TSTP Solution File: SEU519^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU519^1 : 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.VgR8PmZ6LU true

% Computer : n007.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 19:13:30 EDT 2023

% Result   : Theorem 0.59s 0.86s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  139
% Syntax   : Number of formulae    :  150 (  85 unt;  56 typ;   0 def)
%            Number of atoms       :  725 ( 157 equ;   0 cnn)
%            Maximal formula atoms :  102 (   7 avg)
%            Number of connectives : 1824 (  47   ~;  20   |;  98   &;1208   @)
%                                         (  39 <=>; 412  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   44 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  102 ( 102   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   55 (  52 usr;  40 con; 0-4 aty)
%            Number of variables   :  614 (  58   ^; 466   !;  90   ?; 614   :)

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

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

thf(emptyinunitempty_type,type,
    emptyinunitempty: $o ).

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

thf(nonemptyI1_type,type,
    nonemptyI1: $o ).

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

thf(zip_tseitin_2_type,type,
    zip_tseitin_2: $i > $i > $i > $o ).

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

thf(nonemptyE1_type,type,
    nonemptyE1: $o ).

thf(setadjoinIR_type,type,
    setadjoinIR: $o ).

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

thf(setoftrueEq_type,type,
    setoftrueEq: $o ).

thf(emptyI_type,type,
    emptyI: $o ).

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

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

thf(setadjoinOr_type,type,
    setadjoinOr: $o ).

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

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

thf(setext_type,type,
    setext: $o ).

thf(setbeta_type,type,
    setbeta: $o ).

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

thf(setadjoinIL_type,type,
    setadjoinIL: $o ).

thf(descr_type,type,
    descr: ( $i > $o ) > $i ).

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

thf(prop2set_type,type,
    prop2set: $o > $i ).

thf(nonemptyI_type,type,
    nonemptyI: $o ).

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

thf(zip_tseitin_1_type,type,
    zip_tseitin_1: $i > $i > $i > $o ).

thf(powersetI_type,type,
    powersetI: $o ).

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

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

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

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

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

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

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

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

thf(exu_type,type,
    exu: ( $i > $o ) > $o ).

thf(sk__116_type,type,
    sk__116: $i ).

thf(zip_tseitin_3_type,type,
    zip_tseitin_3: $i > $i > $i > ( $i > $i > $o ) > $o ).

thf(sk__117_type,type,
    sk__117: $i > $i > $i ).

thf(noeltsimpempty_type,type,
    noeltsimpempty: $o ).

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

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

thf(powerset_type,type,
    powerset: $i > $i ).

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

thf(setadjoinE_type,type,
    setadjoinE: $o ).

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

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

thf(nonempty_type,type,
    nonempty: $i > $o ).

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

thf(zip_tseitin_0_type,type,
    zip_tseitin_0: $i > $i > $i > $o ).

thf(powersetI,axiom,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

thf('0',plain,
    ( powersetI
    = ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X6 )
             => ( in @ X8 @ X4 ) )
         => ( in @ X6 @ ( powerset @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(setoftrueEq,axiom,
    ( setoftrueEq
    = ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [Xx: $i] : $true )
          = A ) ) ) ).

thf('1',plain,
    ( setoftrueEq
    = ( ! [X4: $i] :
          ( ( dsetconstr @ X4
            @ ^ [V_1: $i] : $true )
          = X4 ) ) ),
    define([status(thm)]) ).

thf(setadjoinOr,axiom,
    ( setadjoinOr
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ) ).

thf('2',plain,
    ( setadjoinOr
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
         => ( ( X8 = X4 )
            | ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('3',plain,
    ( setadjoinE
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
         => ! [X10: $o] :
              ( ( ( X8 = X4 )
               => X10 )
             => ( ( ( in @ X8 @ X6 )
                 => X10 )
               => X10 ) ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinIR,axiom,
    ( setadjoinIR
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ A )
         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).

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

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).

thf('5',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).

thf('6',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    define([status(thm)]) ).

thf(setadjoinIL,axiom,
    ( setadjoinIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).

thf('7',plain,
    ( setadjoinIL
    = ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(nonemptyI1,axiom,
    ( nonemptyI1
    = ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ( nonempty @ A ) ) ) ) ).

thf('8',plain,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X6: $i] : ( in @ X6 @ X4 )
         => ( nonempty @ X4 ) ) ) ),
    define([status(thm)]) ).

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

thf('9',plain,
    ( nonemptyI
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ( ( X6 @ X8 )
           => ( nonempty
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).

thf('10',plain,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( nonempty @ X4 )
         => ? [X6: $i] : ( in @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).

thf('11',plain,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[nonempty]) ).

thf('12',plain,
    ( nonempty
    = ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
    define([status(thm)]) ).

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

thf('13',plain,
    ( setbeta
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ( ( in @ X8
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
          <=> ( X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ) ).

thf('14',plain,
    ( noeltsimpempty
    = ( ! [X4: $i] :
          ( ! [X6: $i] :
              ~ ( in @ X6 @ X4 )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(emptyI,axiom,
    ( emptyI
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ) ).

thf('15',plain,
    ( emptyI
    = ( ! [X4: $i] :
          ( ! [X6: $i] :
              ~ ( in @ X6 @ X4 )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(setext,axiom,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) ) ) ).

thf('16',plain,
    ( setext
    = ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ( in @ X8 @ X6 ) )
         => ( ! [X10: $i] :
                ( ( in @ X10 @ X6 )
               => ( in @ X10 @ X4 ) )
           => ( X4 = X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(exuE3e,axiom,
    ( exuE3e
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).

thf('17',plain,
    ( exuE3e
    = ( ! [X4: $i > $o] :
          ( ( exu
            @ ^ [V_1: $i] : ( X4 @ V_1 ) )
         => ? [X6: $i] : ( X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(notinemptyset,axiom,
    ( notinemptyset
    = ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) ) ) ).

thf('18',plain,
    ( notinemptyset
    = ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset ) ) ),
    define([status(thm)]) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => $false ) ) ) ).

thf('19',plain,
    ( emptysetimpfalse
    = ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => $false ) ) ),
    define([status(thm)]) ).

thf(emptysetE,axiom,
    ( emptysetE
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) ) ) ).

