TSTP Solution File: SEU645^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU645^2 : 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.1ddNlFv6UV true

% Computer : n029.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 19:15:29 EDT 2023

% Result   : Theorem 16.60s 2.76s
% Output   : Refutation 16.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   96 (  56 unt;  19 typ;   0 def)
%            Number of atoms       :  206 (  76 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 1817 (  32   ~;  27   |;  21   &;1706   @)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   9 con; 0-2 aty)
%            Number of variables   :  214 (  47   ^; 146   !;  21   ?; 214   :)

% Comments : 
%------------------------------------------------------------------------------
thf(setukpairinjL1_type,type,
    setukpairinjL1: $o ).

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

thf(kfst_type,type,
    kfst: $i > $i ).

thf(sk__13_type,type,
    sk__13: $i > $i > $i ).

thf(sk__17_type,type,
    sk__17: $i ).

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

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

thf(sk__16_type,type,
    sk__16: $i ).

thf(sk__15_type,type,
    sk__15: $i > $i ).

thf(theprop_type,type,
    theprop: $o ).

thf(sk__14_type,type,
    sk__14: $i > $i > $i ).

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

thf(setunion_type,type,
    setunion: $i > $i ).

thf(iskpair_type,type,
    iskpair: $i > $o ).

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

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

thf(kfstsingleton_type,type,
    kfstsingleton: $o ).

thf(kpairp_type,type,
    kpairp: $o ).

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

thf(kfst,axiom,
    ( kfst
    = ( ^ [Xu: $i] :
          ( setunion
          @ ( dsetconstr @ ( setunion @ Xu )
            @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ).

thf('0',plain,
    ( kfst
    = ( ^ [Xu: $i] :
          ( setunion
          @ ( dsetconstr @ ( setunion @ Xu )
            @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[kfst]) ).

thf('1',plain,
    ( kfst
    = ( ^ [V_1: $i] :
          ( setunion
          @ ( dsetconstr @ ( setunion @ V_1 )
            @ ^ [V_2: $i] : ( in @ ( setadjoin @ V_2 @ emptyset ) @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(theprop,axiom,
    ( theprop
    = ( ! [X: $i] :
          ( ( singleton @ X )
         => ( in @ ( setunion @ X ) @ X ) ) ) ) ).

thf('2',plain,
    ( theprop
    = ( ! [X4: $i] :
          ( ( singleton @ X4 )
         => ( in @ ( setunion @ X4 ) @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(kfstsingleton,axiom,
    ( kfstsingleton
    = ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).

thf('3',plain,
    ( kfstsingleton
    = ( ! [X4: $i] :
          ( ( iskpair @ X4 )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ X4 )
              @ ^ [V_1: $i] : ( in @ ( setadjoin @ V_1 @ emptyset ) @ X4 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(setukpairinjL1,axiom,
    ( setukpairinjL1
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) ) ) ).

thf('4',plain,
    ( setukpairinjL1
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
         => ( X4 = X8 ) ) ) ),
    define([status(thm)]) ).

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(kpairp,axiom,
    ( kpairp
    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).

thf('7',plain,
    ( kpairp
    = ( ! [X4: $i,X6: $i] : ( iskpair @ ( kpair @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(kpair,axiom,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).

thf('8',plain,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[kpair]) ).

thf('9',plain,
    ( kpair
    = ( ^ [V_1: $i,V_2: $i] : ( setadjoin @ ( setadjoin @ V_1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) ) ),
    define([status(thm)]) ).

