TSTP Solution File: SEU505^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU505^1 : 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.c0yhWyrOq4 true

% Computer : n002.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 19:13:23 EDT 2023

% Result   : Theorem 34.89s 5.15s
% Output   : Refutation 34.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   93 (  11 unt;  32 typ;   0 def)
%            Number of atoms       :  760 (  52 equ; 132 cnn)
%            Maximal formula atoms :   34 (  12 avg)
%            Number of connectives : 1921 (  44   ~;  13   |;   0   &;1296   @)
%                                         (  10 <=>; 440  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   38 (  16 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   39 (  32 usr;  31 con; 0-6 aty)
%                                         ( 118  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   53 (  10   ^;  31   !;   0   ?;  53   :)
%                                         (  12  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
    setadjoinAx: $o ).

thf(setunionAx_type,type,
    setunionAx: $o ).

thf(omegaSAx_type,type,
    omegaSAx: $o ).

thf(wellorderingAx_type,type,
    wellorderingAx: $o ).

thf(emptysetE_type,type,
    emptysetE: $o ).

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

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

thf(powersetAx_type,type,
    powersetAx: $o ).

thf(notinemptyset_type,type,
    notinemptyset: $o ).

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

thf(emptysetimpfalse_type,type,
    emptysetimpfalse: $o ).

thf(exuE1_type,type,
    exuE1: $o ).

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

thf(omega0Ax_type,type,
    omega0Ax: $o ).

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

thf(prop2setE_type,type,
    prop2setE: $o ).

thf(setextAx_type,type,
    setextAx: $o ).

thf('#sk14_type',type,
    '#sk14': $i ).

thf(descrp_type,type,
    descrp: $o ).

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(emptysetAx_type,type,
    emptysetAx: $o ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(omega_type,type,
    omega: $i ).

thf(exuE3e_type,type,
    exuE3e: $o ).

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

thf(replAx_type,type,
    replAx: $o ).

thf(omegaIndAx_type,type,
    omegaIndAx: $o ).

thf(s_comb_type,type,
    '#S': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).

thf(c_comb_type,type,
    '#C': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).

thf(b_comb_type,type,
    '#B': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).

thf(k_comb_type,type,
    '#K': 
      !>[A: $tType,B: $tType] : ( B > A > B ) ).

thf(i_comb_type,type,
    '#I': 
      !>[A: $tType] : ( A > A ) ).

thf(setext,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ! [A: $i,B: $i] :
                                                ( ! [Xx: $i] :
                                                    ( ( in @ Xx @ A )
                                                   => ( in @ Xx @ B ) )
                                               => ( ! [Xx: $i] :
                                                      ( ( in @ Xx @ B )
                                                     => ( in @ Xx @ A ) )
                                                 => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ! [A: $i,B: $i] :
                                                  ( ! [Xx: $i] :
                                                      ( ( in @ Xx @ A )
                                                     => ( in @ Xx @ B ) )
                                                 => ( ! [Xx: $i] :
                                                        ( ( in @ Xx @ B )
                                                       => ( in @ Xx @ A ) )
                                                   => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[setext]) ).

thf(zip_derived_cl0,plain,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( !!
                                                @ ^ [Y0: $i] :
                                                    ( !!
                                                    @ ^ [Y1: $i] :
                                                        ( ( !!
                                                          @ ^ [Y2: $i] :
                                                              ( ( in @ Y2 @ Y0 )
                                                             => ( in @ Y2 @ Y1 ) ) )
                                                       => ( ( !!
                                                            @ ^ [Y2: $i] :
                                                                ( ( in @ Y2 @ Y1 )
                                                               => ( in @ Y2 @ Y0 ) ) )
                                                         => ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).

thf(omega0Ax,axiom,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ) ).

thf('0',plain,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ),
    define([status(thm)]) ).

thf(zip_derived_cl2,plain,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( ( in @ emptyset @ omega )
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(rw,[status(thm)],[zip_derived_cl1,'0']) ).

