TSTP Solution File: SEV212^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV212^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qls7Fw4nC7 true

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:00:02 EDT 2023

% Result   : Theorem 50.95s 7.49s
% Output   : Refutation 50.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  137 (   4 unt;  19 typ;   0 def)
%            Number of atoms       : 1161 ( 594 equ;   0 cnn)
%            Maximal formula atoms :   69 (   9 avg)
%            Number of connectives : 3950 (  75   ~; 290   |; 472   &;2565   @)
%                                         (   0 <=>;  96  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (  15 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  379 ( 379   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  18 usr;   8 con; 0-3 aty)
%                                         ( 143  !!; 309  ??;   0 @@+;   0 @@-)
%            Number of variables   :  715 ( 452   ^; 227   !;  36   ?; 715   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iS_type,type,
    iS: $tType ).

thf('#sk8_type',type,
    '#sk8': iS ).

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

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

thf('#form1036_type',type,
    '#form1036': ( iS > iS > iS > $o ) > $o ).

thf('#sk545_type',type,
    '#sk545': ( iS > iS > iS > $o ) > iS ).

thf('#sk106_type',type,
    '#sk106': ( iS > iS > iS > $o ) > iS ).

thf(c0_type,type,
    c0: iS ).

thf('#sk637_type',type,
    '#sk637': ( iS > iS > iS > $o ) > iS ).

thf('#sk851_type',type,
    '#sk851': ( iS > iS > iS > $o ) > iS ).

thf('#sk463_type',type,
    '#sk463': ( iS > iS > iS > $o ) > iS ).

thf('#sk739_type',type,
    '#sk739': ( iS > iS > iS > $o ) > iS ).

thf('#sk391_type',type,
    '#sk391': ( iS > iS > iS > $o ) > iS ).

thf('#sk2_type',type,
    '#sk2': iS ).

thf(cP_type,type,
    cP: iS > iS > iS ).

thf('#sk72_type',type,
    '#sk72': ( iS > iS > iS > $o ) > iS ).

thf('#form1091_type',type,
    '#form1091': ( iS > iS > iS > $o ) > $o ).

thf('#sk158_type',type,
    '#sk158': ( iS > iS > iS > $o ) > iS ).

thf('#sk27_type',type,
    '#sk27': iS > iS > iS > $o ).