thf('20',plain,
    ( emptysetE
    = ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => ! [X6: $o] : X6 ) ) ),
    define([status(thm)]) ).

thf(prop2setE,axiom,
    ( prop2setE
    = ( ! [Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ ( prop2set @ Xphi ) )
         => Xphi ) ) ) ).

thf('21',plain,
    ( prop2setE
    = ( ! [X4: $o,X6: $i] :
          ( ( in @ X6 @ ( prop2set @ X4 ) )
         => X4 ) ) ),
    define([status(thm)]) ).

thf(prop2set,axiom,
    ( prop2set
    = ( ^ [Xphi: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Xx: $i] : Xphi ) ) ) ).

thf('22',plain,
    ( prop2set
    = ( ^ [Xphi: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Xx: $i] : Xphi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[prop2set]) ).

thf('23',plain,
    ( prop2set
    = ( ^ [V_1: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [V_2: $i] : V_1 ) ) ),
    define([status(thm)]) ).

thf(exuE1,axiom,
    ( exuE1
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ! [Xy: $i] :
                  ( ( Xphi @ Xy )
                 => ( Xx = Xy ) )
              & ( Xphi @ Xx ) ) ) ) ) ).

thf('24',plain,
    ( exuE1
    = ( ! [X4: $i > $o] :
          ( ( exu
            @ ^ [V_1: $i] : ( X4 @ V_1 ) )
         => ? [X6: $i] :
              ( ! [X8: $i] :
                  ( ( X4 @ X8 )
                 => ( X6 = X8 ) )
              & ( X4 @ X6 ) ) ) ) ),
    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('25',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(dsetconstrEL,axiom,
    ( dsetconstrEL
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) ) ) ).

thf('26',plain,
    ( dsetconstrEL
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( in @ X8 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

thf('27',plain,
    ( dsetconstrI
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ( ( X6 @ X8 )
           => ( in @ X8
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(descrp,axiom,
    ( descrp
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ( Xphi
            @ ( descr
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).

thf('28',plain,
    ( descrp
    = ( ! [X4: $i > $o] :
          ( ( exu
            @ ^ [V_1: $i] : ( X4 @ V_1 ) )
         => ( X4
            @ ( descr
              @ ^ [V_2: $i] : ( X4 @ V_2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(wellorderingAx,axiom,
    ( wellorderingAx
    = ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ A ) )
                & ? [Xx: $i] : ( in @ Xx @ C ) )
             => ? [D: $i,Xx: $i] :
                  ( ! [E: $i] :
                      ( ( in @ E @ B )
                     => ( ! [Xy: $i] :
                            ( ( in @ Xy @ E )
                           => ( in @ Xy @ D ) )
                        | ( in @ Xx @ E ) ) )
                  & ~ ? [Xy: $i] :
                        ( ( in @ Xy @ C )
                        & ( in @ Xy @ D ) )
                  & ( in @ Xx @ C )
                  & ( in @ D @ B ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ D ) )
                | ! [Xx: $i] :
                    ( ( in @ Xx @ D )
                   => ( in @ Xx @ C ) ) ) )
          & ! [Xx: $i,Xy: $i] :
              ( ( ( in @ Xx @ A )
                & ( in @ Xy @ A ) )
             => ( ! [C: $i] :
                    ( ( in @ C @ B )
                   => ( ( in @ Xx @ C )
                    <=> ( in @ Xy @ C ) ) )
               => ( Xx = Xy ) ) )
          & ! [C: $i] :
              ( ( in @ C @ B )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ C )
                 => ( in @ Xx @ A ) ) ) ) ) ) ).

thf('29',plain,
    ( wellorderingAx
    = ( ! [X4: $i] :
        ? [X6: $i] :
          ( ! [X8: $i] :
              ( ( ! [X10: $i] :
                    ( ( in @ X10 @ X8 )
                   => ( in @ X10 @ X4 ) )
                & ? [X12: $i] : ( in @ X12 @ X8 ) )
             => ? [X14: $i,X16: $i] :
                  ( ! [X18: $i] :
                      ( ( in @ X18 @ X6 )
                     => ( ! [X20: $i] :
                            ( ( in @ X20 @ X18 )
                           => ( in @ X20 @ X14 ) )
                        | ( in @ X16 @ X18 ) ) )
                  & ~ ? [X22: $i] :
                        ( ( in @ X22 @ X8 )
                        & ( in @ X22 @ X14 ) )
                  & ( in @ X16 @ X8 )
                  & ( in @ X14 @ X6 ) ) )
          & ! [X24: $i,X26: $i] :
              ( ( ( in @ X24 @ X6 )
                & ( in @ X26 @ X6 ) )
             => ( ! [X28: $i] :
                    ( ( in @ X28 @ X24 )
                   => ( in @ X28 @ X26 ) )
                | ! [X30: $i] :
                    ( ( in @ X30 @ X26 )
                   => ( in @ X30 @ X24 ) ) ) )
          & ! [X32: $i,X34: $i] :
              ( ( ( in @ X32 @ X4 )
                & ( in @ X34 @ X4 ) )
             => ( ! [X36: $i] :
                    ( ( in @ X36 @ X6 )
                   => ( ( in @ X32 @ X36 )
                    <=> ( in @ X34 @ X36 ) ) )
               => ( X32 = X34 ) ) )
          & ! [X38: $i] :
              ( ( in @ X38 @ X6 )
             => ! [X40: $i] :
                  ( ( in @ X40 @ X38 )
                 => ( in @ X40 @ X4 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(foundationAx,axiom,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ? [B: $i] :
              ( ~ ? [Xx: $i] :
                    ( ( in @ Xx @ A )
                    & ( in @ Xx @ B ) )
              & ( in @ B @ A ) ) ) ) ) ).

thf('30',plain,
    ( foundationAx
    = ( ! [X4: $i] :
          ( ? [X6: $i] : ( in @ X6 @ X4 )
         => ? [X8: $i] :
              ( ~ ? [X10: $i] :
                    ( ( in @ X10 @ X4 )
                    & ( in @ X10 @ X8 ) )
              & ( in @ X8 @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(replAx,axiom,
    ( replAx
    = ( ! [Xphi: $i > $i > $o,A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( exu
                @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( Xphi @ Xy @ Xx )
                  & ( in @ Xy @ A ) ) ) ) ) ) ).

