%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU517^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.N4kg1jjTrH true
% Computer : n003.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 Oct 2 04:54:52 PM UTC 2025
% Result : Theorem 46.58s 6.52s
% Output : Refutation 47.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 82
% Syntax : Number of formulae : 164 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 4530 ( 482 equ; 129 cnn)
% Maximal formula atoms : 210 ( 27 avg)
% Number of connectives : 11871 ( 327 ~; 139 |; 383 &;7051 @)
% ( 102 <=>;1948 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 211 ( 211 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 49 usr; 41 con; 0-2 aty)
% (1626 !!; 295 ??; 0 @@+; 0 @@-)
% Number of variables : 2533 (2039 ^; 423 !; 71 ?;2533 :)
% 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(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(emptyI_type,type,
emptyI: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf('#sk22_type',type,
'#sk22': $i > $i ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf('#form193_type',type,
'#form193': $i > $i > $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('#sk231_type',type,
'#sk231': $i ).
thf(prop2set_type,type,
prop2set: $o > $i ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf('#sk159_type',type,
'#sk159': $i > $i > $i ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf('#sk130_type',type,
'#sk130': $i > $i > $i ).
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(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(setadjoinOr,axiom,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ) ).
thf('0',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('1',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('2',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('3',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).
thf('4',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(setadjoinIL,axiom,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
thf('5',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('6',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('7',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('8',plain,
( nonemptyE1
= ( ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X6: $i] : ( in @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
thf('9',plain,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[nonempty]) ).
thf('10',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('11',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('12',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('13',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('14',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('15',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('16',plain,
( notinemptyset
= ( ! [X4: $i] :
~ ( in @ X4 @ emptyset ) ) ),
define([status(thm)]) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ) ).
thf('17',plain,
( emptysetimpfalse
= ( ! [X4: $i] :
( ( in @ X4 @ emptyset )
=> $false ) ) ),
define([status(thm)]) ).
thf(emptysetE,axiom,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ).
thf('18',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('19',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('20',plain,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ),
inference(simplify_rw_rule,[status(thm)],[prop2set]) ).
thf('21',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('22',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('23',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('24',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('25',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('26',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('27',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('28',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('29',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('30',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('31',plain,
( omegaSAx
= ( ! [X4: $i] :
( ( in @ X4 @ omega )
=> ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) ) ),
define([status(thm)]) ).
thf(omega0Ax,axiom,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf('32',plain,
( omega0Ax
= ( in @ emptyset @ omega ) ),
inference(simplify_rw_rule,[status(thm)],[omega0Ax]) ).
thf('33',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('34',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('35',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('36',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('37',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('38',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('39',plain,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) )
& ( Xphi @ Xx ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[exu]) ).
thf('40',plain,
( exu
= ( ^ [V_1: $i > $o] :
? [X4: $i] :
( ! [X6: $i] :
( ( V_1 @ X6 )
=> ( X4 = X6 ) )
& ( V_1 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(setoftrueEq,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
=> ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= 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 )
=> ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,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 ) )
<=> ( ( 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 )
=> ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
<=> ( in @ Y2 @ Y1 ) ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0
@ ( descr
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
<=> ( in @ Y2 @ Y1 ) ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
<=> ( in @ Y2 @ Y1 ) ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
<=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
<=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl21,plain,
~ ( ( in @ emptyset @ omega )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl27,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ omega )
=> ( in @ ( setadjoin @ Y0 @ Y0 ) @ omega ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ omega ) )
=> ( in @ ( setadjoin @ Y1 @ Y1 ) @ Y0 ) ) )
& ( in @ emptyset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ omega )
=> ( in @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl36,plain,
~ ( ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ??
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
<=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl40,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl49,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl54,plain,
~ ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( Y0 @ ( descr @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl60,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl71,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl85,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl104,plain,
~ ( ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y2: $i] : Y0 ) )
=> Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl122,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $o] : Y1 ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl142,plain,
~ ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl158,plain,
~ ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl171,plain,
~ ( ( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl184,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl199,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl211,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] : ( (~) @ ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl221,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
<=> ( Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl229,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl239,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( dsetconstr @ Y0 @ Y1 )
!= emptyset ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl229]) ).
thf(zip_derived_cl254,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( Y0 != emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl265,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl254]) ).
thf(zip_derived_cl275,plain,
~ ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl281,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl275]) ).
thf(zip_derived_cl288,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl281]) ).
thf(zip_derived_cl292,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl288]) ).
thf(zip_derived_cl297,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true )
= Y0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl292]) ).
