%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU534^1 : 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.WrRU2QPO7R true
% Computer : n001.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 19:13:38 EDT 2023
% Result : Theorem 1.58s 0.98s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 183
% Syntax : Number of formulae : 198 ( 116 unt; 72 typ; 0 def)
% Number of atoms : 963 ( 231 equ; 0 cnn)
% Maximal formula atoms : 134 ( 7 avg)
% Number of connectives : 2409 ( 70 ~; 29 |; 105 &;1600 @)
% ( 44 <=>; 561 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 56 con; 0-4 aty)
% Number of variables : 802 ( 59 ^; 636 !; 107 ?; 802 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(zip_tseitin_1_type,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $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(upairsetE_type,type,
upairsetE: $o ).
thf(sk__153_type,type,
sk__153: $i ).
thf(exuE2_type,type,
exuE2: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(notinsingleton_type,type,
notinsingleton: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(sk__154_type,type,
sk__154: $i > $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(uniqinunit_type,type,
uniqinunit: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(zip_tseitin_3_type,type,
zip_tseitin_3: $i > $i > $i > ( $i > $i > $o ) > $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(sk__155_type,type,
sk__155: $i ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(upairsetIL_type,type,
upairsetIL: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(zip_tseitin_2_type,type,
zip_tseitin_2: $i > $i > $i > $o ).
thf(descrp_type,type,
descrp: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $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(powersetE_type,type,
powersetE: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(omega_type,type,
omega: $i ).
thf(setunionI_type,type,
setunionI: $o ).
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(setunionE_type,type,
setunionE: $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(upairsetIR,axiom,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('0',plain,
( upairsetIR
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(upairsetIL,axiom,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('1',plain,
( upairsetIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(upairsetE,axiom,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ).
thf('2',plain,
( upairsetE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) )
=> ( ( X8 = X4 )
| ( X8 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(singletonsswitch,axiom,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
thf('3',plain,
( singletonsswitch
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(eqinunit,axiom,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('4',plain,
( eqinunit
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(notinsingleton,axiom,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
thf('5',plain,
( notinsingleton
= ( ! [X4: $i,X6: $i] :
( ( X4 != X6 )
=> ~ ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(uniqinunit,axiom,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ).
thf('6',plain,
( uniqinunit
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
thf('7',plain,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X6: $i] : ( in @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(exuE2,axiom,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ) ).
thf('8',plain,
( exuE2
= ( ! [X4: $i > $o] :
( ( exu
@ ^ [V_1: $i] : ( X4 @ V_1 ) )
=> ? [X6: $i] :
! [X8: $i] :
( ( X4 @ X8 )
<=> ( X8 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subPowSU,axiom,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
thf('9',plain,
( subPowSU
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ X4 )
=> ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setunionE,axiom,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ) ).
thf('10',plain,
( setunionE
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( setunion @ X4 ) )
=> ! [X8: $o] :
( ! [X10: $i] :
( ( in @ X6 @ X10 )
=> ( ( in @ X10 @ X4 )
=> X8 ) )
=> X8 ) ) ) ),
define([status(thm)]) ).
thf(setunionI,axiom,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
thf('11',plain,
( setunionI
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X6 @ X8 )
=> ( ( in @ X8 @ X4 )
=> ( in @ X6 @ ( setunion @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(powersetE,axiom,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ) ).
thf('12',plain,
( powersetE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ( ( in @ X8 @ X6 )
=> ( in @ X8 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
thf('13',plain,
( emptyInPowerset
= ( ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ) ),
define([status(thm)]) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
thf('14',plain,
( emptyinPowerset
= ( ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ) ),
define([status(thm)]) ).
thf(powersetI,axiom,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf('15',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('16',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('17',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('18',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('19',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('20',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).
thf('21',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(setadjoinIL,axiom,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
thf('22',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('23',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('24',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('25',plain,
( nonemptyE1
= ( ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X6: $i] : ( in @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
thf('26',plain,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[nonempty]) ).
thf('27',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('28',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('29',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('30',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('31',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('32',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('33',plain,
( notinemptyset
= ( ! [X4: $i] :
~ ( in @ X4 @ emptyset ) ) ),
define([status(thm)]) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ) ).
thf('34',plain,
( emptysetimpfalse
= ( ! [X4: $i] :
( ( in @ X4 @ emptyset )
=> $false ) ) ),
define([status(thm)]) ).
thf(emptysetE,axiom,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ).
