TSTP Solution File: SEV037^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV037^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BcrGUdmrfQ true

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:59:22 EDT 2023

% Result   : Theorem 6.71s 1.44s
% Output   : Refutation 6.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  201 (  19 unt;  23 typ;   0 def)
%            Number of atoms       : 1343 (  52 equ;   0 cnn)
%            Maximal formula atoms :   51 (   7 avg)
%            Number of connectives : 4092 ( 223   ~; 240   |;  98   &;2691   @)
%                                         (   5 <=>; 311  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   9 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  169 ( 169   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;  13 con; 0-3 aty)
%                                         ( 524  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  773 ( 568   ^; 205   !;   0   ?; 773   :)

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

thf(b_type,type,
    b: $tType ).

thf('#sk14_type',type,
    '#sk14': a ).

thf('#sk15_type',type,
    '#sk15': a ).

thf('#sk18_type',type,
    '#sk18': a ).

thf('#sk8_type',type,
    '#sk8': a > b ).

thf('#sk21_type',type,
    '#sk21': a ).

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

thf('#sk7_type',type,
    '#sk7': a > b ).

thf('#sk16_type',type,
    '#sk16': a ).

thf('#sk6_type',type,
    '#sk6': a > b ).

thf('#sk17_type',type,
    '#sk17': a ).

thf('#sk11_type',type,
    '#sk11': a > b ).

thf('#sk20_type',type,
    '#sk20': a ).

thf('#sk13_type',type,
    '#sk13': a ).

thf('#sk10_type',type,
    '#sk10': a > b ).

thf('#_fresh_sk5_type',type,
    '#_fresh_sk5': a > b ).

thf('#form9_type',type,
    '#form9': $o ).

thf('#sk3_type',type,
    '#sk3': a > b > b > $o ).

thf('#form19_type',type,
    '#form19': $o ).

thf('#_fresh_sk4_type',type,
    '#_fresh_sk4': a > b ).

thf('#form12_type',type,
    '#form12': $o ).

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

thf(cTHM516_pme,conjecture,
    ! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o] :
      ( ( ( Xp = Xq )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( ( Xp @ Xy @ Xz )
              & ( Xp @ Xx @ Xy ) )
           => ( Xp @ Xx @ Xz ) )
        & ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( Xp @ Xy @ Xx ) ) )
     => ( ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( ( ( Xr @ Xx )
                = ( Xr @ Xy ) )
              & ! [Xx0: b,Xy0: b,Xz: b] :
                  ( ( ( Xr @ Xx @ Xy0 @ Xz )
                    & ( Xr @ Xx @ Xx0 @ Xy0 ) )
                 => ( Xr @ Xx @ Xx0 @ Xz ) )
              & ! [Xx0: b,Xy0: b] :
                  ( ( Xr @ Xx @ Xx0 @ Xy0 )
                 => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) )
       => ( ( ( ^ [Xf: a > b,Xg: a > b] :
                ! [Xx: a,Xy: a] :
                  ( ( Xp @ Xx @ Xy )
                 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
            = ( ^ [Xf: a > b,Xg: a > b] :
                ! [Xx: a,Xy: a] :
                  ( ( Xq @ Xx @ Xy )
                 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) )
          & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
              ( ( ! [Xx0: a,Xy0: a] :
                    ( ( Xp @ Xx0 @ Xy0 )
                   => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) )
                & ! [Xx0: a,Xy0: a] :
                    ( ( Xp @ Xx0 @ Xy0 )
                   => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) )
             => ! [Xx0: a,Xy0: a] :
                  ( ( Xp @ Xx0 @ Xy0 )
                 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
          & ! [Xx: a > b,Xy: a > b] :
              ( ! [Xx0: a,Xy0: a] :
                  ( ( Xp @ Xx0 @ Xy0 )
                 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
             => ! [Xx0: a,Xy0: a] :
                  ( ( Xp @ Xx0 @ Xy0 )
                 => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o] :
        ( ( ( Xp = Xq )
          & ! [Xx: a,Xy: a,Xz: a] :
              ( ( ( Xp @ Xy @ Xz )
                & ( Xp @ Xx @ Xy ) )
             => ( Xp @ Xx @ Xz ) )
          & ! [Xx: a,Xy: a] :
              ( ( Xp @ Xx @ Xy )
             => ( Xp @ Xy @ Xx ) ) )
       => ( ! [Xx: a,Xy: a] :
              ( ( Xp @ Xx @ Xy )
             => ( ( ( Xr @ Xx )
                  = ( Xr @ Xy ) )
                & ! [Xx0: b,Xy0: b,Xz: b] :
                    ( ( ( Xr @ Xx @ Xy0 @ Xz )
                      & ( Xr @ Xx @ Xx0 @ Xy0 ) )
                   => ( Xr @ Xx @ Xx0 @ Xz ) )
                & ! [Xx0: b,Xy0: b] :
                    ( ( Xr @ Xx @ Xx0 @ Xy0 )
                   => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) )
         => ( ( ( ^ [Xf: a > b,Xg: a > b] :
                  ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
              = ( ^ [Xf: a > b,Xg: a > b] :
                  ! [Xx: a,Xy: a] :
                    ( ( Xq @ Xx @ Xy )
                   => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) )
            & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
                ( ( ! [Xx0: a,Xy0: a] :
                      ( ( Xp @ Xx0 @ Xy0 )
                     => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) )
                  & ! [Xx0: a,Xy0: a] :
                      ( ( Xp @ Xx0 @ Xy0 )
                     => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) )
               => ! [Xx0: a,Xy0: a] :
                    ( ( Xp @ Xx0 @ Xy0 )
                   => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
            & ! [Xx: a > b,Xy: a > b] :
                ( ! [Xx0: a,Xy0: a] :
                    ( ( Xp @ Xx0 @ Xy0 )
                   => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
               => ! [Xx0: a,Xy0: a] :
                    ( ( Xp @ Xx0 @ Xy0 )
                   => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM516_pme]) ).