thf(zip_derived_cl4,plain,
    ~ ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( ( in @ emptyset @ omega )
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ~ ( setadjoinAx
     => ( powersetAx
       => ( setunionAx
         => ( ( in @ emptyset @ omega )
           => ( omegaSAx
             => ( omegaIndAx
               => ( replAx
                 => ( foundationAx
                   => ( wellorderingAx
                     => ( descrp
                       => ( dsetconstrI
                         => ( dsetconstrEL
                           => ( dsetconstrER
                             => ( exuE1
                               => ( prop2setE
                                 => ( emptysetE
                                   => ( emptysetimpfalse
                                     => ( notinemptyset
                                       => ( exuE3e
                                         => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl12,plain,
    ~ ( powersetAx
     => ( setunionAx
       => ( ( in @ emptyset @ omega )
         => ( omegaSAx
           => ( omegaIndAx
             => ( replAx
               => ( foundationAx
                 => ( wellorderingAx
                   => ( descrp
                     => ( dsetconstrI
                       => ( dsetconstrEL
                         => ( dsetconstrER
                           => ( exuE1
                             => ( prop2setE
                               => ( emptysetE
                                 => ( emptysetimpfalse
                                   => ( notinemptyset
                                     => ( exuE3e
                                       => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl18,plain,
    ~ ( setunionAx
     => ( ( in @ emptyset @ omega )
       => ( omegaSAx
         => ( omegaIndAx
           => ( replAx
             => ( foundationAx
               => ( wellorderingAx
                 => ( descrp
                   => ( dsetconstrI
                     => ( dsetconstrEL
                       => ( dsetconstrER
                         => ( exuE1
                           => ( prop2setE
                             => ( emptysetE
                               => ( emptysetimpfalse
                                 => ( notinemptyset
                                   => ( exuE3e
                                     => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl24,plain,
    ~ ( ( in @ emptyset @ omega )
     => ( omegaSAx
       => ( omegaIndAx
         => ( replAx
           => ( foundationAx
             => ( wellorderingAx
               => ( descrp
                 => ( dsetconstrI
                   => ( dsetconstrEL
                     => ( dsetconstrER
                       => ( exuE1
                         => ( prop2setE
                           => ( emptysetE
                             => ( emptysetimpfalse
                               => ( notinemptyset
                                 => ( exuE3e
                                   => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl32,plain,
    ~ ( omegaSAx
     => ( omegaIndAx
       => ( replAx
         => ( foundationAx
           => ( wellorderingAx
             => ( descrp
               => ( dsetconstrI
                 => ( dsetconstrEL
                   => ( dsetconstrER
                     => ( exuE1
                       => ( prop2setE
                         => ( emptysetE
                           => ( emptysetimpfalse
                             => ( notinemptyset
                               => ( exuE3e
                                 => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl39,plain,
    ~ ( omegaIndAx
     => ( replAx
       => ( foundationAx
         => ( wellorderingAx
           => ( descrp
             => ( dsetconstrI
               => ( dsetconstrEL
                 => ( dsetconstrER
                   => ( exuE1
                     => ( prop2setE
                       => ( emptysetE
                         => ( emptysetimpfalse
                           => ( notinemptyset
                             => ( exuE3e
                               => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl45,plain,
    ~ ( replAx
     => ( foundationAx
       => ( wellorderingAx
         => ( descrp
           => ( dsetconstrI
             => ( dsetconstrEL
               => ( dsetconstrER
                 => ( exuE1
                   => ( prop2setE
                     => ( emptysetE
                       => ( emptysetimpfalse
                         => ( notinemptyset
                           => ( exuE3e
                             => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl51,plain,
    ~ ( foundationAx
     => ( wellorderingAx
       => ( descrp
         => ( dsetconstrI
           => ( dsetconstrEL
             => ( dsetconstrER
               => ( exuE1
                 => ( prop2setE
                   => ( emptysetE
                     => ( emptysetimpfalse
                       => ( notinemptyset
                         => ( exuE3e
                           => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl57,plain,
    ~ ( wellorderingAx
     => ( descrp
       => ( dsetconstrI
         => ( dsetconstrEL
           => ( dsetconstrER
             => ( exuE1
               => ( prop2setE
                 => ( emptysetE
                   => ( emptysetimpfalse
                     => ( notinemptyset
                       => ( exuE3e
                         => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl63,plain,
    ~ ( descrp
     => ( dsetconstrI
       => ( dsetconstrEL
         => ( dsetconstrER
           => ( exuE1
             => ( prop2setE
               => ( emptysetE
                 => ( emptysetimpfalse
                   => ( notinemptyset
                     => ( exuE3e
                       => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl70,plain,
    ~ ( dsetconstrI
     => ( dsetconstrEL
       => ( dsetconstrER
         => ( exuE1
           => ( prop2setE
             => ( emptysetE
               => ( emptysetimpfalse
                 => ( notinemptyset
                   => ( exuE3e
                     => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl78,plain,
    ~ ( dsetconstrEL
     => ( dsetconstrER
       => ( exuE1
         => ( prop2setE
           => ( emptysetE
             => ( emptysetimpfalse
               => ( notinemptyset
                 => ( exuE3e
                   => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl88,plain,
    ~ ( dsetconstrER
     => ( exuE1
       => ( prop2setE
         => ( emptysetE
           => ( emptysetimpfalse
             => ( notinemptyset
               => ( exuE3e
                 => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl104,plain,
    ~ ( exuE1
     => ( prop2setE
       => ( emptysetE
         => ( emptysetimpfalse
           => ( notinemptyset
             => ( exuE3e
               => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl122,plain,
    ~ ( prop2setE
     => ( emptysetE
       => ( emptysetimpfalse
         => ( notinemptyset
           => ( exuE3e
             => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl104]) ).