thf('35',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('36',plain,
( prop2setE
= ( ! [X4: $o,X6: $i] :
( ( in @ X6 @ ( prop2set @ X4 ) )
=> X4 ) ) ),
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('37',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('38',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('39',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('40',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('41',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('42',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('43',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('44',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('45',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('46',plain,
( omegaSAx
= ( ! [X4: $i] :
( ( in @ X4 @ omega )
=> ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) ) ),
define([status(thm)]) ).
thf(omega0Ax,axiom,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf('47',plain,
( omega0Ax
= ( in @ emptyset @ omega ) ),
inference(simplify_rw_rule,[status(thm)],[omega0Ax]) ).
thf('48',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('49',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('50',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('51',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('52',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('53',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('54',plain,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) )
& ( Xphi @ Xx ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[exu]) ).
thf('55',plain,
( exu
= ( ^ [V_1: $i > $o] :
? [X4: $i] :
( ! [X6: $i] :
( ( V_1 @ X6 )
=> ( X4 = X6 ) )
& ( V_1 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(emptyE1,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
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ( in @ Xx @ A ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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 @ ( prop2set @ 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_5: $i] : ( X172 @ V_5 ) ) )
<=> ( 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_6: $i] : ( X182 @ V_6 ) )
!= 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_7: $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 ) )
=> ( ! [X224: $i] : ( in @ emptyset @ ( powerset @ X224 ) )
=> ( ! [X226: $i,X228: $i,X230: $i] :
( ( in @ X228 @ ( powerset @ X226 ) )
=> ( ( in @ X230 @ X228 )
=> ( in @ X230 @ X226 ) ) )
=> ( ! [X232: $i,X234: $i,X236: $i] :
( ( in @ X234 @ X236 )
=> ( ( in @ X236 @ X232 )
=> ( in @ X234 @ ( setunion @ X232 ) ) ) )
=> ( ! [X238: $i,X240: $i] :
( ( in @ X240 @ ( setunion @ X238 ) )
=> ! [X242: $o] :
( ! [X244: $i] :
( ( in @ X240 @ X244 )
=> ( ( in @ X244 @ X238 )
=> X242 ) )
=> X242 ) )
=> ( ! [X246: $i,X248: $i] :
( ( in @ X248 @ X246 )
=> ( in @ X248 @ ( powerset @ ( setunion @ X246 ) ) ) )
=> ( ! [X250: $i > $o] :
( ? [X252: $i] :
( ( X250 @ X252 )
& ! [X254: $i] :
( ( X250 @ X254 )
=> ( X252 = X254 ) ) )
=> ? [X256: $i] :
! [X258: $i] :
( ( X250 @ X258 )
<=> ( X258 = X256 ) ) )
=> ( ! [X260: $i] :
( ( X260 != emptyset )
=> ? [X262: $i] : ( in @ X262 @ X260 ) )
=> ( ! [X264: $i,X266: $i] :
( ( in @ X264 @ ( setadjoin @ X266 @ emptyset ) )
=> ( X264 = X266 ) )
=> ( ! [X268: $i,X270: $i] :
( ( X268 != X270 )
=> ~ ( in @ X270 @ ( setadjoin @ X268 @ emptyset ) ) )
=> ( ! [X272: $i,X274: $i] :
( ( X272 = X274 )
=> ( in @ X272 @ ( setadjoin @ X274 @ emptyset ) ) )
=> ( ! [X276: $i,X278: $i] :
( ( in @ X276 @ ( setadjoin @ X278 @ emptyset ) )
=> ( in @ X278 @ ( setadjoin @ X276 @ emptyset ) ) )
=> ( ! [X280: $i,X282: $i,X284: $i] :