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

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

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

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

thf(zip_derived_cl5,plain,
    ~ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( ( ( '#sk3' @ Y0 )
                    = ( '#sk3' @ Y1 ) )
                  & ( !!
                    @ ^ [Y2: b] :
                        ( !!
                        @ ^ [Y3: b] :
                            ( !!
                            @ ^ [Y4: b] :
                                ( ( ( '#sk3' @ Y0 @ Y3 @ Y4 )
                                  & ( '#sk3' @ Y0 @ Y2 @ Y3 ) )
                               => ( '#sk3' @ Y0 @ Y2 @ Y4 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: b] :
                        ( !!
                        @ ^ [Y3: b] :
                            ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
                           => ( '#sk3' @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
     => ( ( ( ^ [Y0: a > b,Y1: a > b] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( '#sk1' @ Y2 @ Y3 )
                       => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
          = ( ^ [Y0: a > b,Y1: a > b] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( '#sk2' @ Y2 @ Y3 )
                       => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: a > b] :
              ( !!
              @ ^ [Y1: a > b] :
                  ( !!
                  @ ^ [Y2: a > b] :
                      ( ( ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( '#sk1' @ Y3 @ Y4 )
                                 => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                        & ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( '#sk1' @ Y3 @ Y4 )
                                 => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                     => ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: a > b] :
              ( !!
              @ ^ [Y1: a > b] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( '#sk1' @ Y2 @ Y3 )
                           => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
                 => ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( '#sk1' @ Y2 @ Y3 )
                           => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ~ ( ( ( ^ [Y0: a > b,Y1: a > b] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( '#sk1' @ Y2 @ Y3 )
                     => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
        = ( ^ [Y0: a > b,Y1: a > b] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( '#sk2' @ Y2 @ Y3 )
                     => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( !!
                @ ^ [Y2: a > b] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( !!
                          @ ^ [Y4: a] :
                              ( ( '#sk1' @ Y3 @ Y4 )
                             => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl16,plain,
    ( ( ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk1' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
     != ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk2' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( !!
                @ ^ [Y2: a > b] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( !!
                          @ ^ [Y4: a] :
                              ( ( '#sk1' @ Y3 @ Y4 )
                             => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl20,plain,
    ( ( ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk1' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
     != ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk2' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( !!
                @ ^ [Y2: a > b] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( !!
                          @ ^ [Y4: a] :
                              ( ( '#sk1' @ Y3 @ Y4 )
                             => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl21,plain,
    ( ( ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk1' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
        @ '#_fresh_sk4'
        @ '#_fresh_sk5' )
     != ( ^ [Y0: a > b,Y1: a > b] :
            ( !!
            @ ^ [Y2: a] :
                ( !!
                @ ^ [Y3: a] :
                    ( ( '#sk2' @ Y2 @ Y3 )
                   => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
        @ '#_fresh_sk4'
        @ '#_fresh_sk5' ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( !!
                @ ^ [Y2: a > b] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( !!
                          @ ^ [Y4: a] :
                              ( ( '#sk1' @ Y3 @ Y4 )
                             => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl22,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( !!
                @ ^ [Y2: a > b] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( !!
                          @ ^ [Y4: a] :
                              ( ( '#sk1' @ Y3 @ Y4 )
                             => ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl23,plain,
    ( ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( '#sk1' @ Y2 @ Y3 )
                           => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( '#sk1' @ Y2 @ Y3 )
                           => ( '#sk3' @ Y2 @ ( '#sk6' @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( '#sk6' @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl27,plain,
    ( ~ ( !!
        @ ^ [Y0: a > b] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( '#sk3' @ Y1 @ ( '#sk7' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y1 @ Y2 )
                       => ( '#sk3' @ Y1 @ ( '#sk6' @ Y1 ) @ ( '#sk7' @ Y2 ) ) ) ) ) )
           => ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( '#sk3' @ Y1 @ ( '#sk6' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl32,plain,
    ( ~ ( ( ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
          & ( !!
            @ ^ [Y0: a] :
                ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl39,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl38,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl42,plain,
    ( '#form9'
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl45,plain,
    ( ~ '#form9'
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl42]) ).