thf('31',plain,
    ( replAx
    = ( ! [X4: $i > $i > $o,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X6 )
             => ( exu
                @ ^ [V_1: $i] : ( X4 @ X8 @ V_1 ) ) )
         => ? [X10: $i] :
            ! [X12: $i] :
              ( ( in @ X12 @ X10 )
            <=> ? [X14: $i] :
                  ( ( X4 @ X14 @ X12 )
                  & ( in @ X14 @ X6 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(omegaIndAx,axiom,
    ( omegaIndAx
    = ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [Xx: $i] :
                ( ( ( in @ Xx @ omega )
                  & ( in @ Xx @ A ) )
               => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ omega )
             => ( in @ Xx @ A ) ) ) ) ) ).

thf('32',plain,
    ( omegaIndAx
    = ( ! [X4: $i] :
          ( ( ( in @ emptyset @ X4 )
            & ! [X6: $i] :
                ( ( ( in @ X6 @ omega )
                  & ( in @ X6 @ X4 ) )
               => ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) )
         => ! [X8: $i] :
              ( ( in @ X8 @ omega )
             => ( in @ X8 @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(omegaSAx,axiom,
    ( omegaSAx
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).

thf('33',plain,
    ( omegaSAx
    = ( ! [X4: $i] :
          ( ( in @ X4 @ omega )
         => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) ) ),
    define([status(thm)]) ).

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

thf('34',plain,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ),
    inference(simplify_rw_rule,[status(thm)],[omega0Ax]) ).

thf('35',plain,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ),
    define([status(thm)]) ).

thf(setunionAx,axiom,
    ( setunionAx
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
        <=> ? [B: $i] :
              ( ( in @ B @ A )
              & ( in @ Xx @ B ) ) ) ) ) ).

thf('36',plain,
    ( setunionAx
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X6 @ ( setunion @ X4 ) )
        <=> ? [X8: $i] :
              ( ( in @ X8 @ X4 )
              & ( in @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(powersetAx,axiom,
    ( powersetAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
        <=> ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) ) ) ) ) ).

thf('37',plain,
    ( powersetAx
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X6 @ ( powerset @ X4 ) )
        <=> ! [X8: $i] :
              ( ( in @ X8 @ X6 )
             => ( in @ X8 @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinAx,axiom,
    ( setadjoinAx
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
        <=> ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ) ).

thf('38',plain,
    ( setadjoinAx
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
        <=> ( ( X8 = X4 )
            | ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(emptysetAx,axiom,
    ( emptysetAx
    = ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) ) ) ).

thf('39',plain,
    ( emptysetAx
    = ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset ) ) ),
    define([status(thm)]) ).

thf(setextAx,axiom,
    ( setextAx
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
            <=> ( in @ Xx @ B ) )
         => ( A = B ) ) ) ) ).

thf('40',plain,
    ( setextAx
    = ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
            <=> ( in @ X8 @ X6 ) )
         => ( X4 = X6 ) ) ) ),
    define([status(thm)]) ).

thf(exu,axiom,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) )
          & ( Xphi @ Xx ) ) ) ) ).

thf('41',plain,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) )
          & ( Xphi @ Xx ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[exu]) ).