thf(cS_LEM2_pme,conjecture,
    ( ( ! [X: iS > $o] :
          ( ( ! [Xx: iS,Xy: iS] :
                ( ( ( X @ Xy )
                  & ( X @ Xx ) )
               => ( X @ ( cP @ Xx @ Xy ) ) )
            & ( X @ c0 ) )
         => ! [Xx: iS] : ( X @ Xx ) )
      & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xu = Xv )
            & ( Xx = Xy ) ) )
      & ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
   => ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
        ( ( ! [R: iS > iS > iS > $o] :
              ( ! [Xa: iS,Xb: iS,Xc: iS] :
                  ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                        ( ( Xa
                          = ( cP @ Xx1 @ Xx2 ) )
                        & ( Xb
                          = ( cP @ Xy1 @ Xy2 ) )
                        & ( Xc
                          = ( cP @ Xz1 @ Xz2 ) )
                        & ( R @ Xx1 @ Xy1 @ Xz1 )
                        & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                    | ( ( Xa = Xc )
                      & ( Xb = c0 ) )
                    | ( ( Xb = Xc )
                      & ( Xa = c0 ) ) )
                 => ( R @ Xa @ Xb @ Xc ) )
             => ( R @ Xu @ Xv @ Xv ) )
          & ! [R: iS > iS > iS > $o] :
              ( ! [Xa: iS,Xb: iS,Xc: iS] :
                  ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                        ( ( Xa
                          = ( cP @ Xx1 @ Xx2 ) )
                        & ( Xb
                          = ( cP @ Xy1 @ Xy2 ) )
                        & ( Xc
                          = ( cP @ Xz1 @ Xz2 ) )
                        & ( R @ Xx1 @ Xy1 @ Xz1 )
                        & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                    | ( ( Xa = Xc )
                      & ( Xb = c0 ) )
                    | ( ( Xb = Xc )
                      & ( Xa = c0 ) ) )
                 => ( R @ Xa @ Xb @ Xc ) )
             => ( R @ Xx @ Xy @ Xy ) ) )
       => ! [R: iS > iS > iS > $o] :
            ( ! [Xa: iS,Xb: iS,Xc: iS] :
                ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                      ( ( Xa
                        = ( cP @ Xx1 @ Xx2 ) )
                      & ( Xb
                        = ( cP @ Xy1 @ Xy2 ) )
                      & ( Xc
                        = ( cP @ Xz1 @ Xz2 ) )
                      & ( R @ Xx1 @ Xy1 @ Xz1 )
                      & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                  | ( ( Xa = Xc )
                    & ( Xb = c0 ) )
                  | ( ( Xb = Xc )
                    & ( Xa = c0 ) ) )
               => ( R @ Xa @ Xb @ Xc ) )
           => ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ! [X: iS > $o] :
            ( ( ! [Xx: iS,Xy: iS] :
                  ( ( ( X @ Xy )
                    & ( X @ Xx ) )
                 => ( X @ ( cP @ Xx @ Xy ) ) )
              & ( X @ c0 ) )
           => ! [Xx: iS] : ( X @ Xx ) )
        & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xu = Xv )
              & ( Xx = Xy ) ) )
        & ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 ) )
     => ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ! [R: iS > iS > iS > $o] :
                ( ! [Xa: iS,Xb: iS,Xc: iS] :
                    ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                          ( ( Xa
                            = ( cP @ Xx1 @ Xx2 ) )
                          & ( Xb
                            = ( cP @ Xy1 @ Xy2 ) )
                          & ( Xc
                            = ( cP @ Xz1 @ Xz2 ) )
                          & ( R @ Xx1 @ Xy1 @ Xz1 )
                          & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                      | ( ( Xa = Xc )
                        & ( Xb = c0 ) )
                      | ( ( Xb = Xc )
                        & ( Xa = c0 ) ) )
                   => ( R @ Xa @ Xb @ Xc ) )
               => ( R @ Xu @ Xv @ Xv ) )
            & ! [R: iS > iS > iS > $o] :
                ( ! [Xa: iS,Xb: iS,Xc: iS] :
                    ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                          ( ( Xa
                            = ( cP @ Xx1 @ Xx2 ) )
                          & ( Xb
                            = ( cP @ Xy1 @ Xy2 ) )
                          & ( Xc
                            = ( cP @ Xz1 @ Xz2 ) )
                          & ( R @ Xx1 @ Xy1 @ Xz1 )
                          & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                      | ( ( Xa = Xc )
                        & ( Xb = c0 ) )
                      | ( ( Xb = Xc )
                        & ( Xa = c0 ) ) )
                   => ( R @ Xa @ Xb @ Xc ) )
               => ( R @ Xx @ Xy @ Xy ) ) )
         => ! [R: iS > iS > iS > $o] :
              ( ! [Xa: iS,Xb: iS,Xc: iS] :
                  ( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
                        ( ( Xa
                          = ( cP @ Xx1 @ Xx2 ) )
                        & ( Xb
                          = ( cP @ Xy1 @ Xy2 ) )
                        & ( Xc
                          = ( cP @ Xz1 @ Xz2 ) )
                        & ( R @ Xx1 @ Xy1 @ Xz1 )
                        & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                    | ( ( Xa = Xc )
                      & ( Xb = c0 ) )
                    | ( ( Xb = Xc )
                      & ( Xa = c0 ) ) )
                 => ( R @ Xa @ Xb @ Xc ) )
             => ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[cS_LEM2_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( ( !!
          @ ^ [Y0: iS > $o] :
              ( ( ( !!
                  @ ^ [Y1: iS] :
                      ( !!
                      @ ^ [Y2: iS] :
                          ( ( ( Y0 @ Y2 )
                            & ( Y0 @ Y1 ) )
                         => ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
                & ( Y0 @ c0 ) )
             => ( !!
                @ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( !!
                  @ ^ [Y2: iS] :
                      ( !!
                      @ ^ [Y3: iS] :
                          ( ( ( cP @ Y0 @ Y2 )
                            = ( cP @ Y1 @ Y3 ) )
                         => ( ( Y2 = Y3 )
                            & ( Y0 = Y1 ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( ( cP @ Y0 @ Y1 )
                 != c0 ) ) ) )
     => ( !!
        @ ^ [Y0: iS] :
            ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( !!
                    @ ^ [Y3: iS] :
                        ( ( ( !!
                            @ ^ [Y4: iS > iS > iS > $o] :
                                ( ( !!
                                  @ ^ [Y5: iS] :
                                      ( !!
                                      @ ^ [Y6: iS] :
                                          ( !!
                                          @ ^ [Y7: iS] :
                                              ( ( ( ??
                                                  @ ^ [Y8: iS] :
                                                      ( ??
                                                      @ ^ [Y9: iS] :
                                                          ( ??
                                                          @ ^ [Y10: iS] :
                                                              ( ??
                                                              @ ^ [Y11: iS] :
                                                                  ( ??
                                                                  @ ^ [Y12: iS] :
                                                                      ( ??
                                                                      @ ^ [Y13: iS] :
                                                                          ( ( Y5
                                                                            = ( cP @ Y8 @ Y9 ) )
                                                                          & ( Y6
                                                                            = ( cP @ Y10 @ Y11 ) )
                                                                          & ( Y7
                                                                            = ( cP @ Y12 @ Y13 ) )
                                                                          & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                          & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                                | ( ( Y5 = Y7 )
                                                  & ( Y6 = c0 ) )
                                                | ( ( Y6 = Y7 )
                                                  & ( Y5 = c0 ) ) )
                                             => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                               => ( Y4 @ Y2 @ Y3 @ Y3 ) ) )
                          & ( !!
                            @ ^ [Y4: iS > iS > iS > $o] :
                                ( ( !!
                                  @ ^ [Y5: iS] :
                                      ( !!
                                      @ ^ [Y6: iS] :
                                          ( !!
                                          @ ^ [Y7: iS] :
                                              ( ( ( ??
                                                  @ ^ [Y8: iS] :
                                                      ( ??
                                                      @ ^ [Y9: iS] :
                                                          ( ??
                                                          @ ^ [Y10: iS] :
                                                              ( ??
                                                              @ ^ [Y11: iS] :
                                                                  ( ??
                                                                  @ ^ [Y12: iS] :
                                                                      ( ??
                                                                      @ ^ [Y13: iS] :
                                                                          ( ( Y5
                                                                            = ( cP @ Y8 @ Y9 ) )
                                                                          & ( Y6
                                                                            = ( cP @ Y10 @ Y11 ) )
                                                                          & ( Y7
                                                                            = ( cP @ Y12 @ Y13 ) )
                                                                          & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                          & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                                | ( ( Y5 = Y7 )
                                                  & ( Y6 = c0 ) )
                                                | ( ( Y6 = Y7 )
                                                  & ( Y5 = c0 ) ) )
                                             => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                               => ( Y4 @ Y0 @ Y1 @ Y1 ) ) ) )
                       => ( !!
                          @ ^ [Y4: iS > iS > iS > $o] :
                              ( ( !!
                                @ ^ [Y5: iS] :
                                    ( !!
                                    @ ^ [Y6: iS] :
                                        ( !!
                                        @ ^ [Y7: iS] :
                                            ( ( ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ??
                                                                @ ^ [Y12: iS] :
                                                                    ( ??
                                                                    @ ^ [Y13: iS] :
                                                                        ( ( Y5
                                                                          = ( cP @ Y8 @ Y9 ) )
                                                                        & ( Y6
                                                                          = ( cP @ Y10 @ Y11 ) )
                                                                        & ( Y7
                                                                          = ( cP @ Y12 @ Y13 ) )
                                                                        & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                        & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                              | ( ( Y5 = Y7 )
                                                & ( Y6 = c0 ) )
                                              | ( ( Y6 = Y7 )
                                                & ( Y5 = c0 ) ) )
                                           => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                             => ( Y4 @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y1 @ Y3 ) @ ( cP @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: iS] :
          ( !!
          @ ^ [Y1: iS] :
              ( !!
              @ ^ [Y2: iS] :
                  ( !!
                  @ ^ [Y3: iS] :
                      ( ( ( !!
                          @ ^ [Y4: iS > iS > iS > $o] :
                              ( ( !!
                                @ ^ [Y5: iS] :
                                    ( !!
                                    @ ^ [Y6: iS] :
                                        ( !!
                                        @ ^ [Y7: iS] :
                                            ( ( ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ??
                                                                @ ^ [Y12: iS] :
                                                                    ( ??
                                                                    @ ^ [Y13: iS] :
                                                                        ( ( Y5
                                                                          = ( cP @ Y8 @ Y9 ) )
                                                                        & ( Y6
                                                                          = ( cP @ Y10 @ Y11 ) )
                                                                        & ( Y7
                                                                          = ( cP @ Y12 @ Y13 ) )
                                                                        & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                        & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                              | ( ( Y5 = Y7 )
                                                & ( Y6 = c0 ) )
                                              | ( ( Y6 = Y7 )
                                                & ( Y5 = c0 ) ) )
                                           => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                             => ( Y4 @ Y2 @ Y3 @ Y3 ) ) )