thf(zip_derived_cl45_001,plain,
    ( ~ '#form9'
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl42]) ).

thf(zip_derived_cl51,plain,
    ( '#form12'
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      <=> ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl54,plain,
    ( ~ '#form12'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
    | ~ '#form9' ),
    inference(renaming,[status(thm)],[zip_derived_cl45,zip_derived_cl51]) ).

thf(zip_derived_cl60,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ '#sk13' @ Y0 )
           => ( '#sk3' @ '#sk13' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ Y0 ) ) ) )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl68,plain,
    ( ~ ( ( '#sk1' @ '#sk13' @ '#sk16' )
       => ( '#sk3' @ '#sk13' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) ) )
    | ~ '#form12'
    | ~ '#form9' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl75,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk16' )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( ( '#sk1' @ Y0 @ Y1 )
           => ( ( ( '#sk3' @ Y0 )
                = ( '#sk3' @ Y1 ) )
              & ( !!
                @ ^ [Y2: b] :
                    ( !!
                    @ ^ [Y3: b] :
                        ( !!
                        @ ^ [Y4: b] :
                            ( ( ( '#sk3' @ Y0 @ Y3 @ Y4 )
                              & ( '#sk3' @ Y0 @ Y2 @ Y3 ) )
                           => ( '#sk3' @ Y0 @ Y2 @ Y4 ) ) ) ) )
              & ( !!
                @ ^ [Y2: b] :
                    ( !!
                    @ ^ [Y3: b] :
                        ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
                       => ( '#sk3' @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( '#sk1' @ X2 @ Y0 )
         => ( ( ( '#sk3' @ X2 )
              = ( '#sk3' @ Y0 ) )
            & ( !!
              @ ^ [Y1: b] :
                  ( !!
                  @ ^ [Y2: b] :
                      ( !!
                      @ ^ [Y3: b] :
                          ( ( ( '#sk3' @ X2 @ Y2 @ Y3 )
                            & ( '#sk3' @ X2 @ Y1 @ Y2 ) )
                         => ( '#sk3' @ X2 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: b] :
                  ( !!
                  @ ^ [Y2: b] :
                      ( ( '#sk3' @ X2 @ Y1 @ Y2 )
                     => ( '#sk3' @ X2 @ Y2 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a,X4: a] :
      ( ( '#sk1' @ X2 @ X4 )
     => ( ( ( '#sk3' @ X2 )
          = ( '#sk3' @ X4 ) )
        & ( !!
          @ ^ [Y0: b] :
              ( !!
              @ ^ [Y1: b] :
                  ( !!
                  @ ^ [Y2: b] :
                      ( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
                        & ( '#sk3' @ X2 @ Y0 @ Y1 ) )
                     => ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: b] :
              ( !!
              @ ^ [Y1: b] :
                  ( ( '#sk3' @ X2 @ Y0 @ Y1 )
                 => ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( ( ( '#sk3' @ X2 )
          = ( '#sk3' @ X4 ) )
        & ( !!
          @ ^ [Y0: b] :
              ( !!
              @ ^ [Y1: b] :
                  ( !!
                  @ ^ [Y2: b] :
                      ( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
                        & ( '#sk3' @ X2 @ Y0 @ Y1 ) )
                     => ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: b] :
              ( !!
              @ ^ [Y1: b] :
                  ( ( '#sk3' @ X2 @ Y0 @ Y1 )
                 => ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk3' @ X2 )
        = ( '#sk3' @ X4 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk3' @ X2 )
        = ( '#sk3' @ X4 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a,X4: a,X6: b,X7: b] :
      ( ( ( '#sk3' @ X2 @ X6 @ X7 )
        = ( '#sk3' @ X4 @ X6 @ X7 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl181,plain,
    ! [X0: b,X1: b] :
      ( ~ '#form12'
      | ~ '#form9'
      | ( ( '#sk3' @ '#sk13' @ X1 @ X0 )
        = ( '#sk3' @ '#sk16' @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl35]) ).

thf(zip_derived_cl38_002,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl42_003,plain,
    ( '#form9'
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl44,plain,
    ( ~ '#form9'
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl38,zip_derived_cl42]) ).

thf(zip_derived_cl49,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ '#form9' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl51_004,plain,
    ( '#form12'
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      <=> ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl57,plain,
    ( ~ '#form12'
    | ~ '#form9'
    | ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#sk6' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl49,zip_derived_cl51]) ).