thf('42',plain,
    ( exu
    = ( ^ [V_1: $i > $o] :
        ? [X4: $i] :
          ( ! [X6: $i] :
              ( ( V_1 @ X6 )
             => ( X4 = X6 ) )
          & ( V_1 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(emptyinPowerset,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i] :
        ( ! [X8: $i] :
            ( ( in @ X8 @ X4 )
          <=> ( in @ X8 @ X6 ) )
       => ( X4 = X6 ) )
   => ( ! [X10: $i] :
          ~ ( in @ X10 @ emptyset )
     => ( ! [X12: $i,X14: $i,X16: $i] :
            ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) )
          <=> ( ( in @ X16 @ X14 )
              | ( X16 = X12 ) ) )
       => ( ! [X18: $i,X20: $i] :
              ( ( in @ X20 @ ( powerset @ X18 ) )
            <=> ! [X22: $i] :
                  ( ( in @ X22 @ X20 )
                 => ( in @ X22 @ X18 ) ) )
         => ( ! [X24: $i,X26: $i] :
                ( ( in @ X26 @ ( setunion @ X24 ) )
              <=> ? [X28: $i] :
                    ( ( in @ X26 @ X28 )
                    & ( in @ X28 @ X24 ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X30: $i] :
                    ( ( in @ X30 @ omega )
                   => ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) )
               => ( ! [X32: $i] :
                      ( ( ! [X34: $i] :
                            ( ( ( in @ X34 @ X32 )
                              & ( in @ X34 @ omega ) )
                           => ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) )
                        & ( in @ emptyset @ X32 ) )
                     => ! [X36: $i] :
                          ( ( in @ X36 @ omega )
                         => ( in @ X36 @ X32 ) ) )
                 => ( ! [X38: $i > $i > $o,X40: $i] :
                        ( ! [X42: $i] :
                            ( ( in @ X42 @ X40 )
                           => ? [X44: $i] :
                                ( ( X38 @ X42 @ X44 )
                                & ! [X46: $i] :
                                    ( ( X38 @ X42 @ X46 )
                                   => ( X44 = X46 ) ) ) )
                       => ? [X48: $i] :
                          ! [X50: $i] :
                            ( ( in @ X50 @ X48 )
                          <=> ? [X52: $i] :
                                ( ( in @ X52 @ X40 )
                                & ( X38 @ X52 @ X50 ) ) ) )
                   => ( ! [X54: $i] :
                          ( ? [X56: $i] : ( in @ X56 @ X54 )
                         => ? [X58: $i] :
                              ( ( in @ X58 @ X54 )
                              & ~ ? [X60: $i] :
                                    ( ( in @ X60 @ X58 )
                                    & ( in @ X60 @ X54 ) ) ) )
                     => ( ! [X62: $i] :
                          ? [X64: $i] :
                            ( ! [X96: $i] :
                                ( ( in @ X96 @ X64 )
                               => ! [X98: $i] :
                                    ( ( in @ X98 @ X96 )
                                   => ( in @ X98 @ X62 ) ) )
                            & ! [X90: $i,X92: $i] :
                                ( ( ( in @ X92 @ X62 )
                                  & ( in @ X90 @ X62 ) )
                               => ( ! [X94: $i] :
                                      ( ( in @ X94 @ X64 )
                                     => ( ( in @ X90 @ X94 )
                                      <=> ( in @ X92 @ X94 ) ) )
                                 => ( X90 = X92 ) ) )
                            & ! [X82: $i,X84: $i] :
                                ( ( ( in @ X84 @ X64 )
                                  & ( in @ X82 @ X64 ) )
                               => ( ! [X88: $i] :
                                      ( ( in @ X88 @ X84 )
                                     => ( in @ X88 @ X82 ) )
                                  | ! [X86: $i] :
                                      ( ( in @ X86 @ X82 )
                                     => ( in @ X86 @ X84 ) ) ) )
                            & ! [X66: $i] :
                                ( ( ? [X70: $i] : ( in @ X70 @ X66 )
                                  & ! [X68: $i] :
                                      ( ( in @ X68 @ X66 )
                                     => ( in @ X68 @ X62 ) ) )
                               => ? [X72: $i,X74: $i] :
                                    ( ( in @ X72 @ X64 )
                                    & ( in @ X74 @ X66 )
                                    & ~ ? [X80: $i] :
                                          ( ( in @ X80 @ X72 )
                                          & ( in @ X80 @ X66 ) )
                                    & ! [X76: $i] :
                                        ( ( in @ X76 @ X64 )
                                       => ( ( in @ X74 @ X76 )
                                          | ! [X78: $i] :
                                              ( ( in @ X78 @ X76 )
                                             => ( in @ X78 @ X72 ) ) ) ) ) ) )
                       => ( ! [X100: $i > $o] :
                              ( ? [X102: $i] :
                                  ( ( X100 @ X102 )
                                  & ! [X104: $i] :
                                      ( ( X100 @ X104 )
                                     => ( X102 = X104 ) ) )
                             => ( X100
                                @ ( descr
                                  @ ^ [V_1: $i] : ( X100 @ V_1 ) ) ) )
                         => ( ! [X106: $i,X108: $i > $o,X110: $i] :
                                ( ( in @ X110 @ X106 )
                               => ( ( X108 @ X110 )
                                 => ( in @ X110
                                    @ ( dsetconstr @ X106
                                      @ ^ [V_2: $i] : ( X108 @ V_2 ) ) ) ) )
                           => ( ! [X112: $i,X114: $i > $o,X116: $i] :
                                  ( ( in @ X116
                                    @ ( dsetconstr @ X112
                                      @ ^ [V_3: $i] : ( X114 @ V_3 ) ) )
                                 => ( in @ X116 @ X112 ) )
                             => ( ! [X118: $i,X120: $i > $o,X122: $i] :
                                    ( ( in @ X122
                                      @ ( dsetconstr @ X118
                                        @ ^ [V_4: $i] : ( X120 @ V_4 ) ) )
                                   => ( X120 @ X122 ) )
                               => ( ! [X124: $i > $o] :
                                      ( ? [X126: $i] :
                                          ( ( X124 @ X126 )
                                          & ! [X128: $i] :
                                              ( ( X124 @ X128 )
                                             => ( X126 = X128 ) ) )
                                     => ? [X130: $i] :
                                          ( ( X124 @ X130 )
                                          & ! [X132: $i] :
                                              ( ( X124 @ X132 )
                                             => ( X130 = X132 ) ) ) )
                                 => ( ! [X134: $o,X136: $i] :
                                        ( ( in @ X136
                                          @ ( dsetconstr @ ( powerset @ emptyset )
                                            @ ^ [V_5: $i] : X134 ) )
                                       => X134 )
                                   => ( ! [X138: $i] :
                                          ( ( in @ X138 @ emptyset )
                                         => ! [X140: $o] : X140 )
                                     => ( ! [X142: $i] :
                                            ( ( in @ X142 @ emptyset )
                                           => $false )
                                       => ( ! [X144: $i] :
                                              ~ ( in @ X144 @ emptyset )
                                         => ( ! [X146: $i > $o] :
                                                ( ? [X148: $i] :
                                                    ( ( X146 @ X148 )
                                                    & ! [X150: $i] :
                                                        ( ( X146 @ X150 )
                                                       => ( X148 = X150 ) ) )
                                               => ? [X152: $i] : ( X146 @ X152 ) )
                                           => ( ! [X154: $i,X156: $i] :
                                                  ( ! [X158: $i] :
                                                      ( ( in @ X158 @ X154 )
                                                     => ( in @ X158 @ X156 ) )
                                                 => ( ! [X160: $i] :
                                                        ( ( in @ X160 @ X156 )
                                                       => ( in @ X160 @ X154 ) )
                                                   => ( X154 = X156 ) ) )
                                             => ( ! [X162: $i] :
                                                    ( ! [X164: $i] :
                                                        ~ ( in @ X164 @ X162 )
                                                   => ( X162 = emptyset ) )
                                               => ( ! [X166: $i] :
                                                      ( ! [X168: $i] :
                                                          ~ ( in @ X168 @ X166 )
                                                     => ( X166 = emptyset ) )
                                                 => ( ! [X170: $i,X172: $i > $o,X174: $i] :
                                                        ( ( in @ X174 @ X170 )
                                                       => ( ( in @ X174
                                                            @ ( dsetconstr @ X170
                                                              @ ^ [V_6: $i] : ( X172 @ V_6 ) ) )
                                                        <=> ( X172 @ X174 ) ) )
                                                   => ( ! [X176: $i] :
                                                          ( ( X176 != emptyset )
                                                         => ? [X178: $i] : ( in @ X178 @ X176 ) )
                                                     => ( ! [X180: $i,X182: $i > $o,X184: $i] :
                                                            ( ( in @ X184 @ X180 )
                                                           => ( ( X182 @ X184 )
                                                             => ( ( dsetconstr @ X180
                                                                  @ ^ [V_7: $i] : ( X182 @ V_7 ) )
                                                               != emptyset ) ) )
                                                       => ( ! [X186: $i] :
                                                              ( ? [X188: $i] : ( in @ X188 @ X186 )
                                                             => ( X186 != emptyset ) )
                                                         => ( ! [X190: $i,X192: $i] : ( in @ X190 @ ( setadjoin @ X190 @ X192 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X194: $i,X196: $i,X198: $i] :
                                                                    ( ( in @ X198 @ X196 )
                                                                   => ( in @ X198 @ ( setadjoin @ X194 @ X196 ) ) )
                                                               => ( ! [X200: $i,X202: $i,X204: $i] :
                                                                      ( ( in @ X204 @ ( setadjoin @ X200 @ X202 ) )
                                                                     => ! [X206: $o] :
                                                                          ( ( ( X204 = X200 )
                                                                           => X206 )
                                                                         => ( ( ( in @ X204 @ X202 )
                                                                             => X206 )
                                                                           => X206 ) ) )
                                                                 => ( ! [X208: $i,X210: $i,X212: $i] :
                                                                        ( ( in @ X212 @ ( setadjoin @ X208 @ X210 ) )
                                                                       => ( ( in @ X212 @ X210 )
                                                                          | ( X212 = X208 ) ) )
                                                                   => ( ! [X214: $i] :
                                                                          ( ( dsetconstr @ X214
                                                                            @ ^ [V_8: $i] : $true )
                                                                          = X214 )
                                                                     => ( ! [X216: $i,X218: $i] :
                                                                            ( ! [X220: $i] :
                                                                                ( ( in @ X220 @ X218 )
                                                                               => ( in @ X220 @ X216 ) )
                                                                           => ( in @ X218 @ ( powerset @ X216 ) ) )
                                                                       => ! [X222: $i] : ( in @ emptyset @ ( powerset @ X222 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,type,
    zip_tseitin_3: $i > $i > $i > ( $i > $i > $o ) > $o ).