                        & ( !!
                          @ ^ [Y4: iS > iS > iS > $o] :
                              ( ( !!
                                @ ^ [Y5: iS] :
                                    ( !!
                                    @ ^ [Y6: iS] :
                                        ( !!
                                        @ ^ [Y7: iS] :
                                            ( ( ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ??
                                                                @ ^ [Y12: iS] :
                                                                    ( ??
                                                                    @ ^ [Y13: iS] :
                                                                        ( ( Y5
                                                                          = ( cP @ Y8 @ Y9 ) )
                                                                        & ( Y6
                                                                          = ( cP @ Y10 @ Y11 ) )
                                                                        & ( Y7
                                                                          = ( cP @ Y12 @ Y13 ) )
                                                                        & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                        & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                              | ( ( Y5 = Y7 )
                                                & ( Y6 = c0 ) )
                                              | ( ( Y6 = Y7 )
                                                & ( Y5 = c0 ) ) )
                                           => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                             => ( Y4 @ Y0 @ Y1 @ Y1 ) ) ) )
                     => ( !!
                        @ ^ [Y4: iS > iS > iS > $o] :
                            ( ( !!
                              @ ^ [Y5: iS] :
                                  ( !!
                                  @ ^ [Y6: iS] :
                                      ( !!
                                      @ ^ [Y7: iS] :
                                          ( ( ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ??
                                                  @ ^ [Y9: iS] :
                                                      ( ??
                                                      @ ^ [Y10: iS] :
                                                          ( ??
                                                          @ ^ [Y11: iS] :
                                                              ( ??
                                                              @ ^ [Y12: iS] :
                                                                  ( ??
                                                                  @ ^ [Y13: iS] :
                                                                      ( ( Y5
                                                                        = ( cP @ Y8 @ Y9 ) )
                                                                      & ( Y6
                                                                        = ( cP @ Y10 @ Y11 ) )
                                                                      & ( Y7
                                                                        = ( cP @ Y12 @ Y13 ) )
                                                                      & ( Y4 @ Y8 @ Y10 @ Y12 )
                                                                      & ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
                                            | ( ( Y5 = Y7 )
                                              & ( Y6 = c0 ) )
                                            | ( ( Y6 = Y7 )
                                              & ( Y5 = c0 ) ) )
                                         => ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
                           => ( Y4 @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y1 @ Y3 ) @ ( cP @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl6,plain,
    ~ ( !!
      @ ^ [Y0: iS] :
          ( !!
          @ ^ [Y1: iS] :
              ( !!
              @ ^ [Y2: iS] :
                  ( ( ( !!
                      @ ^ [Y3: iS > iS > iS > $o] :
                          ( ( !!
                            @ ^ [Y4: iS] :
                                ( !!
                                @ ^ [Y5: iS] :
                                    ( !!
                                    @ ^ [Y6: iS] :
                                        ( ( ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ??
                                                                @ ^ [Y12: iS] :
                                                                    ( ( Y4
                                                                      = ( cP @ Y7 @ Y8 ) )
                                                                    & ( Y5
                                                                      = ( cP @ Y9 @ Y10 ) )
                                                                    & ( Y6
                                                                      = ( cP @ Y11 @ Y12 ) )
                                                                    & ( Y3 @ Y7 @ Y9 @ Y11 )
                                                                    & ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
                                          | ( ( Y4 = Y6 )
                                            & ( Y5 = c0 ) )
                                          | ( ( Y5 = Y6 )
                                            & ( Y4 = c0 ) ) )
                                       => ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
                         => ( Y3 @ Y1 @ Y2 @ Y2 ) ) )
                    & ( !!
                      @ ^ [Y3: iS > iS > iS > $o] :
                          ( ( !!
                            @ ^ [Y4: iS] :
                                ( !!
                                @ ^ [Y5: iS] :
                                    ( !!
                                    @ ^ [Y6: iS] :
                                        ( ( ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ??
                                                                @ ^ [Y12: iS] :
                                                                    ( ( Y4
                                                                      = ( cP @ Y7 @ Y8 ) )
                                                                    & ( Y5
                                                                      = ( cP @ Y9 @ Y10 ) )
                                                                    & ( Y6
                                                                      = ( cP @ Y11 @ Y12 ) )
                                                                    & ( Y3 @ Y7 @ Y9 @ Y11 )
                                                                    & ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
                                          | ( ( Y4 = Y6 )
                                            & ( Y5 = c0 ) )
                                          | ( ( Y5 = Y6 )
                                            & ( Y4 = c0 ) ) )
                                       => ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
                         => ( Y3 @ '#sk1' @ Y0 @ Y0 ) ) ) )
                 => ( !!
                    @ ^ [Y3: iS > iS > iS > $o] :
                        ( ( !!
                          @ ^ [Y4: iS] :
                              ( !!
                              @ ^ [Y5: iS] :
                                  ( !!
                                  @ ^ [Y6: iS] :
                                      ( ( ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ??
                                                  @ ^ [Y9: iS] :
                                                      ( ??
                                                      @ ^ [Y10: iS] :
                                                          ( ??
                                                          @ ^ [Y11: iS] :
                                                              ( ??
                                                              @ ^ [Y12: iS] :
                                                                  ( ( Y4
                                                                    = ( cP @ Y7 @ Y8 ) )
                                                                  & ( Y5
                                                                    = ( cP @ Y9 @ Y10 ) )
                                                                  & ( Y6
                                                                    = ( cP @ Y11 @ Y12 ) )
                                                                  & ( Y3 @ Y7 @ Y9 @ Y11 )
                                                                  & ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
                                        | ( ( Y4 = Y6 )
                                          & ( Y5 = c0 ) )
                                        | ( ( Y5 = Y6 )
                                          & ( Y4 = c0 ) ) )
                                     => ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
                       => ( Y3 @ ( cP @ '#sk1' @ Y1 ) @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y0 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: iS] :
          ( !!
          @ ^ [Y1: iS] :
              ( ( ( !!
                  @ ^ [Y2: iS > iS > iS > $o] :
                      ( ( !!
                        @ ^ [Y3: iS] :
                            ( !!
                            @ ^ [Y4: iS] :
                                ( !!
                                @ ^ [Y5: iS] :
                                    ( ( ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ( Y3
                                                                  = ( cP @ Y6 @ Y7 ) )
                                                                & ( Y4
                                                                  = ( cP @ Y8 @ Y9 ) )
                                                                & ( Y5
                                                                  = ( cP @ Y10 @ Y11 ) )
                                                                & ( Y2 @ Y6 @ Y8 @ Y10 )
                                                                & ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
                                      | ( ( Y3 = Y5 )
                                        & ( Y4 = c0 ) )
                                      | ( ( Y4 = Y5 )
                                        & ( Y3 = c0 ) ) )
                                   => ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
                     => ( Y2 @ Y0 @ Y1 @ Y1 ) ) )
                & ( !!
                  @ ^ [Y2: iS > iS > iS > $o] :
                      ( ( !!
                        @ ^ [Y3: iS] :
                            ( !!
                            @ ^ [Y4: iS] :
                                ( !!
                                @ ^ [Y5: iS] :
                                    ( ( ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ??
                                                            @ ^ [Y11: iS] :
                                                                ( ( Y3
                                                                  = ( cP @ Y6 @ Y7 ) )
                                                                & ( Y4
                                                                  = ( cP @ Y8 @ Y9 ) )
                                                                & ( Y5
                                                                  = ( cP @ Y10 @ Y11 ) )
                                                                & ( Y2 @ Y6 @ Y8 @ Y10 )
                                                                & ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
                                      | ( ( Y3 = Y5 )
                                        & ( Y4 = c0 ) )
                                      | ( ( Y4 = Y5 )
                                        & ( Y3 = c0 ) ) )
                                   => ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
                     => ( Y2 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
             => ( !!
                @ ^ [Y2: iS > iS > iS > $o] :
                    ( ( !!
                      @ ^ [Y3: iS] :
                          ( !!
                          @ ^ [Y4: iS] :
                              ( !!
                              @ ^ [Y5: iS] :
                                  ( ( ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ??
                                                  @ ^ [Y9: iS] :
                                                      ( ??
                                                      @ ^ [Y10: iS] :
                                                          ( ??
                                                          @ ^ [Y11: iS] :
                                                              ( ( Y3
                                                                = ( cP @ Y6 @ Y7 ) )
                                                              & ( Y4
                                                                = ( cP @ Y8 @ Y9 ) )
                                                              & ( Y5
                                                                = ( cP @ Y10 @ Y11 ) )
                                                              & ( Y2 @ Y6 @ Y8 @ Y10 )
                                                              & ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
                                    | ( ( Y3 = Y5 )
                                      & ( Y4 = c0 ) )
                                    | ( ( Y4 = Y5 )
                                      & ( Y3 = c0 ) ) )
                                 => ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
                   => ( Y2 @ ( cP @ '#sk1' @ Y0 ) @ ( cP @ '#sk2' @ Y1 ) @ ( cP @ '#sk2' @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl14,plain,
    ~ ( !!
      @ ^ [Y0: iS] :
          ( ( ( !!
              @ ^ [Y1: iS > iS > iS > $o] :
                  ( ( !!
                    @ ^ [Y2: iS] :
                        ( !!
                        @ ^ [Y3: iS] :
                            ( !!
                            @ ^ [Y4: iS] :
                                ( ( ( ??
                                    @ ^ [Y5: iS] :
                                        ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ( Y2
                                                              = ( cP @ Y5 @ Y6 ) )
                                                            & ( Y3
                                                              = ( cP @ Y7 @ Y8 ) )