thf(zip_derived_cl65,plain,
    ! [X2: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk3' @ X2 @ ( '#sk6' @ X2 ) @ ( '#sk7' @ Y0 ) ) ) )
      | ~ '#form9'
      | ~ '#form12' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl72,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk3' @ X2 @ ( '#sk6' @ X2 ) @ ( '#sk7' @ X4 ) ) )
      | ~ '#form12'
      | ~ '#form9' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl81,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#sk6' @ X2 ) @ ( '#sk7' @ X4 ) )
      | ~ '#form9'
      | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl666,plain,
    ! [X0: a] :
      ( ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk7' @ X0 ) )
      | ~ '#form9'
      | ~ '#form12'
      | ~ '#form12'
      | ~ '#form9'
      | ~ ( '#sk1' @ '#sk13' @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl181,zip_derived_cl81]) ).

thf(zip_derived_cl694,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ '#sk13' @ X0 )
      | ~ '#form12'
      | ~ '#form9'
      | ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk7' @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl666]) ).

thf(zip_derived_cl51_005,plain,
    ( '#form12'
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      <=> ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl53,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
    | '#form12' ),
    inference(lazy_cnf_xor,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl61,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ '#sk14' @ Y0 )
           => ( '#sk3' @ '#sk14' @ ( '#_fresh_sk4' @ '#sk14' ) @ ( '#_fresh_sk5' @ Y0 ) ) ) )
    | '#form12'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl69,plain,
    ( ~ ( ( '#sk1' @ '#sk14' @ '#sk17' )
       => ( '#sk3' @ '#sk14' @ ( '#_fresh_sk4' @ '#sk14' ) @ ( '#_fresh_sk5' @ '#sk17' ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
    | '#form12' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl77,plain,
    ( ( '#sk1' @ '#sk14' @ '#sk17' )
    | '#form12'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl85,plain,
    ( '#form19'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl86,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( '#sk2' @ '#sk20' @ Y0 )
           => ( '#sk3' @ '#sk20' @ ( '#_fresh_sk4' @ '#sk20' ) @ ( '#_fresh_sk5' @ Y0 ) ) ) )
    | '#form19' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl92,plain,
    ( ~ ( ( '#sk2' @ '#sk20' @ '#sk21' )
       => ( '#sk3' @ '#sk20' @ ( '#_fresh_sk4' @ '#sk20' ) @ ( '#_fresh_sk5' @ '#sk21' ) ) )
    | '#form19' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl94,plain,
    ( ( '#sk2' @ '#sk20' @ '#sk21' )
    | '#form19' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl4,plain,
    ( ( '#sk1' = '#sk2' )
    & ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( ( '#sk1' @ Y1 @ Y2 )
                    & ( '#sk1' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl6,plain,
    '#sk1' = '#sk2',
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl11,plain,
    '#sk1' = '#sk2',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a,X3: a] :
      ( ( '#sk1' @ X2 @ X3 )
      = ( '#sk2' @ X2 @ X3 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl105,plain,
    ( ( '#sk1' @ '#sk20' @ '#sk21' )
    | '#form19' ),
    inference('sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl12]) ).

thf(zip_derived_cl51_006,plain,
    ( '#form12'
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      <=> ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl52,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
    | ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk2' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
    | '#form12' ),
    inference(lazy_cnf_xor,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl62,plain,
    ! [X2: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ Y0 ) ) ) )
      | '#form12'
      | ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl70,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) ) )
      | ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      | '#form12' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl79,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) )
      | '#form12'
      | ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl79_007,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) )
      | '#form12'
      | ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl89,plain,
    ( ~ '#form19'
    | ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk2' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl85_008,plain,
    ( '#form19'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl91,plain,
    ! [X2: a,X4: a] :
      ( '#form19'
      | '#form12'
      | ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl89,zip_derived_cl85]) ).

thf(zip_derived_cl463,plain,
    ( '#form19'
    | ( '#sk3' @ '#sk20' @ ( '#_fresh_sk4' @ '#sk20' ) @ ( '#_fresh_sk5' @ '#sk21' ) )
    | '#form12'
    | '#form19' ),
    inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl91]) ).

thf(zip_derived_cl489,plain,
    ( '#form12'
    | ( '#sk3' @ '#sk20' @ ( '#_fresh_sk4' @ '#sk20' ) @ ( '#_fresh_sk5' @ '#sk21' ) )
    | '#form19' ),
    inference(simplify,[status(thm)],[zip_derived_cl463]) ).

thf(zip_derived_cl95,plain,
    ( ~ ( '#sk3' @ '#sk20' @ ( '#_fresh_sk4' @ '#sk20' ) @ ( '#_fresh_sk5' @ '#sk21' ) )
    | '#form19' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl2026,plain,
    ( '#form19'
    | '#form12' ),
    inference(clc,[status(thm)],[zip_derived_cl489,zip_derived_cl95]) ).

thf(zip_derived_cl78,plain,
    ( ~ ( '#sk3' @ '#sk14' @ ( '#_fresh_sk4' @ '#sk14' ) @ ( '#_fresh_sk5' @ '#sk17' ) )
    | '#form12'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl85_009,plain,
    ( '#form19'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl88,plain,
    ( ~ '#form19'
    | '#form12'
    | ~ ( '#sk3' @ '#sk14' @ ( '#_fresh_sk4' @ '#sk14' ) @ ( '#_fresh_sk5' @ '#sk17' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl78,zip_derived_cl85]) ).