( ( in @ X284 @ ( setadjoin @ X280 @ ( setadjoin @ X282 @ emptyset ) ) )
=> ( ( X284 = X282 )
| ( X284 = X280 ) ) )
=> ( ! [X286: $i,X288: $i] : ( in @ X286 @ ( setadjoin @ X286 @ ( setadjoin @ X288 @ emptyset ) ) )
=> ( ! [X290: $i,X292: $i] : ( in @ X292 @ ( setadjoin @ X290 @ ( setadjoin @ X292 @ emptyset ) ) )
=> ! [X294: $i,X296: $i > $o] :
( ? [X298: $i] :
( ( in @ X298 @ X294 )
& ( X296 @ X298 ) )
=> ( ( ( dsetconstr @ X294
@ ^ [V_8: $i] : ( X296 @ V_8 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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 @ ( prop2set @ 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_5: $i] : ( X172 @ V_5 ) ) )
<=> ( 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_6: $i] : ( X182 @ V_6 ) )
!= 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_7: $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 ) )
=> ( ! [X224: $i] : ( in @ emptyset @ ( powerset @ X224 ) )
=> ( ! [X226: $i,X228: $i,X230: $i] :
( ( in @ X228 @ ( powerset @ X226 ) )
=> ( ( in @ X230 @ X228 )
=> ( in @ X230 @ X226 ) ) )
=> ( ! [X232: $i,X234: $i,X236: $i] :
( ( in @ X234 @ X236 )
=> ( ( in @ X236 @ X232 )
=> ( in @ X234 @ ( setunion @ X232 ) ) ) )
=> ( ! [X238: $i,X240: $i] :
( ( in @ X240 @ ( setunion @ X238 ) )
=> ! [X242: $o] :
( ! [X244: $i] :
( ( in @ X240 @ X244 )
=> ( ( in @ X244 @ X238 )
=> X242 ) )
=> X242 ) )
=> ( ! [X246: $i,X248: $i] :
( ( in @ X248 @ X246 )
=> ( in @ X248 @ ( powerset @ ( setunion @ X246 ) ) ) )
=> ( ! [X250: $i > $o] :
( ? [X252: $i] :
( ! [X254: $i] :
( ( X250 @ X254 )
=> ( X252 = X254 ) )
& ( X250 @ X252 ) )
=> ? [X256: $i] :
! [X258: $i] :
( ( X250 @ X258 )
<=> ( X258 = X256 ) ) )
=> ( ! [X260: $i] :
( ( X260 != emptyset )
=> ? [X262: $i] : ( in @ X262 @ X260 ) )
=> ( ! [X264: $i,X266: $i] :
( ( in @ X264 @ ( setadjoin @ X266 @ emptyset ) )
=> ( X264 = X266 ) )
=> ( ! [X268: $i,X270: $i] :
( ( X268 != X270 )
=> ~ ( in @ X270 @ ( setadjoin @ X268 @ emptyset ) ) )
=> ( ! [X272: $i,X274: $i] :
( ( X272 = X274 )
=> ( in @ X272 @ ( setadjoin @ X274 @ emptyset ) ) )
=> ( ! [X276: $i,X278: $i] :
( ( in @ X276 @ ( setadjoin @ X278 @ emptyset ) )
=> ( in @ X278 @ ( setadjoin @ X276 @ emptyset ) ) )
=> ( ! [X280: $i,X282: $i,X284: $i] :
( ( in @ X284 @ ( setadjoin @ X280 @ ( setadjoin @ X282 @ emptyset ) ) )
=> ( ( X284 = X280 )
| ( X284 = X282 ) ) )
=> ( ! [X286: $i,X288: $i] : ( in @ X286 @ ( setadjoin @ X286 @ ( setadjoin @ X288 @ emptyset ) ) )
=> ( ! [X290: $i,X292: $i] : ( in @ X292 @ ( setadjoin @ X290 @ ( setadjoin @ X292 @ emptyset ) ) )
=> ! [X294: $i,X296: $i > $o] :
( ? [X298: $i] :
( ( X296 @ X298 )
& ( in @ X298 @ X294 ) )
=> ( ( dsetconstr @ X294
@ ^ [V_8: $i] : ( X296 @ V_8 ) )
!= emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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 @ ( prop2set @ 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_5: $i] : ( X172 @ V_5 ) ) )
<=> ( 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_6: $i] : ( X182 @ V_6 ) )
!= 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_7: $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 ) )
=> ( ! [X224: $i] : ( in @ emptyset @ ( powerset @ X224 ) )
=> ( ! [X226: $i,X228: $i,X230: $i] :
( ( in @ X228 @ ( powerset @ X226 ) )
=> ( ( in @ X230 @ X228 )
=> ( in @ X230 @ X226 ) ) )
=> ( ! [X232: $i,X234: $i,X236: $i] :
( ( in @ X234 @ X236 )
=> ( ( in @ X236 @ X232 )
=> ( in @ X234 @ ( setunion @ X232 ) ) ) )
=> ( ! [X238: $i,X240: $i] :
( ( in @ X240 @ ( setunion @ X238 ) )
=> ! [X242: $o] :
( ! [X244: $i] :
( ( in @ X240 @ X244 )
=> ( ( in @ X244 @ X238 )
=> X242 ) )
=> X242 ) )
=> ( ! [X246: $i,X248: $i] :
