TSTP Solution File: SEU686^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU686^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vMXI4feYTF true

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:16:12 EDT 2023

% Result   : Theorem 1.45s 0.99s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  155 (  36 unt;  22 typ;   0 def)
%            Number of atoms       :  949 ( 149 equ;   0 cnn)
%            Maximal formula atoms :   52 (   7 avg)
%            Number of connectives : 3751 ( 171   ~; 162   |;  90   &;2874   @)
%                                         (   0 <=>; 256  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   55 (  55   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  22 usr;  12 con; 0-4 aty)
%                                         ( 157  !!;  41  ??;   0 @@+;   0 @@-)
%            Number of variables   :  623 ( 354   ^; 258   !;  11   ?; 623   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk11_type',type,
    '#sk11': $i ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf('#sk35_type',type,
    '#sk35': $i > $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf('#sk25_type',type,
    '#sk25': $i ).

thf(ap_type,type,
    ap: $i > $i > $i > $i > $i ).

thf(func_type,type,
    func: $i > $i > $i > $o ).

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

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

thf(singleton_type,type,
    singleton: $i > $o ).

thf(funcGraphProp1_type,type,
    funcGraphProp1: $o ).

thf('#sk32_type',type,
    '#sk32': $i ).

thf(ex1E2_type,type,
    ex1E2: $o ).

thf('#sk6_type',type,
    '#sk6': $i ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(ex1_type,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

thf('#sk1_type',type,
    '#sk1': $i ).

thf(app_type,type,
    app: $o ).

thf(breln_type,type,
    breln: $i > $i > $i > $o ).

thf(funcGraphProp1,axiom,
    ( funcGraphProp1
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).

thf('0',plain,
    ( funcGraphProp1
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(ex1E2,axiom,
    ( ex1E2
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ( ex1 @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) ) ) ) ) ).

thf('1',plain,
    ( ex1E2
    = ( ! [X4: $i,X6: $i > $o] :
          ( ( ex1 @ X4
            @ ^ [V_1: $i] : ( X6 @ V_1 ) )
         => ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ! [X10: $i] :
                  ( ( in @ X10 @ X4 )
                 => ( ( X6 @ X8 )
                   => ( ( X6 @ X10 )
                     => ( X8 = X10 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(app,axiom,
    ( app
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).

thf('2',plain,
    ( app
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(func,axiom,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).

thf(breln,axiom,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf('3',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('4',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ) ).

thf('5',plain,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[singleton]) ).

thf('6',plain,
    ( singleton
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ( V_1
            = ( setadjoin @ X4 @ emptyset ) )
          & ( in @ X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf('7',plain,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ex1,'6']) ).

thf('8',plain,
    ( ex1
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( singleton
          @ ( dsetconstr @ V_1
            @ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
    define([status(thm)]) ).

thf('9',plain,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[func,'4','8','6']) ).