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

thf('10',plain,
    ( iskpair
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ? [Xy: $i] :
              ( ( A
                = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
              & ( in @ Xy @ ( setunion @ A ) ) )
          & ( in @ Xx @ ( setunion @ A ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iskpair]) ).

thf('11',plain,
    ( iskpair
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ? [X6: $i] :
              ( ( V_1
                = ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
              & ( in @ X6 @ ( setunion @ V_1 ) ) )
          & ( in @ X4 @ ( setunion @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('12',plain,
    ( dsetconstrER
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(kfstpairEq,conjecture,
    ( dsetconstrER
   => ( kpairp
     => ( setukpairinjL1
       => ( kfstsingleton
         => ( theprop
           => ! [Xx: $i,Xy: $i] :
                ( ( kfst @ ( kpair @ Xx @ Xy ) )
                = Xx ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o,X8: $i] :
        ( ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
       => ( X6 @ X8 ) )
   => ( ! [X10: $i,X12: $i] :
        ? [X14: $i] :
          ( ? [X16: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) )
              & ( in @ X16 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) ) ) ) )
          & ( in @ X14 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) ) ) ) )
     => ( ! [X18: $i,X20: $i,X22: $i] :
            ( ( in @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) ) )
           => ( X18 = X22 ) )
       => ( ! [X24: $i] :
              ( ? [X26: $i] :
                  ( ? [X28: $i] :
                      ( ( X24
                        = ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X28 @ emptyset ) ) @ emptyset ) ) )
                      & ( in @ X28 @ ( setunion @ X24 ) ) )
                  & ( in @ X26 @ ( setunion @ X24 ) ) )
             => ? [X30: $i] :
                  ( ( ( dsetconstr @ ( setunion @ X24 )
                      @ ^ [V_2: $i] : ( in @ ( setadjoin @ V_2 @ emptyset ) @ X24 ) )
                    = ( setadjoin @ X30 @ emptyset ) )
                  & ( in @ X30
                    @ ( dsetconstr @ ( setunion @ X24 )
                      @ ^ [V_3: $i] : ( in @ ( setadjoin @ V_3 @ emptyset ) @ X24 ) ) ) ) )
         => ( ! [X32: $i] :
                ( ? [X34: $i] :
                    ( ( X32
                      = ( setadjoin @ X34 @ emptyset ) )
                    & ( in @ X34 @ X32 ) )
               => ( in @ ( setunion @ X32 ) @ X32 ) )
           => ! [X36: $i,X38: $i] :
                ( ( setunion
                  @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) )
                    @ ^ [V_4: $i] : ( in @ ( setadjoin @ V_4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) ) ) )
                = X36 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) )
     => ( ! [X10: $i,X12: $i] :
          ? [X14: $i] :
            ( ? [X16: $i] :
                ( ( ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) )
                & ( in @ X16 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) ) ) ) )
            & ( in @ X14 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X12 @ emptyset ) ) @ emptyset ) ) ) ) )
       => ( ! [X18: $i,X20: $i,X22: $i] :
              ( ( in @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) ) )
             => ( X18 = X22 ) )
         => ( ! [X24: $i] :
                ( ? [X26: $i] :
                    ( ? [X28: $i] :
                        ( ( X24
                          = ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X28 @ emptyset ) ) @ emptyset ) ) )
                        & ( in @ X28 @ ( setunion @ X24 ) ) )
                    & ( in @ X26 @ ( setunion @ X24 ) ) )
               => ? [X30: $i] :
                    ( ( ( dsetconstr @ ( setunion @ X24 )
                        @ ^ [V_2: $i] : ( in @ ( setadjoin @ V_2 @ emptyset ) @ X24 ) )
                      = ( setadjoin @ X30 @ emptyset ) )
                    & ( in @ X30
                      @ ( dsetconstr @ ( setunion @ X24 )
                        @ ^ [V_3: $i] : ( in @ ( setadjoin @ V_3 @ emptyset ) @ X24 ) ) ) ) )
           => ( ! [X32: $i] :
                  ( ? [X34: $i] :
                      ( ( X32
                        = ( setadjoin @ X34 @ emptyset ) )
                      & ( in @ X34 @ X32 ) )
                 => ( in @ ( setunion @ X32 ) @ X32 ) )
             => ! [X36: $i,X38: $i] :
                  ( ( setunion
                    @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) )
                      @ ^ [V_4: $i] : ( in @ ( setadjoin @ V_4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) ) ) )
                  = X36 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ( ( setunion
      @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ sk__16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__16 @ ( setadjoin @ sk__17 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__16 @ ( setadjoin @ sk__17 @ emptyset ) ) @ emptyset ) ) ) ) )
   != sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    ! [X8: $i,X9: $i,X10: $i] :
      ( ( ( dsetconstr @ ( setunion @ X8 )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X8 ) )
        = ( setadjoin @ ( sk__15 @ X8 ) @ emptyset ) )
      | ~ ( in @ X9 @ ( setunion @ X8 ) )
      | ( X8
       != ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ X10 @ ( setunion @ X8 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl233,plain,
    ! [X9: $i,X10: $i] :
      ( ~ ( in @ X10 @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ X9 @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) )
      | ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) )
        = ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl272,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) )
        = ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
      | ~ ( in @ ( sk__13 @ X0 @ X1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ ( sk__14 @ X0 @ X1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl233]) ).