thf(zip_derived_cl141,plain,
    ~ ( emptysetE
     => ( emptysetimpfalse
       => ( notinemptyset
         => ( exuE3e
           => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl157,plain,
    ~ ( emptysetimpfalse
     => ( notinemptyset
       => ( exuE3e
         => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).

thf(zip_derived_cl173,plain,
    ~ ( notinemptyset
     => ( exuE3e
       => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl157]) ).

thf(zip_derived_cl189,plain,
    ~ ( exuE3e
     => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl173]) ).

thf(zip_derived_cl206,plain,
    ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl189]) ).

thf(zip_derived_cl221,plain,
    ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk12' ) ) ) @ ( '#C' @ in ) ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) @ ( '#C' @ in @ '#sk12' ) ) ) ) @ ( $i = '#sk12' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl233,plain,
    ~ ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk12' ) ) @ ( '#C' @ in @ '#sk14' ) ) )
     => ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk14' ) ) @ ( '#C' @ in @ '#sk12' ) ) )
       => ( '#sk12' = '#sk14' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl221]) ).

thf(zip_derived_cl244,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk12' ) ) @ ( '#C' @ in @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl253,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ '#sk12' )
     => ( in @ X2 @ '#sk14' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl244]) ).

thf(zip_derived_cl265,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ '#sk12' )
      | ( in @ X2 @ '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl253]) ).

thf(zip_derived_cl3,plain,
    setextAx,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(setextAx,axiom,
    ( setextAx
   => ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ Y0 )
                    <=> ( in @ Y2 @ Y1 ) ) )
               => ( Y0 = Y1 ) ) ) )
      = $true ) ) ).

thf('1',plain,
    ( setextAx
  <=> ! [X5: $i,X7: $i] :
        ( ! [X9: $i] :
            ( ( in @ X9 @ X5 )
          <=> ( in @ X9 @ X7 ) )
       => ( X5 = X7 ) ) ),
    inference('rw.lit',[status(esa)],[setextAx]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ Y0 )
                <=> ( in @ Y2 @ Y1 ) ) )
           => ( Y0 = Y1 ) ) ) ),
    inference(rw_clause,[status(thm)],[zip_derived_cl3,'1']) ).