thf('10',plain,
    ( func
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] :
          ( ( breln @ V_1 @ V_2 @ V_3 )
          & ! [X4: $i] :
              ( ( in @ X4 @ V_1 )
             => ( ex1 @ V_2
                @ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(funcGraphProp2,conjecture,
    ( app
   => ( ex1E2
     => ( funcGraphProp1
       => ! [A: $i,B: $i,Xf: $i] :
            ( ( func @ A @ B @ Xf )
           => ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ! [Xy: $i] :
                    ( ( in @ Xy @ B )
                   => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                     => ( ( ap @ A @ B @ Xf @ Xx )
                        = Xy ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i,X8: $i] :
        ( ( ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ? [X12: $i] :
                  ( ( in @ X12
                    @ ( dsetconstr @ X6
                      @ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) )
                  & ( ( dsetconstr @ X6
                      @ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
                    = ( setadjoin @ X12 @ emptyset ) ) ) )
          & ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) )
       => ! [X14: $i] :
            ( ( in @ X14 @ X4 )
           => ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) )
   => ( ! [X16: $i,X18: $i > $o] :
          ( ? [X20: $i] :
              ( ( in @ X20
                @ ( dsetconstr @ X16
                  @ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
              & ( ( dsetconstr @ X16
                  @ ^ [V_3: $i] : ( X18 @ V_3 ) )
                = ( setadjoin @ X20 @ emptyset ) ) )
         => ! [X22: $i] :
              ( ( in @ X22 @ X16 )
             => ! [X24: $i] :
                  ( ( in @ X24 @ X16 )
                 => ( ( X18 @ X22 )
                   => ( ( X18 @ X24 )
                     => ( X22 = X24 ) ) ) ) ) )
     => ( ! [X26: $i,X28: $i,X30: $i] :
            ( ( ! [X32: $i] :
                  ( ( in @ X32 @ X26 )
                 => ? [X34: $i] :
                      ( ( in @ X34
                        @ ( dsetconstr @ X28
                          @ ^ [V_6: $i] : ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) )
                      & ( ( dsetconstr @ X28
                          @ ^ [V_5: $i] : ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) )
                        = ( setadjoin @ X34 @ emptyset ) ) ) )
              & ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) )
           => ! [X36: $i] :
                ( ( in @ X36 @ X26 )
               => ( in @ ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) )
       => ! [X38: $i,X40: $i,X42: $i] :
            ( ( ! [X44: $i] :
                  ( ( in @ X44 @ X38 )
                 => ? [X46: $i] :
                      ( ( in @ X46
                        @ ( dsetconstr @ X40
                          @ ^ [V_8: $i] : ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) )
                      & ( ( dsetconstr @ X40
                          @ ^ [V_7: $i] : ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) )
                        = ( setadjoin @ X46 @ emptyset ) ) ) )
              & ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) )
           => ! [X48: $i] :
                ( ( in @ X48 @ X38 )
               => ! [X50: $i] :
                    ( ( in @ X50 @ X40 )
                   => ( ( in @ ( kpair @ X48 @ X50 ) @ X42 )
                     => ( ( ap @ X38 @ X40 @ X42 @ X48 )
                        = X50 ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( ! [X10: $i] :
                ( ( in @ X10 @ X4 )
               => ? [X12: $i] :
                    ( ( in @ X12
                      @ ( dsetconstr @ X6
                        @ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) )
                    & ( ( dsetconstr @ X6
                        @ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
                      = ( setadjoin @ X12 @ emptyset ) ) ) )
            & ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) )
         => ! [X14: $i] :
              ( ( in @ X14 @ X4 )
             => ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) )
     => ( ! [X16: $i,X18: $i > $o] :
            ( ? [X20: $i] :
                ( ( in @ X20
                  @ ( dsetconstr @ X16
                    @ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
                & ( ( dsetconstr @ X16
                    @ ^ [V_3: $i] : ( X18 @ V_3 ) )
                  = ( setadjoin @ X20 @ emptyset ) ) )
           => ! [X22: $i] :
                ( ( in @ X22 @ X16 )
               => ! [X24: $i] :
                    ( ( in @ X24 @ X16 )
                   => ( ( X18 @ X22 )
                     => ( ( X18 @ X24 )
                       => ( X22 = X24 ) ) ) ) ) )
       => ( ! [X26: $i,X28: $i,X30: $i] :
              ( ( ! [X32: $i] :
                    ( ( in @ X32 @ X26 )
                   => ? [X34: $i] :
                        ( ( in @ X34
                          @ ( dsetconstr @ X28
                            @ ^ [V_6: $i] : ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) )
                        & ( ( dsetconstr @ X28
                            @ ^ [V_5: $i] : ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) )
                          = ( setadjoin @ X34 @ emptyset ) ) ) )
                & ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) )
             => ! [X36: $i] :
                  ( ( in @ X36 @ X26 )
                 => ( in @ ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) )
         => ! [X38: $i,X40: $i,X42: $i] :
              ( ( ! [X44: $i] :
                    ( ( in @ X44 @ X38 )
                   => ? [X46: $i] :
                        ( ( in @ X46
                          @ ( dsetconstr @ X40
                            @ ^ [V_8: $i] : ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) )
                        & ( ( dsetconstr @ X40
                            @ ^ [V_7: $i] : ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) )
                          = ( setadjoin @ X46 @ emptyset ) ) ) )
                & ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) )
             => ! [X48: $i] :
                  ( ( in @ X48 @ X38 )
                 => ! [X50: $i] :
                      ( ( in @ X50 @ X40 )
                     => ( ( in @ ( kpair @ X48 @ X50 ) @ X42 )
                       => ( ( ap @ X38 @ X40 @ X42 @ X48 )
                          = X50 ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                   => ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i > $o] :
                  ( ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ Y0
                            @ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
                        & ( ( dsetconstr @ Y0
                            @ ^ [Y3: $i] : ( Y1 @ Y3 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ Y0 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( ( Y1 @ Y2 )
                               => ( ( Y1 @ Y3 )
                                 => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
       => ( ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( !!
                    @ ^ [Y2: $i] :
                        ( ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( in @ Y3 @ Y0 )
                               => ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( in @ Y4
                                        @ ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                      & ( ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                        = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                          & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
         => ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( !!
                    @ ^ [Y2: $i] :
                        ( ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( in @ Y3 @ Y0 )
                               => ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( in @ Y4
                                        @ ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                      & ( ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                        = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                          & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( in @ Y4 @ Y1 )
                                   => ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
                                     => ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
                                        = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                   => ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i > $o] :
                  ( ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                        & ( ( dsetconstr @ Y0 @ Y1 )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ Y0 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( ( Y1 @ Y2 )
                               => ( ( Y1 @ Y3 )
                                 => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
       => ( ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( !!
                    @ ^ [Y2: $i] :
                        ( ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( in @ Y3 @ Y0 )
                               => ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( in @ Y4
                                        @ ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                      & ( ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                        = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                          & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
         => ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( !!
                    @ ^ [Y2: $i] :
                        ( ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( in @ Y3 @ Y0 )
                               => ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( in @ Y4
                                        @ ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                      & ( ( dsetconstr @ Y1
                                          @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                        = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                          & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( in @ Y4 @ Y1 )
                                   => ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
                                     => ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
                                        = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                      & ( ( dsetconstr @ Y0 @ Y1 )
                        = ( setadjoin @ Y2 @ emptyset ) ) ) )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ Y0 )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ( Y1 @ Y2 )
                             => ( ( Y1 @ Y3 )
                               => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( ??
                                @ ^ [Y4: $i] :
                                    ( ( in @ Y4
                                      @ ( dsetconstr @ Y1
                                        @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                    & ( ( dsetconstr @ Y1
                                        @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                      = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                        & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( ??
                                @ ^ [Y4: $i] :
                                    ( ( in @ Y4
                                      @ ( dsetconstr @ Y1
                                        @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                    & ( ( dsetconstr @ Y1
                                        @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                      = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                        & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4 @ Y1 )
                                 => ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
                                   => ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
                                      = Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                   => ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                   => ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( !!
                            @ ^ [Y4: $i] :
                                ( ( in @ Y4 @ Y1 )
                               => ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
                                 => ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
                                    = Y4 ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( ??
                            @ ^ [Y4: $i] :
                                ( ( in @ Y4
                                  @ ( dsetconstr @ Y1
                                    @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                & ( ( dsetconstr @ Y1
                                    @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                  = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                    & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
                 => ( !!
                    @ ^ [Y3: $i] :
                        ( ( in @ Y3 @ Y0 )
                       => ( !!
                          @ ^ [Y4: $i] :
                              ( ( in @ Y4 @ Y1 )
                             => ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
                               => ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
                                  = Y4 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl14,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ '#sk1' )
                     => ( ??
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3
                              @ ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
                            & ( ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
                              = ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