                                                            & ( Y4
                                                              = ( cP @ Y9 @ Y10 ) )
                                                            & ( Y1 @ Y5 @ Y7 @ Y9 )
                                                            & ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
                                  | ( ( Y2 = Y4 )
                                    & ( Y3 = c0 ) )
                                  | ( ( Y3 = Y4 )
                                    & ( Y2 = c0 ) ) )
                               => ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
                 => ( Y1 @ '#sk8' @ Y0 @ Y0 ) ) )
            & ( !!
              @ ^ [Y1: iS > iS > iS > $o] :
                  ( ( !!
                    @ ^ [Y2: iS] :
                        ( !!
                        @ ^ [Y3: iS] :
                            ( !!
                            @ ^ [Y4: iS] :
                                ( ( ( ??
                                    @ ^ [Y5: iS] :
                                        ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ??
                                                        @ ^ [Y10: iS] :
                                                            ( ( Y2
                                                              = ( cP @ Y5 @ Y6 ) )
                                                            & ( Y3
                                                              = ( cP @ Y7 @ Y8 ) )
                                                            & ( Y4
                                                              = ( cP @ Y9 @ Y10 ) )
                                                            & ( Y1 @ Y5 @ Y7 @ Y9 )
                                                            & ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
                                  | ( ( Y2 = Y4 )
                                    & ( Y3 = c0 ) )
                                  | ( ( Y3 = Y4 )
                                    & ( Y2 = c0 ) ) )
                               => ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
                 => ( Y1 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
         => ( !!
            @ ^ [Y1: iS > iS > iS > $o] :
                ( ( !!
                  @ ^ [Y2: iS] :
                      ( !!
                      @ ^ [Y3: iS] :
                          ( !!
                          @ ^ [Y4: iS] :
                              ( ( ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ??
                                                  @ ^ [Y9: iS] :
                                                      ( ??
                                                      @ ^ [Y10: iS] :
                                                          ( ( Y2
                                                            = ( cP @ Y5 @ Y6 ) )
                                                          & ( Y3
                                                            = ( cP @ Y7 @ Y8 ) )
                                                          & ( Y4
                                                            = ( cP @ Y9 @ Y10 ) )
                                                          & ( Y1 @ Y5 @ Y7 @ Y9 )
                                                          & ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
                                | ( ( Y2 = Y4 )
                                  & ( Y3 = c0 ) )
                                | ( ( Y3 = Y4 )
                                  & ( Y2 = c0 ) ) )
                             => ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
               => ( Y1 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ Y0 ) @ ( cP @ '#sk2' @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl18,plain,
    ~ ( ( ( !!
          @ ^ [Y0: iS > iS > iS > $o] :
              ( ( !!
                @ ^ [Y1: iS] :
                    ( !!
                    @ ^ [Y2: iS] :
                        ( !!
                        @ ^ [Y3: iS] :
                            ( ( ( ??
                                @ ^ [Y4: iS] :
                                    ( ??
                                    @ ^ [Y5: iS] :
                                        ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ( Y1
                                                          = ( cP @ Y4 @ Y5 ) )
                                                        & ( Y2
                                                          = ( cP @ Y6 @ Y7 ) )
                                                        & ( Y3
                                                          = ( cP @ Y8 @ Y9 ) )
                                                        & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                        & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                              | ( ( Y1 = Y3 )
                                & ( Y2 = c0 ) )
                              | ( ( Y2 = Y3 )
                                & ( Y1 = c0 ) ) )
                           => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) )
        & ( !!
          @ ^ [Y0: iS > iS > iS > $o] :
              ( ( !!
                @ ^ [Y1: iS] :
                    ( !!
                    @ ^ [Y2: iS] :
                        ( !!
                        @ ^ [Y3: iS] :
                            ( ( ( ??
                                @ ^ [Y4: iS] :
                                    ( ??
                                    @ ^ [Y5: iS] :
                                        ( ??
                                        @ ^ [Y6: iS] :
                                            ( ??
                                            @ ^ [Y7: iS] :
                                                ( ??
                                                @ ^ [Y8: iS] :
                                                    ( ??
                                                    @ ^ [Y9: iS] :
                                                        ( ( Y1
                                                          = ( cP @ Y4 @ Y5 ) )
                                                        & ( Y2
                                                          = ( cP @ Y6 @ Y7 ) )
                                                        & ( Y3
                                                          = ( cP @ Y8 @ Y9 ) )
                                                        & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                        & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                              | ( ( Y1 = Y3 )
                                & ( Y2 = c0 ) )
                              | ( ( Y2 = Y3 )
                                & ( Y1 = c0 ) ) )
                           => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
     => ( !!
        @ ^ [Y0: iS > iS > iS > $o] :
            ( ( !!
              @ ^ [Y1: iS] :
                  ( !!
                  @ ^ [Y2: iS] :
                      ( !!
                      @ ^ [Y3: iS] :
                          ( ( ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ??
                                                  @ ^ [Y9: iS] :
                                                      ( ( Y1
                                                        = ( cP @ Y4 @ Y5 ) )
                                                      & ( Y2
                                                        = ( cP @ Y6 @ Y7 ) )
                                                      & ( Y3
                                                        = ( cP @ Y8 @ Y9 ) )
                                                      & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                      & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                            | ( ( Y1 = Y3 )
                              & ( Y2 = c0 ) )
                            | ( ( Y2 = Y3 )
                              & ( Y1 = c0 ) ) )
                         => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
           => ( Y0 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl22,plain,
    ~ ( !!
      @ ^ [Y0: iS > iS > iS > $o] :
          ( ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( !!
                    @ ^ [Y3: iS] :
                        ( ( ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ??
                                                @ ^ [Y9: iS] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl27,plain,
    ~ ( ( !!
        @ ^ [Y0: iS] :
            ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( ( ( ??
                        @ ^ [Y3: iS] :
                            ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( '#sk27' @ Y3 @ Y5 @ Y7 )
                                                & ( '#sk27' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( '#sk27' @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( '#sk27' @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl38,plain,
    ~ ( '#sk27' @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl37,plain,
    ( !!
    @ ^ [Y0: iS] :
        ( !!
        @ ^ [Y1: iS] :
            ( !!
            @ ^ [Y2: iS] :
                ( ( ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ??
                            @ ^ [Y5: iS] :
                                ( ??
                                @ ^ [Y6: iS] :
                                    ( ??
                                    @ ^ [Y7: iS] :
                                        ( ??
                                        @ ^ [Y8: iS] :
                                            ( ( Y0
                                              = ( cP @ Y3 @ Y4 ) )
                                            & ( Y1
                                              = ( cP @ Y5 @ Y6 ) )
                                            & ( Y2
                                              = ( cP @ Y7 @ Y8 ) )
                                            & ( '#sk27' @ Y3 @ Y5 @ Y7 )
                                            & ( '#sk27' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                  | ( ( Y0 = Y2 )
                    & ( Y1 = c0 ) )
                  | ( ( Y1 = Y2 )
                    & ( Y0 = c0 ) ) )
               => ( '#sk27' @ Y0 @ Y1 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl46,plain,
    ! [X2: iS] :
      ( !!
      @ ^ [Y0: iS] :
          ( !!
          @ ^ [Y1: iS] :
              ( ( ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ??
                                  @ ^ [Y6: iS] :
                                      ( ??
                                      @ ^ [Y7: iS] :
                                          ( ( X2
                                            = ( cP @ Y2 @ Y3 ) )
                                          & ( Y0
                                            = ( cP @ Y4 @ Y5 ) )
                                          & ( Y1
                                            = ( cP @ Y6 @ Y7 ) )
                                          & ( '#sk27' @ Y2 @ Y4 @ Y6 )
                                          & ( '#sk27' @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                | ( ( X2 = Y1 )
                  & ( Y0 = c0 ) )
                | ( ( Y0 = Y1 )
                  & ( X2 = c0 ) ) )
             => ( '#sk27' @ X2 @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl51,plain,
    ! [X2: iS,X4: iS] :
      ( !!
      @ ^ [Y0: iS] :
          ( ( ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ??
                                  @ ^ [Y6: iS] :
                                      ( ( X2
                                        = ( cP @ Y1 @ Y2 ) )
                                      & ( X4
                                        = ( cP @ Y3 @ Y4 ) )
                                      & ( Y0
                                        = ( cP @ Y5 @ Y6 ) )
                                      & ( '#sk27' @ Y1 @ Y3 @ Y5 )
                                      & ( '#sk27' @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
            | ( ( X2 = Y0 )
              & ( X4 = c0 ) )
            | ( ( X4 = Y0 )
              & ( X2 = c0 ) ) )
         => ( '#sk27' @ X2 @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl56,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ( ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ( X2
                                    = ( cP @ Y0 @ Y1 ) )
                                  & ( X4
                                    = ( cP @ Y2 @ Y3 ) )
                                  & ( X6
                                    = ( cP @ Y4 @ Y5 ) )
                                  & ( '#sk27' @ Y0 @ Y2 @ Y4 )
                                  & ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
        | ( ( X2 = X6 )
          & ( X4 = c0 ) )
        | ( ( X4 = X6 )
          & ( X2 = c0 ) ) )
     => ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl59,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ~ ( ( ??
            @ ^ [Y0: iS] :
                ( ??
                @ ^ [Y1: iS] :
                    ( ??
                    @ ^ [Y2: iS] :
                        ( ??
                        @ ^ [Y3: iS] :
                            ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ( X2
                                      = ( cP @ Y0 @ Y1 ) )
                                    & ( X4
                                      = ( cP @ Y2 @ Y3 ) )
                                    & ( X6
                                      = ( cP @ Y4 @ Y5 ) )
                                    & ( '#sk27' @ Y0 @ Y2 @ Y4 )
                                    & ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
          | ( ( X2 = X6 )
            & ( X4 = c0 ) )
          | ( ( X4 = X6 )
            & ( X2 = c0 ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl66,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ~ ( ( X4 = X6 )
          & ( X2 = c0 ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl71,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ( X4 != X6 )
      | ( X2 != c0 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl77,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ( X4 != X6 )
      | ( X2 != c0 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl78,plain,
    ! [X6: iS] : ( '#sk27' @ c0 @ X6 @ X6 ),
    inference(simplify,[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl65,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ~ ( ( X2 = X6 )
          & ( X4 = c0 ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl70,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ( X2 != X6 )
      | ( X4 != c0 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl75,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ( X2 != X6 )
      | ( X4 != c0 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl76,plain,
    ! [X6: iS] : ( '#sk27' @ X6 @ c0 @ X6 ),
    inference(simplify,[status(thm)],[zip_derived_cl75]) ).