thf(zip_derived_cl7_001,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_002,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_003,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    ! [X11: $i,X12: $i] : ( in @ ( sk__13 @ X11 @ X12 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_004,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    ! [X11: $i,X12: $i] : ( in @ ( sk__14 @ X11 @ X12 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl336,plain,
    ! [X0: $i,X1: $i] :
      ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
      = ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl7,zip_derived_cl7,zip_derived_cl7,zip_derived_cl8,zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl349,plain,
    ( ( setunion @ ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ sk__16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__16 @ ( setadjoin @ sk__17 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
   != sk__16 ),
    inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl336]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ( X0 @ X1 )
      | ~ ( in @ X1
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ( X0 @ X1 )
      | ~ ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl7_005,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    ! [X8: $i,X9: $i,X10: $i] :
      ( ( in @ ( sk__15 @ X8 )
        @ ( dsetconstr @ ( setunion @ X8 )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X8 ) ) )
      | ~ ( in @ X9 @ ( setunion @ X8 ) )
      | ( X8
       != ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ X10 @ ( setunion @ X8 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl450,plain,
    ! [X9: $i,X10: $i] :
      ( ~ ( in @ X10 @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ X9 @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) )
      | ( in @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
        @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X9 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl455,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) )
          @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) ) )
      | ~ ( in @ ( sk__13 @ X0 @ X1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) )
      | ~ ( in @ ( sk__14 @ X0 @ X1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X0 @ X1 ) @ ( setadjoin @ ( sk__14 @ X0 @ X1 ) @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl450]) ).

thf(zip_derived_cl7_006,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_007,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_008,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8_009,plain,
    ! [X11: $i,X12: $i] : ( in @ ( sk__13 @ X11 @ X12 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_010,plain,
    ! [X11: $i,X12: $i] :
      ( ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sk__13 @ X11 @ X12 ) @ ( setadjoin @ ( sk__14 @ X11 @ X12 ) @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6_011,plain,
    ! [X11: $i,X12: $i] : ( in @ ( sk__14 @ X11 @ X12 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl471,plain,
    ! [X0: $i,X1: $i] :
      ( in @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
      @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl455,zip_derived_cl7,zip_derived_cl7,zip_derived_cl7,zip_derived_cl8,zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl514,plain,
    ! [X0: $i,X1: $i] :
      ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
      @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl26,zip_derived_cl471]) ).

thf(zip_derived_cl527,plain,
    ! [X0: $i,X1: $i] : ( in @ ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl514]) ).

thf(zip_derived_cl1,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X3 )
      | ~ ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl534,plain,
    ! [X0: $i,X1: $i] :
      ( X1
      = ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl527,zip_derived_cl1]) ).

thf(zip_derived_cl566,plain,
    ( ( setunion @ ( setadjoin @ sk__16 @ emptyset ) )
   != sk__16 ),
    inference(demod,[status(thm)],[zip_derived_cl349,zip_derived_cl534]) ).