                & ( subset @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) ) )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ '#sk1' )
                   => ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
                           => ( ( ap @ '#sk1' @ Y0 @ Y1 @ Y2 )
                              = Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl18,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ '#sk1' )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ '#sk6'
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ '#sk6'
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk6' ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ '#sk1' )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ '#sk6' )
                     => ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
                       => ( ( ap @ '#sk1' @ '#sk6' @ Y0 @ Y1 )
                          = Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl22,plain,
    ~ ( ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ '#sk1' )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ '#sk6'
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
                    & ( ( dsetconstr @ '#sk6'
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ '#sk1' )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ '#sk6' )
                 => ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk11' )
                   => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ Y0 )
                      = Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl26,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ '#sk1' )
         => ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1
                  @ ( dsetconstr @ '#sk6'
                    @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
                & ( ( dsetconstr @ '#sk6'
                    @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
                  = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
    & ( subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl34,plain,
    subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl33,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ '#sk1' )
       => ( ??
          @ ^ [Y1: $i] :
              ( ( in @ Y1
                @ ( dsetconstr @ '#sk6'
                  @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
              & ( ( dsetconstr @ '#sk6'
                  @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
                = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ '#sk1' )
     => ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0
              @ ( dsetconstr @ '#sk6'
                @ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) ) )
            & ( ( dsetconstr @ '#sk6'
                @ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) )
              = ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ '#sk1' )
      | ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0
              @ ( dsetconstr @ '#sk6'
                @ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) ) )
            & ( ( dsetconstr @ '#sk6'
                @ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) )
              = ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl55,plain,
    ! [X2: $i] :
      ( ( ( in @ ( '#sk35' @ X2 )
          @ ( dsetconstr @ '#sk6'
            @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
        & ( ( dsetconstr @ '#sk6'
            @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
          = ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl62,plain,
    ! [X2: $i] :
      ( ( in @ ( '#sk35' @ X2 )
        @ ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( !!
                    @ ^ [Y3: $i] :
                        ( ( in @ Y3 @ Y0 )
                       => ( ??
                          @ ^ [Y4: $i] :
                              ( ( in @ Y4
                                @ ( dsetconstr @ Y1
                                  @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                              & ( ( dsetconstr @ Y1
                                  @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                  & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
               => ( !!
                  @ ^ [Y3: $i] :
                      ( ( in @ Y3 @ Y0 )
                     => ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl4,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ X2 )
                     => ( ??
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3
                              @ ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
                            & ( ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
                              = ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
                & ( subset @ Y1 @ ( cartprod @ X2 @ Y0 ) ) )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ X2 )
                   => ( in @ ( ap @ X2 @ Y0 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X4
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X4
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ X2 )
               => ( in @ ( ap @ X2 @ X4 @ Y0 @ Y1 ) @ X4 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ X2 )
               => ( ??
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1
                        @ ( dsetconstr @ X4
                          @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                      & ( ( dsetconstr @ X4
                          @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                        = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
          & ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
         => ( ??
            @ ^ [Y0: $i] :
                ( ( in @ Y0
                  @ ( dsetconstr @ X4
                    @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
                  = ( setadjoin @ Y0 @ emptyset ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0
                @ ( dsetconstr @ X4
                  @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
                = ( setadjoin @ Y0 @ emptyset ) ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl37,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
          & ( ( dsetconstr @ X4
              @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
            = ( setadjoin @ X8 @ emptyset ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
      ( ( ( in @ X10 @ X2 )
       => ( in @ ( ap @ X2 @ X4 @ X6 @ X10 ) @ X4 ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl58,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
      ( ~ ( in @ X10 @ X2 )
      | ( in @ ( ap @ X2 @ X4 @ X6 @ X10 ) @ X4 )
      | ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl113,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
      | ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ Y0 ) @ '#sk11' ) )
       != ( setadjoin @ ( '#sk35' @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) ) @ emptyset ) )
      | ( in @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) @ '#sk6' )
      | ~ ( in @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl58]) ).