thf(zip_derived_cl21,plain,
    ( ( !!
      @ ^ [Y0: iS > iS > iS > $o] :
          ( ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( !!
                    @ ^ [Y3: iS] :
                        ( ( ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ??
                                                @ ^ [Y9: iS] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) )
    & ( !!
      @ ^ [Y0: iS > iS > iS > $o] :
          ( ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( !!
                    @ ^ [Y3: iS] :
                        ( ( ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ??
                                                @ ^ [Y9: iS] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl25,plain,
    ( !!
    @ ^ [Y0: iS > iS > iS > $o] :
        ( ( !!
          @ ^ [Y1: iS] :
              ( !!
              @ ^ [Y2: iS] :
                  ( !!
                  @ ^ [Y3: iS] :
                      ( ( ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ??
                                  @ ^ [Y6: iS] :
                                      ( ??
                                      @ ^ [Y7: iS] :
                                          ( ??
                                          @ ^ [Y8: iS] :
                                              ( ??
                                              @ ^ [Y9: iS] :
                                                  ( ( Y1
                                                    = ( cP @ Y4 @ Y5 ) )
                                                  & ( Y2
                                                    = ( cP @ Y6 @ Y7 ) )
                                                  & ( Y3
                                                    = ( cP @ Y8 @ Y9 ) )
                                                  & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                  & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                        | ( ( Y1 = Y3 )
                          & ( Y2 = c0 ) )
                        | ( ( Y2 = Y3 )
                          & ( Y1 = c0 ) ) )
                     => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
       => ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl33,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( !!
        @ ^ [Y0: iS] :
            ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( ( ( ??
                        @ ^ [Y3: iS] :
                            ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( X2 @ Y3 @ Y5 @ Y7 )
                                                & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl44,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( !!
                  @ ^ [Y2: iS] :
                      ( ( ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ( Y0
                                                    = ( cP @ Y3 @ Y4 ) )
                                                  & ( Y1
                                                    = ( cP @ Y5 @ Y6 ) )
                                                  & ( Y2
                                                    = ( cP @ Y7 @ Y8 ) )
                                                  & ( X2 @ Y3 @ Y5 @ Y7 )
                                                  & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                        | ( ( Y0 = Y2 )
                          & ( Y1 = c0 ) )
                        | ( ( Y1 = Y2 )
                          & ( Y0 = c0 ) ) )
                     => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl49,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( ( ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ( ( '#sk72' @ X2 )
                                                = ( cP @ Y2 @ Y3 ) )
                                              & ( Y0
                                                = ( cP @ Y4 @ Y5 ) )
                                              & ( Y1
                                                = ( cP @ Y6 @ Y7 ) )
                                              & ( X2 @ Y2 @ Y4 @ Y6 )
                                              & ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                    | ( ( ( '#sk72' @ X2 )
                        = Y1 )
                      & ( Y0 = c0 ) )
                    | ( ( Y0 = Y1 )
                      & ( ( '#sk72' @ X2 )
                        = c0 ) ) )
                 => ( X2 @ ( '#sk72' @ X2 ) @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl54,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( ( ( ??
                  @ ^ [Y1: iS] :
                      ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ( ( '#sk72' @ X2 )
                                            = ( cP @ Y1 @ Y2 ) )
                                          & ( ( '#sk106' @ X2 )
                                            = ( cP @ Y3 @ Y4 ) )
                                          & ( Y0
                                            = ( cP @ Y5 @ Y6 ) )
                                          & ( X2 @ Y1 @ Y3 @ Y5 )
                                          & ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
                | ( ( ( '#sk72' @ X2 )
                    = Y0 )
                  & ( ( '#sk106' @ X2 )
                    = c0 ) )
                | ( ( ( '#sk106' @ X2 )
                    = Y0 )
                  & ( ( '#sk72' @ X2 )
                    = c0 ) ) )
             => ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl57,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( ( ( ??
              @ ^ [Y0: iS] :
                  ( ??
                  @ ^ [Y1: iS] :
                      ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ( ( '#sk72' @ X2 )
                                        = ( cP @ Y0 @ Y1 ) )
                                      & ( ( '#sk106' @ X2 )
                                        = ( cP @ Y2 @ Y3 ) )
                                      & ( ( '#sk158' @ X2 )
                                        = ( cP @ Y4 @ Y5 ) )
                                      & ( X2 @ Y0 @ Y2 @ Y4 )
                                      & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
            | ( ( ( '#sk72' @ X2 )
                = ( '#sk158' @ X2 ) )
              & ( ( '#sk106' @ X2 )
                = c0 ) )
            | ( ( ( '#sk106' @ X2 )
                = ( '#sk158' @ X2 ) )
              & ( ( '#sk72' @ X2 )
                = c0 ) ) )
         => ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl60,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ??
                            @ ^ [Y5: iS] :
                                ( ( ( '#sk72' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk106' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk158' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl67,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ??
                            @ ^ [Y5: iS] :
                                ( ( ( '#sk72' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk106' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk158' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl72,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ( ( '#sk72' @ X2 )
                              = ( cP @ ( '#sk391' @ X2 ) @ Y0 ) )
                            & ( ( '#sk106' @ X2 )
                              = ( cP @ Y1 @ Y2 ) )
                            & ( ( '#sk158' @ X2 )
                              = ( cP @ Y3 @ Y4 ) )
                            & ( X2 @ ( '#sk391' @ X2 ) @ Y1 @ Y3 )
                            & ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl79,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ( ( '#sk72' @ X2 )
                          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                        & ( ( '#sk106' @ X2 )
                          = ( cP @ Y0 @ Y1 ) )
                        & ( ( '#sk158' @ X2 )
                          = ( cP @ Y2 @ Y3 ) )
                        & ( X2 @ ( '#sk391' @ X2 ) @ Y0 @ Y2 )
                        & ( X2 @ ( '#sk463' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl82,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ( ( '#sk72' @ X2 )
                      = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                    & ( ( '#sk106' @ X2 )
                      = ( cP @ ( '#sk545' @ X2 ) @ Y0 ) )
                    & ( ( '#sk158' @ X2 )
                      = ( cP @ Y1 @ Y2 ) )
                    & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y1 )
                    & ( X2 @ ( '#sk463' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl85,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ( ( '#sk72' @ X2 )
                  = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                & ( ( '#sk106' @ X2 )
                  = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
                & ( ( '#sk158' @ X2 )
                  = ( cP @ Y0 @ Y1 ) )
                & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y1 ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).