thf(zf_stmt_2,axiom,
    ! [X52: $i,X50: $i,X40: $i,X38: $i > $i > $o] :
      ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 )
    <=> ( ( X38 @ X52 @ X50 )
        & ( in @ X52 @ X40 ) ) ) ).

thf(zf_stmt_3,type,
    zip_tseitin_2: $i > $i > $i > $o ).

thf(zf_stmt_4,axiom,
    ! [X28: $i,X26: $i,X24: $i] :
      ( ( zip_tseitin_2 @ X28 @ X26 @ X24 )
    <=> ( ( in @ X28 @ X24 )
        & ( in @ X26 @ X28 ) ) ) ).

thf(zf_stmt_5,type,
    zip_tseitin_1: $i > $i > $i > $o ).

thf(zf_stmt_6,axiom,
    ! [X22: $i,X20: $i,X18: $i] :
      ( ( zip_tseitin_1 @ X22 @ X20 @ X18 )
    <=> ( ( in @ X22 @ X20 )
       => ( in @ X22 @ X18 ) ) ) ).

thf(zf_stmt_7,type,
    zip_tseitin_0: $i > $i > $i > $o ).

thf(zf_stmt_8,axiom,
    ! [X16: $i,X14: $i,X12: $i] :
      ( ( zip_tseitin_0 @ X16 @ X14 @ X12 )
    <=> ( ( X16 = X12 )
        | ( in @ X16 @ X14 ) ) ) ).