thf(zip_derived_cl63,plain,
    ! [X2: $i] :
      ( ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
        = ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl69,plain,
    ! [X2: $i] :
      ( ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
        = ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl125,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ( in @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) @ '#sk6' )
      | ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
      | ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
    inference(clc,[status(thm)],[zip_derived_cl113,zip_derived_cl69]) ).

thf(zip_derived_cl126,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl125]) ).

thf(zip_derived_cl34_001,plain,
    subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( ( in @ X8 @ X2 )
       => ( in @ ( ap @ X2 @ X4 @ X6 @ X8 ) @ X4 ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8 @ X2 )
      | ( in @ ( ap @ X2 @ X4 @ X6 @ X8 ) @ X4 )
      | ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl96,plain,
    ! [X0: $i] :
      ( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl43]) ).

thf(zip_derived_cl128,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' ) ),
    inference(clc,[status(thm)],[zip_derived_cl126,zip_derived_cl96]) ).

thf(zip_derived_cl27,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ '#sk1' )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ '#sk6' )
               => ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk11' )
                 => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ Y0 )
                    = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl35,plain,
    ~ ( ( in @ '#sk25' @ '#sk1' )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ '#sk6' )
           => ( ( in @ ( kpair @ '#sk25' @ Y0 ) @ '#sk11' )
             => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
                = Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl42,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ '#sk6' )
         => ( ( in @ ( kpair @ '#sk25' @ Y0 ) @ '#sk11' )
           => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
              = Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl49,plain,
    ~ ( ( in @ '#sk32' @ '#sk6' )
     => ( ( in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11' )
       => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
          = '#sk32' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl57,plain,
    ~ ( ( in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11' )
     => ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
        = '#sk32' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl64,plain,
    in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl62_002,plain,
    ! [X2: $i] :
      ( ( in @ ( '#sk35' @ X2 )
        @ ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( ( ??
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                  & ( ( dsetconstr @ Y0 @ Y1 )
                    = ( setadjoin @ Y2 @ emptyset ) ) ) )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ Y0 )
                 => ( !!
                    @ ^ [Y3: $i] :
                        ( ( in @ Y3 @ Y0 )
                       => ( ( Y1 @ Y2 )
                         => ( ( Y1 @ Y3 )
                           => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $o] :
          ( ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
                & ( ( dsetconstr @ X2 @ Y0 )
                  = ( setadjoin @ Y1 @ emptyset ) ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ X2 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ X2 )
                     => ( ( Y0 @ Y1 )
                       => ( ( Y0 @ Y2 )
                         => ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
            & ( ( dsetconstr @ X2 @ X4 )
              = ( setadjoin @ Y0 @ emptyset ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ( X4 @ Y0 )
                   => ( ( X4 @ Y1 )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ~ ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
              & ( ( dsetconstr @ X2 @ X4 )
                = ( setadjoin @ Y0 @ emptyset ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ( X4 @ Y0 )
                   => ( ( X4 @ Y1 )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
          & ( ( dsetconstr @ X2 @ X4 )
            = ( setadjoin @ X6 @ emptyset ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ( X4 @ Y0 )
                   => ( ( X4 @ Y1 )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ( X4 @ Y0 )
                   => ( ( X4 @ Y1 )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ( X4 @ Y0 )
                   => ( ( X4 @ Y1 )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( ( in @ X8 @ X2 )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( ( X4 @ X8 )
               => ( ( X4 @ Y0 )
                 => ( X8 = Y0 ) ) ) ) ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( in @ X8 @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( ( X4 @ X8 )
             => ( ( X4 @ Y0 )
               => ( X8 = Y0 ) ) ) ) )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl45,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
      ( ( ( in @ X10 @ X2 )
       => ( ( X4 @ X8 )
         => ( ( X4 @ X10 )
           => ( X8 = X10 ) ) ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ~ ( in @ X8 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl52,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
      ( ~ ( in @ X10 @ X2 )
      | ( ( X4 @ X8 )
       => ( ( X4 @ X10 )
         => ( X8 = X10 ) ) )
      | ~ ( in @ X8 @ X2 )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl59,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
      ( ~ ( X4 @ X8 )
      | ( ( X4 @ X10 )
       => ( X8 = X10 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ~ ( in @ X8 @ X2 )
      | ~ ( in @ X10 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl66,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
      ( ~ ( X4 @ X10 )
      | ( X8 = X10 )
      | ~ ( in @ X10 @ X2 )
      | ~ ( in @ X8 @ X2 )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ~ ( X4 @ X8 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl71,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
      ( ~ ( X4 @ X10 )
      | ( X8 = X10 )
      | ~ ( in @ X10 @ X2 )
      | ~ ( in @ X8 @ X2 )
      | ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( ( dsetconstr @ X2 @ X4 )
       != ( setadjoin @ X6 @ emptyset ) )
      | ~ ( X4 @ X8 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl81,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ~ ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' )
          @ X1 )
      | ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' ) )
       != ( setadjoin @ ( '#sk35' @ X0 ) @ emptyset ) )
      | ~ ( in @ X1 @ '#sk6' )
      | ~ ( in @ X2 @ '#sk6' )
      | ( X1 = X2 )
      | ~ ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' )
          @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl71]) ).