thf(zip_derived_cl88,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ( ( '#sk72' @ X2 )
              = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
            & ( ( '#sk106' @ X2 )
              = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
            & ( ( '#sk158' @ X2 )
              = ( cP @ ( '#sk739' @ X2 ) @ Y0 ) )
            & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
            & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl91,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( ( '#sk72' @ X2 )
          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
        & ( ( '#sk106' @ X2 )
          = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
        & ( ( '#sk158' @ X2 )
          = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
        & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
        & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl94,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl105,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl106,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl107,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( '#sk158' @ X2 ) )
      | ~ ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl106]) ).

thf(zip_derived_cl120,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( '#sk158' @ X2 ) )
      | ~ ( '#form1091' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl107]) ).

thf(zip_derived_cl26,plain,
    ( !!
    @ ^ [Y0: iS > iS > iS > $o] :
        ( ( !!
          @ ^ [Y1: iS] :
              ( !!
              @ ^ [Y2: iS] :
                  ( !!
                  @ ^ [Y3: iS] :
                      ( ( ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ??
                                  @ ^ [Y6: iS] :
                                      ( ??
                                      @ ^ [Y7: iS] :
                                          ( ??
                                          @ ^ [Y8: iS] :
                                              ( ??
                                              @ ^ [Y9: iS] :
                                                  ( ( Y1
                                                    = ( cP @ Y4 @ Y5 ) )
                                                  & ( Y2
                                                    = ( cP @ Y6 @ Y7 ) )
                                                  & ( Y3
                                                    = ( cP @ Y8 @ Y9 ) )
                                                  & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                  & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                        | ( ( Y1 = Y3 )
                          & ( Y2 = c0 ) )
                        | ( ( Y2 = Y3 )
                          & ( Y1 = c0 ) ) )
                     => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
       => ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl35,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( !!
        @ ^ [Y0: iS] :
            ( !!
            @ ^ [Y1: iS] :
                ( !!
                @ ^ [Y2: iS] :
                    ( ( ( ??
                        @ ^ [Y3: iS] :
                            ( ??
                            @ ^ [Y4: iS] :
                                ( ??
                                @ ^ [Y5: iS] :
                                    ( ??
                                    @ ^ [Y6: iS] :
                                        ( ??
                                        @ ^ [Y7: iS] :
                                            ( ??
                                            @ ^ [Y8: iS] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( X2 @ Y3 @ Y5 @ Y7 )
                                                & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl45,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( !!
                  @ ^ [Y2: iS] :
                      ( ( ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ??
                                              @ ^ [Y8: iS] :
                                                  ( ( Y0
                                                    = ( cP @ Y3 @ Y4 ) )
                                                  & ( Y1
                                                    = ( cP @ Y5 @ Y6 ) )
                                                  & ( Y2
                                                    = ( cP @ Y7 @ Y8 ) )
                                                  & ( X2 @ Y3 @ Y5 @ Y7 )
                                                  & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                        | ( ( Y0 = Y2 )
                          & ( Y1 = c0 ) )
                        | ( ( Y1 = Y2 )
                          & ( Y0 = c0 ) ) )
                     => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl50,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( !!
              @ ^ [Y1: iS] :
                  ( ( ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ??
                                          @ ^ [Y7: iS] :
                                              ( ( ( '#sk72' @ X2 )
                                                = ( cP @ Y2 @ Y3 ) )
                                              & ( Y0
                                                = ( cP @ Y4 @ Y5 ) )
                                              & ( Y1
                                                = ( cP @ Y6 @ Y7 ) )
                                              & ( X2 @ Y2 @ Y4 @ Y6 )
                                              & ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                    | ( ( ( '#sk72' @ X2 )
                        = Y1 )
                      & ( Y0 = c0 ) )
                    | ( ( Y0 = Y1 )
                      & ( ( '#sk72' @ X2 )
                        = c0 ) ) )
                 => ( X2 @ ( '#sk72' @ X2 ) @ Y0 @ Y1 ) ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl55,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( !!
          @ ^ [Y0: iS] :
              ( ( ( ??
                  @ ^ [Y1: iS] :
                      ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ??
                                      @ ^ [Y6: iS] :
                                          ( ( ( '#sk72' @ X2 )
                                            = ( cP @ Y1 @ Y2 ) )
                                          & ( ( '#sk106' @ X2 )
                                            = ( cP @ Y3 @ Y4 ) )
                                          & ( Y0
                                            = ( cP @ Y5 @ Y6 ) )
                                          & ( X2 @ Y1 @ Y3 @ Y5 )
                                          & ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
                | ( ( ( '#sk72' @ X2 )
                    = Y0 )
                  & ( ( '#sk106' @ X2 )
                    = c0 ) )
                | ( ( ( '#sk106' @ X2 )
                    = Y0 )
                  & ( ( '#sk72' @ X2 )
                    = c0 ) ) )
             => ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl58,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( ( ( ??
              @ ^ [Y0: iS] :
                  ( ??
                  @ ^ [Y1: iS] :
                      ( ??
                      @ ^ [Y2: iS] :
                          ( ??
                          @ ^ [Y3: iS] :
                              ( ??
                              @ ^ [Y4: iS] :
                                  ( ??
                                  @ ^ [Y5: iS] :
                                      ( ( ( '#sk72' @ X2 )
                                        = ( cP @ Y0 @ Y1 ) )
                                      & ( ( '#sk106' @ X2 )
                                        = ( cP @ Y2 @ Y3 ) )
                                      & ( ( '#sk158' @ X2 )
                                        = ( cP @ Y4 @ Y5 ) )
                                      & ( X2 @ Y0 @ Y2 @ Y4 )
                                      & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
            | ( ( ( '#sk72' @ X2 )
                = ( '#sk158' @ X2 ) )
              & ( ( '#sk106' @ X2 )
                = c0 ) )
            | ( ( ( '#sk106' @ X2 )
                = ( '#sk158' @ X2 ) )
              & ( ( '#sk72' @ X2 )
                = c0 ) ) )
         => ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl62,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ??
                            @ ^ [Y5: iS] :
                                ( ( ( '#sk72' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk106' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk158' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl68,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ??
                            @ ^ [Y5: iS] :
                                ( ( ( '#sk72' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk106' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk158' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl73,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ??
                        @ ^ [Y4: iS] :
                            ( ( ( '#sk72' @ X2 )
                              = ( cP @ ( '#sk391' @ X2 ) @ Y0 ) )
                            & ( ( '#sk106' @ X2 )
                              = ( cP @ Y1 @ Y2 ) )
                            & ( ( '#sk158' @ X2 )
                              = ( cP @ Y3 @ Y4 ) )
                            & ( X2 @ ( '#sk391' @ X2 ) @ Y1 @ Y3 )
                            & ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl80,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ??
                    @ ^ [Y3: iS] :
                        ( ( ( '#sk72' @ X2 )
                          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                        & ( ( '#sk106' @ X2 )
                          = ( cP @ Y0 @ Y1 ) )
                        & ( ( '#sk158' @ X2 )
                          = ( cP @ Y2 @ Y3 ) )
                        & ( X2 @ ( '#sk391' @ X2 ) @ Y0 @ Y2 )
                        & ( X2 @ ( '#sk463' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl83,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ??
                @ ^ [Y2: iS] :
                    ( ( ( '#sk72' @ X2 )
                      = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                    & ( ( '#sk106' @ X2 )
                      = ( cP @ ( '#sk545' @ X2 ) @ Y0 ) )
                    & ( ( '#sk158' @ X2 )
                      = ( cP @ Y1 @ Y2 ) )
                    & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y1 )
                    & ( X2 @ ( '#sk463' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl86,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ??
            @ ^ [Y1: iS] :
                ( ( ( '#sk72' @ X2 )
                  = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
                & ( ( '#sk106' @ X2 )
                  = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
                & ( ( '#sk158' @ X2 )
                  = ( cP @ Y0 @ Y1 ) )
                & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y1 ) ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl89,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ??
        @ ^ [Y0: iS] :
            ( ( ( '#sk72' @ X2 )
              = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
            & ( ( '#sk106' @ X2 )
              = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
            & ( ( '#sk158' @ X2 )
              = ( cP @ ( '#sk739' @ X2 ) @ Y0 ) )
            & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
            & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl92,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( ( '#sk72' @ X2 )
          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
        & ( ( '#sk106' @ X2 )
          = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
        & ( ( '#sk158' @ X2 )
          = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
        & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
        & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl99,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl100,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( '#sk158' @ X2 ) )
      | ~ ( '#form1036' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).