thf(zf_stmt_9,conjecture,
    ( ! [X4: $i,X6: $i] :
        ( ! [X8: $i] :
            ( ( in @ X8 @ X4 )
          <=> ( in @ X8 @ X6 ) )
       => ( X4 = X6 ) )
   => ( ! [X10: $i] :
          ~ ( in @ X10 @ emptyset )
     => ( ! [X12: $i,X14: $i,X16: $i] :
            ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) )
          <=> ( zip_tseitin_0 @ X16 @ X14 @ X12 ) )
       => ( ! [X18: $i,X20: $i] :
              ( ( in @ X20 @ ( powerset @ X18 ) )
            <=> ! [X22: $i] : ( zip_tseitin_1 @ X22 @ X20 @ X18 ) )
         => ( ! [X24: $i,X26: $i] :
                ( ( in @ X26 @ ( setunion @ X24 ) )
              <=> ? [X28: $i] : ( zip_tseitin_2 @ X28 @ X26 @ X24 ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X30: $i] :
                    ( ( in @ X30 @ omega )
                   => ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) )
               => ( ! [X32: $i] :
                      ( ( ( in @ emptyset @ X32 )
                        & ! [X34: $i] :
                            ( ( ( in @ X34 @ omega )
                              & ( in @ X34 @ X32 ) )
                           => ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) )
                     => ! [X36: $i] :
                          ( ( in @ X36 @ omega )
                         => ( in @ X36 @ X32 ) ) )
                 => ( ! [X38: $i > $i > $o,X40: $i] :
                        ( ! [X42: $i] :
                            ( ( in @ X42 @ X40 )
                           => ? [X44: $i] :
                                ( ! [X46: $i] :
                                    ( ( X38 @ X42 @ X46 )
                                   => ( X44 = X46 ) )
                                & ( X38 @ X42 @ X44 ) ) )
                       => ? [X48: $i] :
                          ! [X50: $i] :
                            ( ( in @ X50 @ X48 )
                          <=> ? [X52: $i] : ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) )
                   => ( ! [X54: $i] :
                          ( ? [X56: $i] : ( in @ X56 @ X54 )
                         => ? [X58: $i] :
                              ( ~ ? [X60: $i] :
                                    ( ( in @ X60 @ X54 )
                                    & ( in @ X60 @ X58 ) )
                              & ( in @ X58 @ X54 ) ) )
                     => ( ! [X62: $i] :
                          ? [X64: $i] :
                            ( ! [X66: $i] :
                                ( ( ! [X68: $i] :
                                      ( ( in @ X68 @ X66 )
                                     => ( in @ X68 @ X62 ) )
                                  & ? [X70: $i] : ( in @ X70 @ X66 ) )
                               => ? [X72: $i,X74: $i] :
                                    ( ! [X76: $i] :
                                        ( ( in @ X76 @ X64 )
                                       => ( ! [X78: $i] :
                                              ( ( in @ X78 @ X76 )
                                             => ( in @ X78 @ X72 ) )
                                          | ( in @ X74 @ X76 ) ) )
                                    & ~ ? [X80: $i] :
                                          ( ( in @ X80 @ X66 )
                                          & ( in @ X80 @ X72 ) )
                                    & ( in @ X74 @ X66 )
                                    & ( in @ X72 @ X64 ) ) )
                            & ! [X82: $i,X84: $i] :
                                ( ( ( in @ X82 @ X64 )
                                  & ( in @ X84 @ X64 ) )
                               => ( ! [X86: $i] :
                                      ( ( in @ X86 @ X82 )
                                     => ( in @ X86 @ X84 ) )
                                  | ! [X88: $i] :
                                      ( ( in @ X88 @ X84 )
                                     => ( in @ X88 @ X82 ) ) ) )
                            & ! [X90: $i,X92: $i] :
                                ( ( ( in @ X90 @ X62 )
                                  & ( in @ X92 @ X62 ) )
                               => ( ! [X94: $i] :
                                      ( ( in @ X94 @ X64 )
                                     => ( ( in @ X90 @ X94 )
                                      <=> ( in @ X92 @ X94 ) ) )
                                 => ( X90 = X92 ) ) )
                            & ! [X96: $i] :
                                ( ( in @ X96 @ X64 )
                               => ! [X98: $i] :
                                    ( ( in @ X98 @ X96 )
                                   => ( in @ X98 @ X62 ) ) ) )
                       => ( ! [X100: $i > $o] :
                              ( ? [X102: $i] :
                                  ( ! [X104: $i] :
                                      ( ( X100 @ X104 )
                                     => ( X102 = X104 ) )
                                  & ( X100 @ X102 ) )
                             => ( X100
                                @ ( descr
                                  @ ^ [V_1: $i] : ( X100 @ V_1 ) ) ) )
                         => ( ! [X106: $i,X108: $i > $o,X110: $i] :
                                ( ( in @ X110 @ X106 )
                               => ( ( X108 @ X110 )
                                 => ( in @ X110
                                    @ ( dsetconstr @ X106
                                      @ ^ [V_2: $i] : ( X108 @ V_2 ) ) ) ) )
                           => ( ! [X112: $i,X114: $i > $o,X116: $i] :
                                  ( ( in @ X116
                                    @ ( dsetconstr @ X112
                                      @ ^ [V_3: $i] : ( X114 @ V_3 ) ) )
                                 => ( in @ X116 @ X112 ) )
                             => ( ! [X118: $i,X120: $i > $o,X122: $i] :
                                    ( ( in @ X122
                                      @ ( dsetconstr @ X118
                                        @ ^ [V_4: $i] : ( X120 @ V_4 ) ) )
                                   => ( X120 @ X122 ) )
                               => ( ! [X124: $i > $o] :
                                      ( ? [X126: $i] :
                                          ( ! [X128: $i] :
                                              ( ( X124 @ X128 )
                                             => ( X126 = X128 ) )
                                          & ( X124 @ X126 ) )
                                     => ? [X130: $i] :
                                          ( ! [X132: $i] :
                                              ( ( X124 @ X132 )
                                             => ( X130 = X132 ) )
                                          & ( X124 @ X130 ) ) )
                                 => ( ! [X134: $o,X136: $i] :
                                        ( ( in @ X136
                                          @ ( dsetconstr @ ( powerset @ emptyset )
                                            @ ^ [V_5: $i] : X134 ) )
                                       => X134 )
                                   => ( ! [X138: $i] :
                                          ( ( in @ X138 @ emptyset )
                                         => ! [X140: $o] : X140 )
                                     => ( ! [X142: $i] :
                                            ~ ( in @ X142 @ emptyset )
                                       => ( ! [X144: $i] :
                                              ~ ( in @ X144 @ emptyset )
                                         => ( ! [X146: $i > $o] :
                                                ( ? [X148: $i] :
                                                    ( ! [X150: $i] :
                                                        ( ( X146 @ X150 )
                                                       => ( X148 = X150 ) )
                                                    & ( X146 @ X148 ) )
                                               => ? [X152: $i] : ( X146 @ X152 ) )
                                           => ( ! [X154: $i,X156: $i] :
                                                  ( ! [X158: $i] :
                                                      ( ( in @ X158 @ X154 )
                                                     => ( in @ X158 @ X156 ) )
                                                 => ( ! [X160: $i] :
                                                        ( ( in @ X160 @ X156 )
                                                       => ( in @ X160 @ X154 ) )
                                                   => ( X154 = X156 ) ) )
                                             => ( ! [X162: $i] :
                                                    ( ! [X164: $i] :
                                                        ~ ( in @ X164 @ X162 )
                                                   => ( X162 = emptyset ) )
                                               => ( ! [X166: $i] :
                                                      ( ! [X168: $i] :
                                                          ~ ( in @ X168 @ X166 )
                                                     => ( X166 = emptyset ) )
                                                 => ( ! [X170: $i,X172: $i > $o,X174: $i] :
                                                        ( ( in @ X174 @ X170 )
                                                       => ( ( in @ X174
                                                            @ ( dsetconstr @ X170