thf(zip_derived_cl336_012,plain,
    ! [X0: $i,X1: $i] :
      ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
      = ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl7,zip_derived_cl7,zip_derived_cl7,zip_derived_cl8,zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl26_013,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ( X0 @ X1 )
      | ~ ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl351,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
      | ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl336,zip_derived_cl26]) ).

thf(zip_derived_cl421,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
      | ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl351]) ).

thf(zip_derived_cl534_014,plain,
    ! [X0: $i,X1: $i] :
      ( X1
      = ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl527,zip_derived_cl1]) ).

thf(zip_derived_cl958,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
      | ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl421,zip_derived_cl534]) ).

thf(zip_derived_cl1_015,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X3 )
      | ~ ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl959,plain,
    ! [X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
      | ( X1 = X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl958,zip_derived_cl1]) ).

thf(zip_derived_cl2,plain,
    ! [X6: $i,X7: $i] :
      ( ( in @ ( setunion @ X6 ) @ X6 )
      | ~ ( in @ X7 @ X6 )
      | ( X6
       != ( setadjoin @ X7 @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9,plain,
    ! [X7: $i] :
      ( ~ ( in @ X7 @ ( setadjoin @ X7 @ emptyset ) )
      | ( in @ ( setunion @ ( setadjoin @ X7 @ emptyset ) ) @ ( setadjoin @ X7 @ emptyset ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl973,plain,
    ! [X0: $i] :
      ( ( X0
        = ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
      | ~ ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl959,zip_derived_cl9]) ).

thf(zip_derived_cl471_016,plain,
    ! [X0: $i,X1: $i] :
      ( in @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
      @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl455,zip_derived_cl7,zip_derived_cl7,zip_derived_cl7,zip_derived_cl8,zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl534_017,plain,
    ! [X0: $i,X1: $i] :
      ( X1
      = ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl527,zip_derived_cl1]) ).

thf(zip_derived_cl567,plain,
    ! [X0: $i,X1: $i] :
      ( in @ X1
      @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl471,zip_derived_cl534]) ).

thf(zip_derived_cl336_018,plain,
    ! [X0: $i,X1: $i] :
      ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
      = ( setadjoin @ ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl7,zip_derived_cl7,zip_derived_cl7,zip_derived_cl8,zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl534_019,plain,
    ! [X0: $i,X1: $i] :
      ( X1
      = ( sk__15 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl527,zip_derived_cl1]) ).

thf(zip_derived_cl565,plain,
    ! [X0: $i,X1: $i] :
      ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
        @ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
      = ( setadjoin @ X1 @ emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl336,zip_derived_cl534]) ).

thf(zip_derived_cl2782,plain,
    ! [X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl567,zip_derived_cl565]) ).

thf(zip_derived_cl2859,plain,
    ! [X0: $i] :
      ( X0
      = ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl973,zip_derived_cl2782]) ).

thf(zip_derived_cl2880,plain,
    sk__16 != sk__16,
    inference(demod,[status(thm)],[zip_derived_cl566,zip_derived_cl2859]) ).

thf(zip_derived_cl2881,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl2880]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU645^2 : 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.1ddNlFv6UV true
% 0.13/0.34  % Computer : n029.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 : Thu Aug 24 01:55:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % 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
% 0.22/0.65  % Total configuration time : 828
% 0.22/0.65  % Estimated wc time : 1656
% 0.22/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.40/0.79  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 16.60/2.76  % Solved by lams/40_c_ic.sh.
% 16.60/2.76  % done 165 iterations in 1.978s
% 16.60/2.76  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 16.60/2.76  % SZS output start Refutation
% See solution above
% 16.60/2.77  
% 16.60/2.77  
% 16.60/2.77  % Terminating...
% 16.60/2.91  % Runner terminated.
% 16.60/2.93  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------