thf(zip_derived_cl117,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( '#sk158' @ X2 ) )
      | ~ ( '#form1036' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl92_001,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( ( '#sk72' @ X2 )
          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
        & ( ( '#sk106' @ X2 )
          = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
        & ( ( '#sk158' @ X2 )
          = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
        & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
        & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl99_002,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl102,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
        & ( ( '#sk106' @ X2 )
          = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
        & ( ( '#sk158' @ X2 )
          = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
        & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
        & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl92,zip_derived_cl99]) ).

thf(zip_derived_cl106_003,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl116,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
        & ( ( '#sk106' @ X2 )
          = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
        & ( ( '#sk158' @ X2 )
          = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
        & ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
        & ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1036' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl102,zip_derived_cl106]) ).

thf(zip_derived_cl126,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl131,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl101,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = c0 )
      | ~ ( '#form1036' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).

thf(zip_derived_cl118,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = c0 )
      | ~ ( '#form1036' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl101]) ).

thf(zip_derived_cl63,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl127,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl132,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl127]) ).

thf(zip_derived_cl105_004,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl106_005,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl109,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl105,zip_derived_cl106]) ).

thf(zip_derived_cl99_006,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl119,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( ( '#sk72' @ X2 )
        = ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( '#form1091' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl109,zip_derived_cl99]) ).

thf(zip_derived_cl108,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = c0 )
      | ~ ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl106]) ).

thf(zip_derived_cl121,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk72' @ X2 )
        = c0 )
      | ~ ( '#form1091' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl128,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl133,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl128]) ).