thf(zip_derived_cl89_010,plain,
    ( ~ '#form19'
    | ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk2' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl90,plain,
    ! [X2: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk2' @ X2 @ Y0 )
           => ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ Y0 ) ) ) )
      | ~ '#form19' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl93,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk2' @ X2 @ X4 )
       => ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) ) )
      | ~ '#form19' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl96,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk2' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#_fresh_sk4' @ X2 ) @ ( '#_fresh_sk5' @ X4 ) )
      | ~ '#form19' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl538,plain,
    ( '#form12'
    | ~ '#form19'
    | ~ '#form19'
    | ~ ( '#sk2' @ '#sk14' @ '#sk17' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl96]) ).

thf(zip_derived_cl545,plain,
    ( ~ ( '#sk2' @ '#sk14' @ '#sk17' )
    | ~ '#form19'
    | '#form12' ),
    inference(simplify,[status(thm)],[zip_derived_cl538]) ).

thf(zip_derived_cl12_011,plain,
    ! [X2: a,X3: a] :
      ( ( '#sk1' @ X2 @ X3 )
      = ( '#sk2' @ X2 @ X3 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl549,plain,
    ( ~ ( '#sk1' @ '#sk14' @ '#sk17' )
    | '#form12'
    | ~ '#form19' ),
    inference('sup+',[status(thm)],[zip_derived_cl545,zip_derived_cl12]) ).

thf(zip_derived_cl77_012,plain,
    ( ( '#sk1' @ '#sk14' @ '#sk17' )
    | '#form12'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl85_013,plain,
    ( '#form19'
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl87,plain,
    ( ~ '#form19'
    | '#form12'
    | ( '#sk1' @ '#sk14' @ '#sk17' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl77,zip_derived_cl85]) ).

thf(zip_derived_cl553,plain,
    ( ~ '#form19'
    | '#form12' ),
    inference(clc,[status(thm)],[zip_derived_cl549,zip_derived_cl87]) ).

thf(zip_derived_cl2027,plain,
    '#form12',
    inference(clc,[status(thm)],[zip_derived_cl2026,zip_derived_cl553]) ).

thf(zip_derived_cl42_014,plain,
    ( '#form9'
    | ~ ( !!
        @ ^ [Y0: a > b] :
            ( !!
            @ ^ [Y1: a > b] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
               => ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y2 @ Y3 )
                         => ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl43,plain,
    ( ~ ( !!
        @ ^ [Y0: a > b] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( '#sk3' @ Y1 @ ( '#sk10' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
           => ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( '#sk3' @ Y1 @ ( Y0 @ Y1 ) @ ( '#sk10' @ Y2 ) ) ) ) ) ) )
    | '#form9' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl50,plain,
    ( ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#sk10' @ Y0 ) @ ( '#sk11' @ Y1 ) ) ) ) )
       => ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#sk11' @ Y0 ) @ ( '#sk10' @ Y1 ) ) ) ) ) )
    | '#form9' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl59,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#sk11' @ Y0 ) @ ( '#sk10' @ Y1 ) ) ) ) )
    | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl67,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ '#sk15' @ Y0 )
           => ( '#sk3' @ '#sk15' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ Y0 ) ) ) )
    | '#form9' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl74,plain,
    ( ~ ( ( '#sk1' @ '#sk15' @ '#sk18' )
       => ( '#sk3' @ '#sk15' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ '#sk18' ) ) )
    | '#form9' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl83,plain,
    ( ( '#sk1' @ '#sk15' @ '#sk18' )
    | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( ( '#sk1' @ Y0 @ Y1 )
           => ( '#sk1' @ Y1 @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( '#sk1' @ X2 @ Y0 )
         => ( '#sk1' @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a,X4: a] :
      ( ( '#sk1' @ X2 @ X4 )
     => ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl109,plain,
    ( '#form9'
    | ( '#sk1' @ '#sk18' @ '#sk15' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl83,zip_derived_cl25]) ).

thf(zip_derived_cl83_015,plain,
    ( ( '#sk1' @ '#sk15' @ '#sk18' )
    | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl7,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( !!
            @ ^ [Y2: a] :
                ( ( ( '#sk1' @ Y1 @ Y2 )
                  & ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk1' @ Y0 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl13,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( '#sk1' @ Y0 @ Y1 )
                & ( '#sk1' @ X2 @ Y0 ) )
             => ( '#sk1' @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl17,plain,
    ! [X2: a,X4: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( '#sk1' @ X4 @ Y0 )
            & ( '#sk1' @ X2 @ X4 ) )
         => ( '#sk1' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl24,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( ( '#sk1' @ X4 @ X6 )
        & ( '#sk1' @ X2 @ X4 ) )
     => ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl28,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( '#sk1' @ X4 @ X6 )
          & ( '#sk1' @ X2 @ X4 ) )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl33,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk1' @ X4 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl144,plain,
    ! [X0: a] :
      ( '#form9'
      | ( '#sk1' @ X0 @ '#sk18' )
      | ~ ( '#sk1' @ X0 @ '#sk15' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl83,zip_derived_cl33]) ).