                                                              @ ^ [V_6: $i] : ( X172 @ V_6 ) ) )
                                                        <=> ( X172 @ X174 ) ) )
                                                   => ( ! [X176: $i] :
                                                          ( ( X176 != emptyset )
                                                         => ? [X178: $i] : ( in @ X178 @ X176 ) )
                                                     => ( ! [X180: $i,X182: $i > $o,X184: $i] :
                                                            ( ( in @ X184 @ X180 )
                                                           => ( ( X182 @ X184 )
                                                             => ( ( dsetconstr @ X180
                                                                  @ ^ [V_7: $i] : ( X182 @ V_7 ) )
                                                               != emptyset ) ) )
                                                       => ( ! [X186: $i] :
                                                              ( ? [X188: $i] : ( in @ X188 @ X186 )
                                                             => ( X186 != emptyset ) )
                                                         => ( ! [X190: $i,X192: $i] : ( in @ X190 @ ( setadjoin @ X190 @ X192 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X194: $i,X196: $i,X198: $i] :
                                                                    ( ( in @ X198 @ X196 )
                                                                   => ( in @ X198 @ ( setadjoin @ X194 @ X196 ) ) )
                                                               => ( ! [X200: $i,X202: $i,X204: $i] :
                                                                      ( ( in @ X204 @ ( setadjoin @ X200 @ X202 ) )
                                                                     => ! [X206: $o] :
                                                                          ( ( ( X204 = X200 )
                                                                           => X206 )
                                                                         => ( ( ( in @ X204 @ X202 )
                                                                             => X206 )
                                                                           => X206 ) ) )
                                                                 => ( ! [X208: $i,X210: $i,X212: $i] :
                                                                        ( ( in @ X212 @ ( setadjoin @ X208 @ X210 ) )
                                                                       => ( ( X212 = X208 )
                                                                          | ( in @ X212 @ X210 ) ) )
                                                                   => ( ! [X214: $i] :
                                                                          ( ( dsetconstr @ X214
                                                                            @ ^ [V_8: $i] : $true )
                                                                          = X214 )
                                                                     => ( ! [X216: $i,X218: $i] :
                                                                            ( ! [X220: $i] :
                                                                                ( ( in @ X220 @ X218 )
                                                                               => ( in @ X220 @ X216 ) )
                                                                           => ( in @ X218 @ ( powerset @ X216 ) ) )
                                                                       => ! [X222: $i] : ( in @ emptyset @ ( powerset @ X222 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_10,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
            <=> ( in @ X8 @ X6 ) )
         => ( X4 = X6 ) )
     => ( ! [X10: $i] :
            ~ ( in @ X10 @ emptyset )
       => ( ! [X12: $i,X14: $i,X16: $i] :
              ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) )
            <=> ( zip_tseitin_0 @ X16 @ X14 @ X12 ) )
         => ( ! [X18: $i,X20: $i] :
                ( ( in @ X20 @ ( powerset @ X18 ) )
              <=> ! [X22: $i] : ( zip_tseitin_1 @ X22 @ X20 @ X18 ) )
           => ( ! [X24: $i,X26: $i] :
                  ( ( in @ X26 @ ( setunion @ X24 ) )
                <=> ? [X28: $i] : ( zip_tseitin_2 @ X28 @ X26 @ X24 ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X30: $i] :
                      ( ( in @ X30 @ omega )
                     => ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) )
                 => ( ! [X32: $i] :
                        ( ( ( in @ emptyset @ X32 )
                          & ! [X34: $i] :
                              ( ( ( in @ X34 @ omega )
                                & ( in @ X34 @ X32 ) )
                             => ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) )
                       => ! [X36: $i] :
                            ( ( in @ X36 @ omega )
                           => ( in @ X36 @ X32 ) ) )
                   => ( ! [X38: $i > $i > $o,X40: $i] :
                          ( ! [X42: $i] :
                              ( ( in @ X42 @ X40 )
                             => ? [X44: $i] :
                                  ( ! [X46: $i] :
                                      ( ( X38 @ X42 @ X46 )
                                     => ( X44 = X46 ) )
                                  & ( X38 @ X42 @ X44 ) ) )
                         => ? [X48: $i] :
                            ! [X50: $i] :
                              ( ( in @ X50 @ X48 )
                            <=> ? [X52: $i] : ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) )
                     => ( ! [X54: $i] :
                            ( ? [X56: $i] : ( in @ X56 @ X54 )
                           => ? [X58: $i] :
                                ( ~ ? [X60: $i] :
                                      ( ( in @ X60 @ X54 )
                                      & ( in @ X60 @ X58 ) )
                                & ( in @ X58 @ X54 ) ) )
                       => ( ! [X62: $i] :
                            ? [X64: $i] :
                              ( ! [X66: $i] :
                                  ( ( ! [X68: $i] :
                                        ( ( in @ X68 @ X66 )
                                       => ( in @ X68 @ X62 ) )
                                    & ? [X70: $i] : ( in @ X70 @ X66 ) )
                                 => ? [X72: $i,X74: $i] :
                                      ( ! [X76: $i] :
                                          ( ( in @ X76 @ X64 )
                                         => ( ! [X78: $i] :
                                                ( ( in @ X78 @ X76 )
                                               => ( in @ X78 @ X72 ) )
                                            | ( in @ X74 @ X76 ) ) )
                                      & ~ ? [X80: $i] :
                                            ( ( in @ X80 @ X66 )
                                            & ( in @ X80 @ X72 ) )
                                      & ( in @ X74 @ X66 )
                                      & ( in @ X72 @ X64 ) ) )
                              & ! [X82: $i,X84: $i] :
                                  ( ( ( in @ X82 @ X64 )
                                    & ( in @ X84 @ X64 ) )
                                 => ( ! [X86: $i] :
                                        ( ( in @ X86 @ X82 )
                                       => ( in @ X86 @ X84 ) )
                                    | ! [X88: $i] :
                                        ( ( in @ X88 @ X84 )
                                       => ( in @ X88 @ X82 ) ) ) )
                              & ! [X90: $i,X92: $i] :
                                  ( ( ( in @ X90 @ X62 )
                                    & ( in @ X92 @ X62 ) )
                                 => ( ! [X94: $i] :
                                        ( ( in @ X94 @ X64 )
                                       => ( ( in @ X90 @ X94 )
                                        <=> ( in @ X92 @ X94 ) ) )
                                   => ( X90 = X92 ) ) )
                              & ! [X96: $i] :
                                  ( ( in @ X96 @ X64 )
                                 => ! [X98: $i] :
                                      ( ( in @ X98 @ X96 )
                                     => ( in @ X98 @ X62 ) ) ) )
                         => ( ! [X100: $i > $o] :
                                ( ? [X102: $i] :
                                    ( ! [X104: $i] :
                                        ( ( X100 @ X104 )
                                       => ( X102 = X104 ) )
                                    & ( X100 @ X102 ) )
                               => ( X100
                                  @ ( descr
                                    @ ^ [V_1: $i] : ( X100 @ V_1 ) ) ) )
                           => ( ! [X106: $i,X108: $i > $o,X110: $i] :
                                  ( ( in @ X110 @ X106 )
                                 => ( ( X108 @ X110 )
                                   => ( in @ X110
                                      @ ( dsetconstr @ X106
                                        @ ^ [V_2: $i] : ( X108 @ V_2 ) ) ) ) )