thf(zip_derived_cl95,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ~ ( in @ ( kpair @ X0 @ X1 ) @ '#sk11' )
      | ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' ) )
       != ( setadjoin @ ( '#sk35' @ X0 ) @ emptyset ) )
      | ~ ( in @ X1 @ '#sk6' )
      | ~ ( in @ X2 @ '#sk6' )
      | ( X1 = X2 )
      | ~ ( in @ ( kpair @ X0 @ X2 ) @ '#sk11' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl69_003,plain,
    ! [X2: $i] :
      ( ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
        = ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl130,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ ( kpair @ X0 @ X2 ) @ '#sk11' )
      | ( X1 = X2 )
      | ~ ( in @ X2 @ '#sk6' )
      | ~ ( in @ X1 @ '#sk6' )
      | ~ ( in @ ( kpair @ X0 @ X1 ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference(clc,[status(thm)],[zip_derived_cl95,zip_derived_cl69]) ).

thf(zip_derived_cl131,plain,
    ! [X0: $i] :
      ( ~ ( in @ '#sk25' @ '#sk1' )
      | ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk6' )
      | ~ ( in @ '#sk32' @ '#sk6' )
      | ( X0 = '#sk32' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl130]) ).

thf(zip_derived_cl41,plain,
    in @ '#sk25' @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl56,plain,
    in @ '#sk32' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl138,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk6' )
      | ( X0 = '#sk32' ) ),
    inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl41,zip_derived_cl56]) ).

thf(zip_derived_cl34_004,plain,
    subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl62_005,plain,
    ! [X2: $i] :
      ( ( in @ ( '#sk35' @ X2 )
        @ ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( !!
                    @ ^ [Y3: $i] :
                        ( ( in @ Y3 @ Y0 )
                       => ( ??
                          @ ^ [Y4: $i] :
                              ( ( in @ Y4
                                @ ( dsetconstr @ Y1
                                  @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                              & ( ( dsetconstr @ Y1
                                  @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                  & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
               => ( !!
                  @ ^ [Y3: $i] :
                      ( ( in @ Y3 @ Y0 )
                     => ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ X2 )
                     => ( ??
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3
                              @ ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
                            & ( ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
                              = ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
                & ( subset @ Y1 @ ( cartprod @ X2 @ Y0 ) ) )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ X2 )
                   => ( in @ ( kpair @ Y2 @ ( ap @ X2 @ Y0 @ Y1 @ Y2 ) ) @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X2 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X4
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X4
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ X2 )
               => ( in @ ( kpair @ Y1 @ ( ap @ X2 @ X4 @ Y0 @ Y1 ) ) @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ X2 )
               => ( ??
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1
                        @ ( dsetconstr @ X4
                          @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                      & ( ( dsetconstr @ X4
                          @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                        = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
          & ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
         => ( ??
            @ ^ [Y0: $i] :
                ( ( in @ Y0
                  @ ( dsetconstr @ X4
                    @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
                  = ( setadjoin @ Y0 @ emptyset ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl47,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0
                @ ( dsetconstr @ X4
                  @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
                = ( setadjoin @ Y0 @ emptyset ) ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl54,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
          & ( ( dsetconstr @ X4
              @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
            = ( setadjoin @ X8 @ emptyset ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl67,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl68,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
      ( ( ( in @ X10 @ X2 )
       => ( in @ ( kpair @ X10 @ ( ap @ X2 @ X4 @ X6 @ X10 ) ) @ X6 ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl72,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
      ( ~ ( in @ X10 @ X2 )
      | ( in @ ( kpair @ X10 @ ( ap @ X2 @ X4 @ X6 @ X10 ) ) @ X6 )
      | ~ ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
      | ( ( dsetconstr @ X4
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
       != ( setadjoin @ X8 @ emptyset ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl144,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
      | ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ Y0 ) @ '#sk11' ) )
       != ( setadjoin @ ( '#sk35' @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) ) @ emptyset ) )
      | ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) ) @ '#sk11' )
      | ~ ( in @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl72]) ).