thf(zip_derived_cl261,plain,
    ( '#form9'
    | ( '#sk1' @ '#sk18' @ '#sk18' )
    | '#form9' ),
    inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl144]) ).

thf(zip_derived_cl265,plain,
    ( ( '#sk1' @ '#sk18' @ '#sk18' )
    | '#form9' ),
    inference(simplify,[status(thm)],[zip_derived_cl261]) ).

thf(zip_derived_cl109_016,plain,
    ( '#form9'
    | ( '#sk1' @ '#sk18' @ '#sk15' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl83,zip_derived_cl25]) ).

thf(zip_derived_cl58,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#sk10' @ Y0 ) @ ( '#sk11' @ Y1 ) ) ) ) )
    | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl66,plain,
    ! [X2: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk3' @ X2 @ ( '#sk10' @ X2 ) @ ( '#sk11' @ Y0 ) ) ) )
      | '#form9' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl73,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk3' @ X2 @ ( '#sk10' @ X2 ) @ ( '#sk11' @ X4 ) ) )
      | '#form9' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl82,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#sk10' @ X2 ) @ ( '#sk11' @ X4 ) )
      | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl361,plain,
    ( '#form9'
    | '#form9'
    | ( '#sk3' @ '#sk18' @ ( '#sk10' @ '#sk18' ) @ ( '#sk11' @ '#sk15' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl82]) ).

thf(zip_derived_cl378,plain,
    ( ( '#sk3' @ '#sk18' @ ( '#sk10' @ '#sk18' ) @ ( '#sk11' @ '#sk15' ) )
    | '#form9' ),
    inference(simplify,[status(thm)],[zip_derived_cl361]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a,X4: a] :
      ( ( !!
        @ ^ [Y0: b] :
            ( !!
            @ ^ [Y1: b] :
                ( ( '#sk3' @ X2 @ Y0 @ Y1 )
               => ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a,X4: a,X6: b] :
      ( ( !!
        @ ^ [Y0: b] :
            ( ( '#sk3' @ X2 @ X6 @ Y0 )
           => ( '#sk3' @ X2 @ Y0 @ X6 ) ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a,X4: a,X6: b,X8: b] :
      ( ( ( '#sk3' @ X2 @ X6 @ X8 )
       => ( '#sk3' @ X2 @ X8 @ X6 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a,X4: a,X6: b,X8: b] :
      ( ~ ( '#sk3' @ X2 @ X6 @ X8 )
      | ( '#sk3' @ X2 @ X8 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl986,plain,
    ! [X0: a] :
      ( '#form9'
      | ~ ( '#sk1' @ '#sk18' @ X0 )
      | ( '#sk3' @ '#sk18' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ '#sk18' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl378,zip_derived_cl47]) ).

thf(zip_derived_cl84,plain,
    ( ~ ( '#sk3' @ '#sk15' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ '#sk18' ) )
    | '#form9' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl109_017,plain,
    ( '#form9'
    | ( '#sk1' @ '#sk18' @ '#sk15' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl83,zip_derived_cl25]) ).

thf(zip_derived_cl35_018,plain,
    ! [X2: a,X4: a,X6: b,X7: b] :
      ( ( ( '#sk3' @ X2 @ X6 @ X7 )
        = ( '#sk3' @ X4 @ X6 @ X7 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl179,plain,
    ! [X0: b,X1: b] :
      ( '#form9'
      | ( ( '#sk3' @ '#sk18' @ X1 @ X0 )
        = ( '#sk3' @ '#sk15' @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl35]) ).

thf(zip_derived_cl625,plain,
    ( ~ ( '#sk3' @ '#sk18' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ '#sk18' ) )
    | '#form9'
    | '#form9' ),
    inference('sup+',[status(thm)],[zip_derived_cl84,zip_derived_cl179]) ).

thf(zip_derived_cl648,plain,
    ( '#form9'
    | ~ ( '#sk3' @ '#sk18' @ ( '#sk11' @ '#sk15' ) @ ( '#sk10' @ '#sk18' ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl625]) ).

thf(zip_derived_cl1779,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ '#sk18' @ X0 )
      | '#form9' ),
    inference(clc,[status(thm)],[zip_derived_cl986,zip_derived_cl648]) ).

thf(zip_derived_cl1783,plain,
    ( '#form9'
    | '#form9' ),
    inference('sup-',[status(thm)],[zip_derived_cl265,zip_derived_cl1779]) ).

thf(zip_derived_cl1792,plain,
    '#form9',
    inference(simplify,[status(thm)],[zip_derived_cl1783]) ).

thf(zip_derived_cl3454,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ '#sk13' @ X0 )
      | ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk7' @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl694,zip_derived_cl2027,zip_derived_cl1792]) ).