thf(zip_derived_cl301,plain,
( ( dsetconstr @ '#sk231'
@ ^ [Y0: $i] : $true )
!= '#sk231' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl297]) ).
thf(zip_derived_cl304,plain,
( ( dsetconstr @ '#sk231'
@ ^ [Y0: $i] : $true )
!= '#sk231' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl301]) ).
thf(zip_derived_cl70,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl83,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl98,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl101,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( $true
=> ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : $true ) ) ) ) ),
inference('ho.refine.early.bird',[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl363,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : $true ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl53,plain,
( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y0 )
& ( in @ Y2 @ Y0 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ Y2 @ Y4 )
<=> ( in @ Y3 @ Y4 ) ) ) )
=> ( Y2 = Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( in @ Y3 @ Y1 )
& ( in @ Y2 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y2 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( ( ??
@ ^ [Y3: $i] : ( in @ Y3 @ Y2 ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y4 @ Y2 )
& ( (~)
@ ( ??
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
& ( in @ Y5 @ Y2 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ Y4 @ Y5 )
| ( !!
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y5 )
=> ( in @ Y6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl58,plain,
! [X2: $i] :
( ??
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X2 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( in @ Y2 @ X2 )
& ( in @ Y1 @ X2 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y1 @ Y3 )
<=> ( in @ Y2 @ Y3 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( in @ Y2 @ Y0 )
& ( in @ Y1 @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( ( ??
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X2 ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y3 @ Y1 )
& ( (~)
@ ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
& ( in @ Y4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ Y3 @ Y4 )
| ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y4 )
=> ( in @ Y5 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ X2 )
& ( in @ Y0 @ X2 ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y0 @ Y2 )
<=> ( in @ Y1 @ Y2 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( in @ Y1 @ ( '#sk22' @ X2 ) )
& ( in @ Y0 @ ( '#sk22' @ X2 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( '#sk22' @ X2 ) )
& ( in @ Y2 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y3 @ Y0 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y2 @ Y3 )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( ??
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( '#sk22' @ X2 ) )
& ( in @ Y2 @ Y0 )
& ( (~)
@ ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( in @ Y3 @ Y0 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y2 @ Y3 )
| ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( in @ Y4 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: $i] :
( ( ( ??
@ ^ [Y0: $i] : ( in @ Y0 @ X4 ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
& ( in @ Y1 @ X4 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y2 @ X4 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y1 @ Y2 )
| ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl113,plain,
! [X2: $i,X4: $i] :
( ~ ( ( ??
@ ^ [Y0: $i] : ( in @ Y0 @ X4 ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( ??
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
& ( in @ Y1 @ X4 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y2 @ X4 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y1 @ Y2 )
| ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl129,plain,
! [X2: $i,X4: $i] :
( ~ ( ??
@ ^ [Y0: $i] : ( in @ Y0 @ X4 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( ??
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
& ( in @ Y1 @ X4 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y2 @ X4 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y1 @ Y2 )
| ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl149,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X4 )
| ( ??
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
& ( in @ Y1 @ X4 )
& ( (~)
@ ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y2 @ X4 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y1 @ Y2 )
| ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl164,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ??
@ ^ [Y0: $i] :
( ( in @ ( '#sk130' @ X2 @ X4 ) @ ( '#sk22' @ X2 ) )
& ( in @ Y0 @ X4 )
& ( (~)
@ ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk130' @ X2 @ X4 ) )
& ( in @ Y1 @ X4 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk22' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( '#sk130' @ X2 @ X4 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ~ ( in @ X6 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl177,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ ( '#sk130' @ X2 @ X4 ) @ ( '#sk22' @ X2 ) )
& ( in @ ( '#sk159' @ X2 @ X4 ) @ X4 )
& ( (~)
@ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk130' @ X2 @ X4 ) )
& ( in @ Y0 @ X4 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
=> ( ( in @ ( '#sk159' @ X2 @ X4 ) @ Y0 )
| ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( '#sk130' @ X2 @ X4 ) ) ) ) ) ) ) )
| ~ ( in @ X6 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl164]) ).
thf(zip_derived_cl193,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
=> ( ( in @ ( '#sk159' @ X2 @ X4 ) @ Y0 )
| ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( '#sk130' @ X2 @ X4 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ~ ( in @ X6 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl177]) ).
thf(zip_derived_cl190,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk130' @ X2 @ X4 ) @ ( '#sk22' @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ~ ( in @ X6 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl177]) ).