thf(zip_derived_cl8,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) @ (=) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (<=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#C' @ in ) ) ) ) @ ( $i = X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i] :
      ( ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#C' @ in @ X2 ) ) @ ( '#C' @ in @ X4 ) ) )
     => ( X2 = X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#C' @ in @ X2 ) ) @ ( '#C' @ in @ X4 ) ) )
      | ( X2 = X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#C' @ in @ X2 ) ) @ ( '#C' @ in @ X4 ) ) )
      | ( X2 = X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( ( in @ ( '#sk1' @ X2 @ X4 ) @ X2 )
        <=> ( in @ ( '#sk1' @ X2 @ X4 ) @ X4 ) )
      | ( X2 = X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( in @ ( '#sk1' @ X2 @ X4 ) @ X2 )
       != ( in @ ( '#sk1' @ X2 @ X4 ) @ X4 ) )
      | ( X2 = X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl290,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( '#sk1' @ '#sk14' @ X0 ) @ X0 )
      | ~ ( in @ ( '#sk1' @ '#sk14' @ X0 ) @ '#sk12' )
      | ( '#sk14' = X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl265,zip_derived_cl33]) ).

thf(zip_derived_cl8238,plain,
    ( ( '#sk14' = '#sk12' )
    | ~ ( in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk12' ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl290]) ).

thf(zip_derived_cl245,plain,
    ~ ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk14' ) ) @ ( '#C' @ in @ '#sk12' ) ) )
     => ( '#sk12' = '#sk14' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl255,plain,
    '#sk12' != '#sk14',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl245]) ).

thf(zip_derived_cl267,plain,
    '#sk12' != '#sk14',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl255]) ).

thf(zip_derived_cl8239,plain,
    ~ ( in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk12' ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8238,zip_derived_cl267]) ).

thf(zip_derived_cl254,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ '#sk14' ) ) @ ( '#C' @ in @ '#sk12' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl245]) ).

thf(zip_derived_cl266,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ '#sk14' )
     => ( in @ X2 @ '#sk12' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl254]) ).

thf(zip_derived_cl272,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ '#sk14' )
      | ( in @ X2 @ '#sk12' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl266]) ).

thf(zip_derived_cl8258,plain,
    ~ ( in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk14' ),
    inference('sup+',[status(thm)],[zip_derived_cl8239,zip_derived_cl272]) ).

thf(zip_derived_cl33_001,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( in @ ( '#sk1' @ X2 @ X4 ) @ X2 )
       != ( in @ ( '#sk1' @ X2 @ X4 ) @ X4 ) )
      | ( X2 = X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl287,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ ( '#sk1' @ X2 @ X4 ) @ X2 )
      | ( in @ ( '#sk1' @ X2 @ X4 ) @ X4 )
      | ( X2 = X4 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl8239_002,plain,
    ~ ( in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk12' ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8238,zip_derived_cl267]) ).

thf(zip_derived_cl8264,plain,
    ( ( '#sk14' = '#sk12' )
    | ( in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk14' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl8239]) ).

thf(zip_derived_cl267_003,plain,
    '#sk12' != '#sk14',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl255]) ).

thf(zip_derived_cl8267,plain,
    in @ ( '#sk1' @ '#sk14' @ '#sk12' ) @ '#sk14',
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8264,zip_derived_cl267]) ).

thf(zip_derived_cl8283,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl8258,zip_derived_cl8267]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU505^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.c0yhWyrOq4 true
% 0.16/0.36  % Computer : n002.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Wed Aug 23 19:50:01 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.16/0.36  % Running portfolio for 300 s
% 0.16/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.36  % Number of cores: 8
% 0.16/0.36  % Python version: Python 3.6.8
% 0.16/0.36  % Running in HO mode
% 0.22/0.68  % Total configuration time : 828
% 0.22/0.68  % Estimated wc time : 1656
% 0.22/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 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/15_e_short1.sh running for 30s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.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/40_noforms.sh running for 90s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.01/0.85  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.01/0.86  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 34.89/5.15  % Solved by lams/40_b.comb.sh.
% 34.89/5.15  % done 407 iterations in 4.338s
% 34.89/5.15  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 34.89/5.15  % SZS output start Refutation
% See solution above
% 34.89/5.15  
% 34.89/5.15  
% 34.89/5.15  % Terminating...
% 35.20/5.21  % Runner terminated.
% 35.20/5.21  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------