thf(zip_derived_cl48,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
     != ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) )
    | ~ '#form9' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl51_019,plain,
    ( '#form12'
    | ~ ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) )
      <=> ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk3' @ Y0 @ ( '#_fresh_sk4' @ Y0 ) @ ( '#_fresh_sk5' @ Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl56,plain,
    ( ~ '#form12'
    | ~ '#form9'
    | ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl48,zip_derived_cl51]) ).

thf(zip_derived_cl64,plain,
    ! [X2: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ Y0 ) ) ) )
      | ~ '#form9'
      | ~ '#form12' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl71,plain,
    ! [X2: a,X4: a] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X4 ) ) )
      | ~ '#form12'
      | ~ '#form9' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl80,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X4 ) )
      | ~ '#form9'
      | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a,X4: a] :
      ( ( !!
        @ ^ [Y0: b] :
            ( !!
            @ ^ [Y1: b] :
                ( !!
                @ ^ [Y2: b] :
                    ( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
                      & ( '#sk3' @ X2 @ Y0 @ Y1 ) )
                   => ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a,X4: a,X6: b] :
      ( ( !!
        @ ^ [Y0: b] :
            ( !!
            @ ^ [Y1: b] :
                ( ( ( '#sk3' @ X2 @ Y0 @ Y1 )
                  & ( '#sk3' @ X2 @ X6 @ Y0 ) )
               => ( '#sk3' @ X2 @ X6 @ Y1 ) ) ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl40,plain,
    ! [X2: a,X4: a,X6: b,X8: b] :
      ( ( !!
        @ ^ [Y0: b] :
            ( ( ( '#sk3' @ X2 @ X8 @ Y0 )
              & ( '#sk3' @ X2 @ X6 @ X8 ) )
           => ( '#sk3' @ X2 @ X6 @ Y0 ) ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a,X4: a,X6: b,X8: b,X10: b] :
      ( ( ( ( '#sk3' @ X2 @ X8 @ X10 )
          & ( '#sk3' @ X2 @ X6 @ X8 ) )
       => ( '#sk3' @ X2 @ X6 @ X10 ) )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl55,plain,
    ! [X2: a,X4: a,X6: b,X8: b,X10: b] :
      ( ~ ( ( '#sk3' @ X2 @ X8 @ X10 )
          & ( '#sk3' @ X2 @ X6 @ X8 ) )
      | ( '#sk3' @ X2 @ X6 @ X10 )
      | ~ ( '#sk1' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl63,plain,
    ! [X2: a,X4: a,X6: b,X8: b,X10: b] :
      ( ~ ( '#sk3' @ X2 @ X8 @ X10 )
      | ~ ( '#sk3' @ X2 @ X6 @ X8 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk3' @ X2 @ X6 @ X10 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl267,plain,
    ! [X0: a,X1: a,X2: b,X3: a] :
      ( ~ '#form12'
      | ~ '#form9'
      | ~ ( '#sk1' @ X1 @ X0 )
      | ( '#sk3' @ X1 @ X2 @ ( '#sk8' @ X0 ) )
      | ~ ( '#sk1' @ X1 @ X3 )
      | ~ ( '#sk3' @ X1 @ X2 @ ( '#sk7' @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl63]) ).

thf(zip_derived_cl1136,plain,
    ! [X0: a,X1: b,X2: a] :
      ( ~ '#form12'
      | ~ '#form9'
      | ~ ( '#sk3' @ X0 @ X1 @ ( '#sk7' @ X0 ) )
      | ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X2 ) )
      | ~ ( '#sk1' @ X0 @ X2 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl267]) ).

thf(zip_derived_cl1792_020,plain,
    '#form9',
    inference(simplify,[status(thm)],[zip_derived_cl1783]) ).

thf(zip_derived_cl1829,plain,
    ! [X0: a,X1: b,X2: a] :
      ( ~ '#form12'
      | ~ ( '#sk3' @ X0 @ X1 @ ( '#sk7' @ X0 ) )
      | ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X2 ) )
      | ~ ( '#sk1' @ X0 @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1136,zip_derived_cl1792]) ).

thf(zip_derived_cl2027_021,plain,
    '#form12',
    inference(clc,[status(thm)],[zip_derived_cl2026,zip_derived_cl553]) ).

thf(zip_derived_cl4007,plain,
    ! [X0: a,X1: b,X2: a] :
      ( ~ ( '#sk3' @ X0 @ X1 @ ( '#sk7' @ X0 ) )
      | ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X2 ) )
      | ~ ( '#sk1' @ X0 @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1829,zip_derived_cl2027]) ).

thf(zip_derived_cl4011,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ '#sk13' @ '#sk16' )
      | ~ ( '#sk1' @ '#sk16' @ X0 )
      | ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3454,zip_derived_cl4007]) ).

thf(zip_derived_cl75_022,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk16' )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl1792_023,plain,
    '#form9',
    inference(simplify,[status(thm)],[zip_derived_cl1783]) ).