                             => ( ! [X112: $i,X114: $i > $o,X116: $i] :
                                    ( ( in @ X116
                                      @ ( dsetconstr @ X112
                                        @ ^ [V_3: $i] : ( X114 @ V_3 ) ) )
                                   => ( in @ X116 @ X112 ) )
                               => ( ! [X118: $i,X120: $i > $o,X122: $i] :
                                      ( ( in @ X122
                                        @ ( dsetconstr @ X118
                                          @ ^ [V_4: $i] : ( X120 @ V_4 ) ) )
                                     => ( X120 @ X122 ) )
                                 => ( ! [X124: $i > $o] :
                                        ( ? [X126: $i] :
                                            ( ! [X128: $i] :
                                                ( ( X124 @ X128 )
                                               => ( X126 = X128 ) )
                                            & ( X124 @ X126 ) )
                                       => ? [X130: $i] :
                                            ( ! [X132: $i] :
                                                ( ( X124 @ X132 )
                                               => ( X130 = X132 ) )
                                            & ( X124 @ X130 ) ) )
                                   => ( ! [X134: $o,X136: $i] :
                                          ( ( in @ X136
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [V_5: $i] : X134 ) )
                                         => X134 )
                                     => ( ! [X138: $i] :
                                            ( ( in @ X138 @ emptyset )
                                           => ! [X140: $o] : X140 )
                                       => ( ! [X142: $i] :
                                              ~ ( in @ X142 @ emptyset )
                                         => ( ! [X144: $i] :
                                                ~ ( in @ X144 @ emptyset )
                                           => ( ! [X146: $i > $o] :
                                                  ( ? [X148: $i] :
                                                      ( ! [X150: $i] :
                                                          ( ( X146 @ X150 )
                                                         => ( X148 = X150 ) )
                                                      & ( X146 @ X148 ) )
                                                 => ? [X152: $i] : ( X146 @ X152 ) )
                                             => ( ! [X154: $i,X156: $i] :
                                                    ( ! [X158: $i] :
                                                        ( ( in @ X158 @ X154 )
                                                       => ( in @ X158 @ X156 ) )
                                                   => ( ! [X160: $i] :
                                                          ( ( in @ X160 @ X156 )
                                                         => ( in @ X160 @ X154 ) )
                                                     => ( X154 = X156 ) ) )
                                               => ( ! [X162: $i] :
                                                      ( ! [X164: $i] :
                                                          ~ ( in @ X164 @ X162 )
                                                     => ( X162 = emptyset ) )
                                                 => ( ! [X166: $i] :
                                                        ( ! [X168: $i] :
                                                            ~ ( in @ X168 @ X166 )
                                                       => ( X166 = emptyset ) )
                                                   => ( ! [X170: $i,X172: $i > $o,X174: $i] :
                                                          ( ( in @ X174 @ X170 )
                                                         => ( ( in @ X174
                                                              @ ( dsetconstr @ X170
                                                                @ ^ [V_6: $i] : ( X172 @ V_6 ) ) )
                                                          <=> ( X172 @ X174 ) ) )
                                                     => ( ! [X176: $i] :
                                                            ( ( X176 != emptyset )
                                                           => ? [X178: $i] : ( in @ X178 @ X176 ) )
                                                       => ( ! [X180: $i,X182: $i > $o,X184: $i] :
                                                              ( ( in @ X184 @ X180 )
                                                             => ( ( X182 @ X184 )
                                                               => ( ( dsetconstr @ X180
                                                                    @ ^ [V_7: $i] : ( X182 @ V_7 ) )
                                                                 != emptyset ) ) )
                                                         => ( ! [X186: $i] :
                                                                ( ? [X188: $i] : ( in @ X188 @ X186 )
                                                               => ( X186 != emptyset ) )
                                                           => ( ! [X190: $i,X192: $i] : ( in @ X190 @ ( setadjoin @ X190 @ X192 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X194: $i,X196: $i,X198: $i] :
                                                                      ( ( in @ X198 @ X196 )
                                                                     => ( in @ X198 @ ( setadjoin @ X194 @ X196 ) ) )
                                                                 => ( ! [X200: $i,X202: $i,X204: $i] :
                                                                        ( ( in @ X204 @ ( setadjoin @ X200 @ X202 ) )
                                                                       => ! [X206: $o] :
                                                                            ( ( ( X204 = X200 )
                                                                             => X206 )
                                                                           => ( ( ( in @ X204 @ X202 )
                                                                               => X206 )
                                                                             => X206 ) ) )
                                                                   => ( ! [X208: $i,X210: $i,X212: $i] :
                                                                          ( ( in @ X212 @ ( setadjoin @ X208 @ X210 ) )
                                                                         => ( ( X212 = X208 )
                                                                            | ( in @ X212 @ X210 ) ) )
                                                                     => ( ! [X214: $i] :
                                                                            ( ( dsetconstr @ X214
                                                                              @ ^ [V_8: $i] : $true )
                                                                            = X214 )
                                                                       => ( ! [X216: $i,X218: $i] :
                                                                              ( ! [X220: $i] :
                                                                                  ( ( in @ X220 @ X218 )
                                                                                 => ( in @ X220 @ X216 ) )
                                                                             => ( in @ X218 @ ( powerset @ X216 ) ) )
                                                                         => ! [X222: $i] : ( in @ emptyset @ ( powerset @ X222 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl53,plain,
    ~ ( in @ emptyset @ ( powerset @ sk__116 ) ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl52,plain,
    ! [X57: $i,X58: $i] :
      ( ( in @ X57 @ ( powerset @ X58 ) )
      | ( in @ ( sk__117 @ X57 @ X58 ) @ X57 ) ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl41,plain,
    ! [X39: $i] :
      ~ ( in @ X39 @ emptyset ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl136,plain,
    ! [X0: $i] : ( in @ emptyset @ ( powerset @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl41]) ).

thf(zip_derived_cl140,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl136]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU519^1 : 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.VgR8PmZ6LU true
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Wed Aug 23 20:01:55 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.37  % Running in HO mode
% 0.23/0.69  % Total configuration time : 828
% 0.23/0.69  % Estimated wc time : 1656
% 0.23/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.80  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.86  % Solved by lams/40_c.s.sh.
% 0.59/0.86  % done 22 iterations in 0.084s
% 0.59/0.86  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.59/0.86  % SZS output start Refutation
% See solution above
% 0.62/0.87  
% 0.62/0.87  
% 0.62/0.87  % Terminating...
% 1.69/0.94  % Runner terminated.
% 1.69/0.95  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------