thf(zip_derived_cl202,plain,
! [X2: $i,X4: $i] :
( ( '#form193' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl207,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#form193' @ X2 @ X4 )
| ~ ( in @ X6 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk22' @ X2 ) )
=> ( ( in @ ( '#sk159' @ X2 @ X4 ) @ Y0 )
| ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( '#sk130' @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl193,zip_derived_cl202]) ).
thf(zip_derived_cl216,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ ( '#sk22' @ X2 ) )
=> ( ( in @ ( '#sk159' @ X2 @ X4 ) @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X8 )
=> ( in @ Y0 @ ( '#sk130' @ X2 @ X4 ) ) ) ) ) )
| ~ ( in @ X6 @ X4 )
| ~ ( '#form193' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl207]) ).
thf(zip_derived_cl223,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( '#sk22' @ X2 ) )
| ( in @ ( '#sk159' @ X2 @ X4 ) @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X8 )
=> ( in @ Y0 @ ( '#sk130' @ X2 @ X4 ) ) ) )
| ~ ( '#form193' @ X2 @ X4 )
| ~ ( in @ X6 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl231,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( '#sk159' @ X2 @ X4 ) @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X8 )
=> ( in @ Y0 @ ( '#sk130' @ X2 @ X4 ) ) ) )
| ~ ( in @ X6 @ X4 )
| ~ ( '#form193' @ X2 @ X4 )
| ~ ( in @ X8 @ ( '#sk22' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl240,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form193' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl202_001,plain,
! [X2: $i,X4: $i] :
( ( '#form193' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl364,plain,
! [X0: $i] :
( '#form193'
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : $true )
@ X0 ),
inference(renaming,[status(thm)],[zip_derived_cl363,zip_derived_cl240,zip_derived_cl202]) ).
thf(zip_derived_cl198,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl209,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) )
=> ( X2 = Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl198]) ).
thf(zip_derived_cl218,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X4 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl209]) ).
thf(zip_derived_cl225,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X4 ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl218]) ).
thf(zip_derived_cl202_002,plain,
! [X2: $i,X4: $i] :
( ( '#form193' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl233,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form193' @ X4 @ X2 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl225,zip_derived_cl202]) ).
thf(zip_derived_cl245,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ~ ( '#form193' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl233]) ).
thf(zip_derived_cl259,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ~ ( '#form193' @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl245]) ).
thf(zip_derived_cl240_003,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form193' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl202_004,plain,
! [X2: $i,X4: $i] :
( ( '#form193' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl260,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form193' @ X2 @ X4 )
| ~ ( '#form193' @ X4 @ X2 )
| ( X2 = X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl259,zip_derived_cl240,zip_derived_cl202]) ).
thf(zip_derived_cl3665,plain,
! [X0: $i] :
( ( X0
= ( dsetconstr @ X0
@ ^ [Y0: $i] : $true ) )
| ~ ( '#form193' @ X0
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : $true ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl364,zip_derived_cl260]) ).
thf(zip_derived_cl84,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl102,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( in @ Y1 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl116,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
=> ( in @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl119,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : $true ) )
=> ( in @ Y0 @ X0 ) ) ),
inference('ho.refine.early.bird',[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl240_005,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form193' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl202_006,plain,
! [X2: $i,X4: $i] :
( ( '#form193' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl359,plain,
! [X0: $i] :
( '#form193' @ X0
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : $true ) ),
inference(renaming,[status(thm)],[zip_derived_cl119,zip_derived_cl240,zip_derived_cl202]) ).
thf(zip_derived_cl3691,plain,
! [X0: $i] :
( X0
= ( dsetconstr @ X0
@ ^ [Y0: $i] : $true ) ),
inference(demod,[status(thm)],[zip_derived_cl3665,zip_derived_cl359]) ).
thf(zip_derived_cl3699,plain,
'#sk231' != '#sk231',
inference(demod,[status(thm)],[zip_derived_cl304,zip_derived_cl3691]) ).
thf(zip_derived_cl3700,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl3699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU517^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.N4kg1jjTrH true
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 1 16:11:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.52/0.65 % Total configuration time : 828
% 0.52/0.65 % Estimated wc time : 1656
% 0.52/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 46.58/6.52 % Solved by lams/30_sp5.sh.
% 46.58/6.52 % done 193 iterations in 5.395s
% 46.58/6.52 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 46.58/6.52 % SZS output start Refutation
% See solution above
% 47.21/6.54
% 47.21/6.54
% 47.21/6.54 % Terminating...
% 53.46/6.67 % Runner terminated.
% 53.46/6.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------