thf(zip_derived_cl1800,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk16' )
    | ~ '#form12' ),
    inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl1792]) ).

thf(zip_derived_cl2027_024,plain,
    '#form12',
    inference(clc,[status(thm)],[zip_derived_cl2026,zip_derived_cl553]) ).

thf(zip_derived_cl2028,plain,
    '#sk1' @ '#sk13' @ '#sk16',
    inference(demod,[status(thm)],[zip_derived_cl1800,zip_derived_cl2027]) ).

thf(zip_derived_cl4025,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ '#sk16' @ X0 )
      | ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4011,zip_derived_cl2028]) ).

thf(zip_derived_cl181_025,plain,
    ! [X0: b,X1: b] :
      ( ~ '#form12'
      | ~ '#form9'
      | ( ( '#sk3' @ '#sk13' @ X1 @ X0 )
        = ( '#sk3' @ '#sk16' @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl35]) ).

thf(zip_derived_cl76,plain,
    ( ~ ( '#sk3' @ '#sk13' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl664,plain,
    ( ~ ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) )
    | ~ '#form9'
    | ~ '#form12'
    | ~ '#form12'
    | ~ '#form9' ),
    inference('sup-',[status(thm)],[zip_derived_cl181,zip_derived_cl76]) ).

thf(zip_derived_cl692,plain,
    ( ~ '#form12'
    | ~ '#form9'
    | ~ ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl664]) ).

thf(zip_derived_cl1792_026,plain,
    '#form9',
    inference(simplify,[status(thm)],[zip_derived_cl1783]) ).

thf(zip_derived_cl1820,plain,
    ( ~ '#form12'
    | ~ ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl692,zip_derived_cl1792]) ).

thf(zip_derived_cl2027_027,plain,
    '#form12',
    inference(clc,[status(thm)],[zip_derived_cl2026,zip_derived_cl553]) ).

thf(zip_derived_cl2043,plain,
    ~ ( '#sk3' @ '#sk16' @ ( '#sk6' @ '#sk13' ) @ ( '#sk8' @ '#sk16' ) ),
    inference(demod,[status(thm)],[zip_derived_cl1820,zip_derived_cl2027]) ).

thf(zip_derived_cl4073,plain,
    ~ ( '#sk1' @ '#sk16' @ '#sk16' ),
    inference('sup-',[status(thm)],[zip_derived_cl4025,zip_derived_cl2043]) ).

thf(zip_derived_cl75_028,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk16' )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl25_029,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl131,plain,
    ( ~ '#form12'
    | ~ '#form9'
    | ( '#sk1' @ '#sk16' @ '#sk13' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl25]) ).

thf(zip_derived_cl75_030,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk16' )
    | ~ '#form9'
    | ~ '#form12' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl33_031,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk1' @ X4 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl145,plain,
    ! [X0: a] :
      ( ~ '#form12'
      | ~ '#form9'
      | ( '#sk1' @ X0 @ '#sk16' )
      | ~ ( '#sk1' @ X0 @ '#sk13' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl33]) ).

thf(zip_derived_cl199,plain,
    ( ~ '#form9'
    | ~ '#form12'
    | ( '#sk1' @ '#sk16' @ '#sk16' )
    | ~ '#form9'
    | ~ '#form12' ),
    inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl145]) ).

thf(zip_derived_cl211,plain,
    ( ( '#sk1' @ '#sk16' @ '#sk16' )
    | ~ '#form12'
    | ~ '#form9' ),
    inference(simplify,[status(thm)],[zip_derived_cl199]) ).

thf(zip_derived_cl1792_032,plain,
    '#form9',
    inference(simplify,[status(thm)],[zip_derived_cl1783]) ).

thf(zip_derived_cl1811,plain,
    ( ( '#sk1' @ '#sk16' @ '#sk16' )
    | ~ '#form12' ),
    inference(demod,[status(thm)],[zip_derived_cl211,zip_derived_cl1792]) ).

thf(zip_derived_cl2027_033,plain,
    '#form12',
    inference(clc,[status(thm)],[zip_derived_cl2026,zip_derived_cl553]) ).

thf(zip_derived_cl2036,plain,
    '#sk1' @ '#sk16' @ '#sk16',
    inference(demod,[status(thm)],[zip_derived_cl1811,zip_derived_cl2027]) ).

thf(zip_derived_cl4100,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl4073,zip_derived_cl2036]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEV037^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BcrGUdmrfQ true
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug 24 04:01:21 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.55/0.66  % Total configuration time : 828
% 0.55/0.66  % Estimated wc time : 1656
% 0.55/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.71  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.75  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.75  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.76  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.76  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 6.71/1.44  % Solved by lams/20_acsne_simpl.sh.
% 6.71/1.44  % done 989 iterations in 0.620s
% 6.71/1.44  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.71/1.44  % SZS output start Refutation
% See solution above
% 6.71/1.45  
% 6.71/1.45  
% 6.71/1.45  % Terminating...
% 7.10/1.57  % Runner terminated.
% 7.10/1.58  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------