( ( in @ X248 @ X246 )
=> ( in @ X248 @ ( powerset @ ( setunion @ X246 ) ) ) )
=> ( ! [X250: $i > $o] :
( ? [X252: $i] :
( ! [X254: $i] :
( ( X250 @ X254 )
=> ( X252 = X254 ) )
& ( X250 @ X252 ) )
=> ? [X256: $i] :
! [X258: $i] :
( ( X250 @ X258 )
<=> ( X258 = X256 ) ) )
=> ( ! [X260: $i] :
( ( X260 != emptyset )
=> ? [X262: $i] : ( in @ X262 @ X260 ) )
=> ( ! [X264: $i,X266: $i] :
( ( in @ X264 @ ( setadjoin @ X266 @ emptyset ) )
=> ( X264 = X266 ) )
=> ( ! [X268: $i,X270: $i] :
( ( X268 != X270 )
=> ~ ( in @ X270 @ ( setadjoin @ X268 @ emptyset ) ) )
=> ( ! [X272: $i,X274: $i] :
( ( X272 = X274 )
=> ( in @ X272 @ ( setadjoin @ X274 @ emptyset ) ) )
=> ( ! [X276: $i,X278: $i] :
( ( in @ X276 @ ( setadjoin @ X278 @ emptyset ) )
=> ( in @ X278 @ ( setadjoin @ X276 @ emptyset ) ) )
=> ( ! [X280: $i,X282: $i,X284: $i] :
( ( in @ X284 @ ( setadjoin @ X280 @ ( setadjoin @ X282 @ emptyset ) ) )
=> ( ( X284 = X280 )
| ( X284 = X282 ) ) )
=> ( ! [X286: $i,X288: $i] : ( in @ X286 @ ( setadjoin @ X286 @ ( setadjoin @ X288 @ emptyset ) ) )
=> ( ! [X290: $i,X292: $i] : ( in @ X292 @ ( setadjoin @ X290 @ ( setadjoin @ X292 @ emptyset ) ) )
=> ! [X294: $i,X296: $i > $o] :
( ? [X298: $i] :
( ( X296 @ X298 )
& ( in @ X298 @ X294 ) )
=> ( ( dsetconstr @ X294
@ ^ [V_8: $i] : ( X296 @ V_8 ) )
!= emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_9]) ).
thf(zip_derived_cl61,plain,
( ( dsetconstr @ sk__153
@ ^ [Y0: $i] : ( sk__154 @ Y0 ) )
= emptyset ),
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl264,plain,
( ( dsetconstr @ sk__153 @ sk__154 )
= emptyset ),
inference(ho_norm,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl63,plain,
sk__154 @ sk__155,
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl62,plain,
in @ sk__155 @ sk__153,
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl48,plain,
! [X46: $i,X47: $i > $o,X48: $i] :
( ( ( dsetconstr @ X46
@ ^ [Y0: $i] : ( X47 @ Y0 ) )
!= emptyset )
| ~ ( in @ X48 @ X46 )
| ~ ( X47 @ X48 ) ),
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl118,plain,
! [X46: $i,X47: $i > $o,X48: $i] :
( ( ( dsetconstr @ X46 @ X47 )
!= emptyset )
| ~ ( in @ X48 @ X46 )
| ~ ( X47 @ X48 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl119,plain,
! [X0: $i > $o] :
( ~ ( X0 @ sk__155 )
| ( ( dsetconstr @ sk__153 @ X0 )
!= emptyset ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl118]) ).
thf(zip_derived_cl134,plain,
( ( dsetconstr @ sk__153
@ ^ [Y0: $i] :
( sk__154
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
!= emptyset ),
inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl119]) ).
thf(zip_derived_cl140,plain,
( ( dsetconstr @ sk__153 @ sk__154 )
!= emptyset ),
inference(ho_norm,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl265,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl264,zip_derived_cl140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU534^1 : 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.WrRU2QPO7R true
% 0.14/0.36 % Computer : n001.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 14:12:24 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
% 0.14/0.36 % Running in HO mode
% 0.22/0.68 % Total configuration time : 828
% 0.22/0.68 % Estimated wc time : 1656
% 0.22/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.58/0.98 % Solved by lams/40_noforms.sh.
% 1.58/0.98 % done 61 iterations in 0.113s
% 1.58/0.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.58/0.98 % SZS output start Refutation
% See solution above
% 1.58/0.99
% 1.58/0.99
% 1.58/0.99 % Terminating...
% 1.70/1.08 % Runner terminated.
% 1.70/1.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------