thf(zip_derived_cl69_006,plain,
    ! [X2: $i] :
      ( ( ( dsetconstr @ '#sk6'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
        = ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ '#sk1' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl201,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) ) @ '#sk11' )
      | ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
      | ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
    inference(clc,[status(thm)],[zip_derived_cl144,zip_derived_cl69]) ).

thf(zip_derived_cl202,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl201]) ).

thf(zip_derived_cl128_007,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' ) ),
    inference(clc,[status(thm)],[zip_derived_cl126,zip_derived_cl96]) ).

thf(zip_derived_cl34_008,plain,
    subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl46,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl53,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( ( in @ X8 @ X2 )
       => ( in @ ( kpair @ X8 @ ( ap @ X2 @ X4 @ X6 @ X8 ) ) @ X6 ) )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
      | ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl60,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8 @ X2 )
      | ( in @ ( kpair @ X8 @ ( ap @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
      | ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
      | ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl98,plain,
    ! [X0: $i] :
      ( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
      | ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl60]) ).

thf(zip_derived_cl138_009,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk6' )
      | ( X0 = '#sk32' ) ),
    inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl41,zip_derived_cl56]) ).

thf(zip_derived_cl148,plain,
    ( ~ ( in @ '#sk25' @ '#sk1' )
    | ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
    | ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
      = '#sk32' )
    | ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl98,zip_derived_cl138]) ).

thf(zip_derived_cl41_010,plain,
    in @ '#sk25' @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl154,plain,
    ( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
    | ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
      = '#sk32' )
    | ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl148,zip_derived_cl41]) ).

thf(zip_derived_cl65,plain,
    ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
   != '#sk32' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl70,plain,
    ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
   != '#sk32' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl155,plain,
    ( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
    | ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl154,zip_derived_cl70]) ).

thf(zip_derived_cl166,plain,
    ( ~ ( in @ '#sk25' @ '#sk1' )
    | ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl155]) ).

thf(zip_derived_cl41_011,plain,
    in @ '#sk25' @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl169,plain,
    in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1',
    inference(demod,[status(thm)],[zip_derived_cl166,zip_derived_cl41]) ).

thf(zip_derived_cl204,plain,
    ! [X0: $i] :
      ( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
      | ~ ( in @ X0 @ '#sk1' ) ),
    inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl169]) ).

thf(zip_derived_cl208,plain,
    ( ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
      = '#sk32' )
    | ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' )
    | ~ ( in @ '#sk25' @ '#sk1' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl138,zip_derived_cl204]) ).

thf(zip_derived_cl41_012,plain,
    in @ '#sk25' @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl212,plain,
    ( ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
      = '#sk32' )
    | ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl208,zip_derived_cl41]) ).

thf(zip_derived_cl70_013,plain,
    ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
   != '#sk32' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl213,plain,
    ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl212,zip_derived_cl70]) ).

thf(zip_derived_cl223,plain,
    ~ ( in @ '#sk25' @ '#sk1' ),
    inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl213]) ).

thf(zip_derived_cl41_014,plain,
    in @ '#sk25' @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl227,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl223,zip_derived_cl41]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU686^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vMXI4feYTF true
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 14:27:50 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.68  % Total configuration time : 828
% 0.20/0.68  % Estimated wc time : 1656
% 0.20/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.78  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.27/0.81  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.27/0.82  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.45/0.99  % Solved by lams/35_full_unif4.sh.
% 1.45/0.99  % done 45 iterations in 0.144s
% 1.45/0.99  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.45/0.99  % SZS output start Refutation
% See solution above
% 1.45/0.99  
% 1.45/0.99  
% 1.45/0.99  % Terminating...
% 1.66/1.08  % Runner terminated.
% 1.76/1.09  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------