) )
      | ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ) )
      | ( X4 @ ( '#sk85' @ X2 ) @ ( '#sk109' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl86,plain,
    ! [X4: a > a > $o] :
      ( ( '#form695' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl321,plain,
    ( ~ ( '#form695' @ '#sk5' )
    | ~ ( '#form1894' @ '#sk5' )
    | ( '#form646' @ '#sk5' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl320,zip_derived_cl86]) ).

thf(zip_derived_cl86_013,plain,
    ! [X4: a > a > $o] :
      ( ( '#form695' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( X4 @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl87,plain,
    ! [X4: a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk2' @ ( '#sk696' @ X4 ) @ Y0 )
             => ( X4 @ ( '#sk696' @ X4 ) @ Y0 ) ) )
      | ( '#form695' @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl94,plain,
    ! [X4: a > a > $o] :
      ( ~ ( ( '#sk2' @ ( '#sk696' @ X4 ) @ ( '#sk806' @ X4 ) )
         => ( X4 @ ( '#sk696' @ X4 ) @ ( '#sk806' @ X4 ) ) )
      | ( '#form695' @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl106,plain,
    ! [X4: a > a > $o] :
      ( ( '#sk2' @ ( '#sk696' @ X4 ) @ ( '#sk806' @ X4 ) )
      | ( '#form695' @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl17,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( ( ( '#sk2' @ Y0 @ Y1 )
              | ( '#sk1' @ Y0 @ Y1 ) )
           => ( '#sk5' @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( '#sk2' @ X2 @ Y0 )
            | ( '#sk1' @ X2 @ Y0 ) )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk2' @ X2 @ X4 )
        | ( '#sk1' @ X2 @ X4 ) )
     => ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( '#sk2' @ X2 @ X4 )
          | ( '#sk1' @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk2' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl131,plain,
    ! [X0: a > a > $o] :
      ( ( '#form695' @ X0 )
      | ( '#sk5' @ ( '#sk696' @ X0 ) @ ( '#sk806' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl30]) ).

thf(zip_derived_cl107,plain,
    ! [X4: a > a > $o] :
      ( ~ ( X4 @ ( '#sk696' @ X4 ) @ ( '#sk806' @ X4 ) )
      | ( '#form695' @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl275,plain,
    ( ( '#form695' @ '#sk5' )
    | ( '#form695' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl107]) ).

thf(zip_derived_cl284,plain,
    '#form695' @ '#sk5',
    inference(simplify,[status(thm)],[zip_derived_cl275]) ).

thf(zip_derived_cl322,plain,
    ( ~ ( '#form1894' @ '#sk5' )
    | ( '#form646' @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl321,zip_derived_cl284]) ).

thf(zip_derived_cl938_014,plain,
    '#form1894' @ '#sk5',
    inference(clc,[status(thm)],[zip_derived_cl846,zip_derived_cl266]) ).

thf(zip_derived_cl939,plain,
    '#form646' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl322,zip_derived_cl938]) ).

thf(zip_derived_cl2008,plain,
    '#sk1' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ),
    inference(demod,[status(thm)],[zip_derived_cl2001,zip_derived_cl939]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl2018,plain,
    '#sk5' @ ( '#sk1275' @ '#sk5' ) @ ( '#sk1315' @ '#sk5' ),
    inference('sup-',[status(thm)],[zip_derived_cl2008,zip_derived_cl31]) ).

thf(zip_derived_cl2034,plain,
    ! [X0: a > a > $o] :
      ( ~ ( '#form646' @ X0 )
      | ( '#sk5' @ ( '#sk85' @ X0 ) @ ( '#sk109' @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1994,zip_derived_cl2018]) ).

thf(zip_derived_cl2040,plain,
    ~ ( '#form646' @ '#sk5' ),
    inference('sup+',[status(thm)],[zip_derived_cl802,zip_derived_cl2034]) ).

thf(zip_derived_cl939_015,plain,
    '#form646' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl322,zip_derived_cl938]) ).

thf(zip_derived_cl2044,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl2040,zip_derived_cl939]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEV140^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.n3iWP6O8yy true
% 0.13/0.35  % Computer : n031.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 02:21:35 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  % Running portfolio for 300 s
% 0.13/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  % Number of cores: 8
% 0.13/0.36  % Python version: Python 3.6.8
% 0.13/0.36  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 30.10/4.60  % Solved by lams/35_full_unif4.sh.
% 30.10/4.60  % done 192 iterations in 3.726s
% 30.10/4.60  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 30.10/4.60  % SZS output start Refutation
% See solution above
% 30.10/4.61  
% 30.10/4.61  
% 30.10/4.61  % Terminating...
% 31.28/4.73  % Runner terminated.
% 31.28/4.74  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------