thf(zip_derived_cl61,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl95,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl110,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl95]) ).

thf(zip_derived_cl106_007,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl111,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl110,zip_derived_cl106]) ).

thf(zip_derived_cl99_008,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl122,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( ( '#sk106' @ X2 )
        = ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( '#form1091' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl111,zip_derived_cl99]) ).

thf(zip_derived_cl129,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl96,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl112,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl106_009,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl113,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl112,zip_derived_cl106]) ).

thf(zip_derived_cl99_010,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl123,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( ( '#sk158' @ X2 )
        = ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( '#form1091' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl113,zip_derived_cl99]) ).

thf(zip_derived_cl130,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
      | ( '#form1036' @ X2 )
      | ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
      | ( '#form1091' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl97,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl106_011,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl114,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl97,zip_derived_cl106]) ).

thf(zip_derived_cl99_012,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl124,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( '#form1091' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl114,zip_derived_cl99]) ).

thf(zip_derived_cl98,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl106_013,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1091' @ X2 )
      | ( ( ( '#sk106' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk72' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl115,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1091' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl98,zip_derived_cl106]) ).

thf(zip_derived_cl99_014,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ~ ( '#form1036' @ X2 )
      | ( ( ( '#sk72' @ X2 )
          = ( '#sk158' @ X2 ) )
        & ( ( '#sk106' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl125,plain,
    ! [X2: iS > iS > iS > $o] :
      ( ( '#form1036' @ X2 )
      | ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
      | ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
      | ( '#form1091' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl115,zip_derived_cl99]) ).

thf(zip_derived_cl64,plain,
    ! [X2: iS,X4: iS,X6: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ??
                          @ ^ [Y4: iS] :
                              ( ??
                              @ ^ [Y5: iS] :
                                  ( ( X2
                                    = ( cP @ Y0 @ Y1 ) )
                                  & ( X4
                                    = ( cP @ Y2 @ Y3 ) )
                                  & ( X6
                                    = ( cP @ Y4 @ Y5 ) )
                                  & ( '#sk27' @ Y0 @ Y2 @ Y4 )
                                  & ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl69,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ??
                          @ ^ [Y4: iS] :
                              ( ( X2
                                = ( cP @ X8 @ Y0 ) )
                              & ( X4
                                = ( cP @ Y1 @ Y2 ) )
                              & ( X6
                                = ( cP @ Y3 @ Y4 ) )
                              & ( '#sk27' @ X8 @ Y1 @ Y3 )
                              & ( '#sk27' @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl74,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ??
                      @ ^ [Y3: iS] :
                          ( ( X2
                            = ( cP @ X8 @ X10 ) )
                          & ( X4
                            = ( cP @ Y0 @ Y1 ) )
                          & ( X6
                            = ( cP @ Y2 @ Y3 ) )
                          & ( '#sk27' @ X8 @ Y0 @ Y2 )
                          & ( '#sk27' @ X10 @ Y1 @ Y3 ) ) ) ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl81,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ??
                  @ ^ [Y2: iS] :
                      ( ( X2
                        = ( cP @ X8 @ X10 ) )
                      & ( X4
                        = ( cP @ X12 @ Y0 ) )
                      & ( X6
                        = ( cP @ Y1 @ Y2 ) )
                      & ( '#sk27' @ X8 @ X12 @ Y1 )
                      & ( '#sk27' @ X10 @ Y0 @ Y2 ) ) ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl84,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ??
              @ ^ [Y1: iS] :
                  ( ( X2
                    = ( cP @ X8 @ X10 ) )
                  & ( X4
                    = ( cP @ X12 @ X14 ) )
                  & ( X6
                    = ( cP @ Y0 @ Y1 ) )
                  & ( '#sk27' @ X8 @ X12 @ Y0 )
                  & ( '#sk27' @ X10 @ X14 @ Y1 ) ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl87,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS] :
      ( ~ ( ??
          @ ^ [Y0: iS] :
              ( ( X2
                = ( cP @ X8 @ X10 ) )
              & ( X4
                = ( cP @ X12 @ X14 ) )
              & ( X6
                = ( cP @ X16 @ Y0 ) )
              & ( '#sk27' @ X8 @ X12 @ X16 )
              & ( '#sk27' @ X10 @ X14 @ Y0 ) ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).

thf(zip_derived_cl90,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
      ( ~ ( ( X2
            = ( cP @ X8 @ X10 ) )
          & ( X4
            = ( cP @ X12 @ X14 ) )
          & ( X6
            = ( cP @ X16 @ X18 ) )
          & ( '#sk27' @ X8 @ X12 @ X16 )
          & ( '#sk27' @ X10 @ X14 @ X18 ) )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl93,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
      ( ( X2
       != ( cP @ X8 @ X10 ) )
      | ( X4
       != ( cP @ X12 @ X14 ) )
      | ( X6
       != ( cP @ X16 @ X18 ) )
      | ~ ( '#sk27' @ X8 @ X12 @ X16 )
      | ~ ( '#sk27' @ X10 @ X14 @ X18 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl103,plain,
    ! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
      ( ( X2
       != ( cP @ X8 @ X10 ) )
      | ( X4
       != ( cP @ X12 @ X14 ) )
      | ( X6
       != ( cP @ X16 @ X18 ) )
      | ~ ( '#sk27' @ X8 @ X12 @ X16 )
      | ~ ( '#sk27' @ X10 @ X14 @ X18 )
      | ( '#sk27' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl104,plain,
    ! [X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
      ( ( '#sk27' @ ( cP @ X8 @ X10 ) @ ( cP @ X12 @ X14 ) @ ( cP @ X16 @ X18 ) )
      | ~ ( '#sk27' @ X10 @ X14 @ X18 )
      | ~ ( '#sk27' @ X8 @ X12 @ X16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl103]) ).

thf(zip_derived_cl7264,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl38,zip_derived_cl78,zip_derived_cl76,zip_derived_cl120,zip_derived_cl117,zip_derived_cl131,zip_derived_cl118,zip_derived_cl63,zip_derived_cl132,zip_derived_cl119,zip_derived_cl121,zip_derived_cl133,zip_derived_cl61,zip_derived_cl122,zip_derived_cl129,zip_derived_cl123,zip_derived_cl130,zip_derived_cl124,zip_derived_cl125,zip_derived_cl104]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEV212^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qls7Fw4nC7 true
% 0.15/0.37  % Computer : n016.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug 24 03:05:53 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  % Running portfolio for 300 s
% 0.15/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37  % Number of cores: 8
% 0.15/0.37  % Python version: Python 3.6.8
% 0.15/0.37  % Running in HO mode
% 0.22/0.69  % Total configuration time : 828
% 0.22/0.69  % Estimated wc time : 1656
% 0.22/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 50.95/7.49  % Solved by lams/20_acsne_simpl.sh.
% 50.95/7.49  % done 617 iterations in 6.598s
% 50.95/7.49  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 50.95/7.49  % SZS output start Refutation
% See solution above
% 50.95/7.50  
% 50.95/7.50  
% 50.95/7.50  % Terminating...
% 50.95/7.61  % Runner terminated.
% 50.95/7.63  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------