%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU617^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ci8iYljcNj true
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:14:45 EDT 2023
% Result : Theorem 2.14s 0.91s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 216
% Syntax : Number of formulae : 225 ( 72 unt; 145 typ; 0 def)
% Number of atoms : 887 ( 151 equ; 0 cnn)
% Maximal formula atoms : 162 ( 11 avg)
% Number of connectives : 1579 ( 37 ~; 17 |; 4 &; 834 @)
% ( 12 <=>; 675 =>; 0 <=; 0 <~>)
% Maximal formula depth : 145 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 145 ( 143 usr; 137 con; 0-3 aty)
% Number of variables : 377 ( 0 ^; 372 !; 5 ?; 377 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setminusELneg_type,type,
setminusELneg: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(exuI1_type,type,
exuI1: $o ).
thf(exuI2_type,type,
exuI2: $o ).
thf(notequalI2_type,type,
notequalI2: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(sk__75_type,type,
sk__75: $i ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(setbeta_type,type,
setbeta: $o ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(upairsetIL_type,type,
upairsetIL: $o ).
thf(powersetI1_type,type,
powersetI1: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(zip_tseitin_1_type,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(inCongP_type,type,
inCongP: $o ).
thf(setadjoinSub_type,type,
setadjoinSub: $o ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(binintersectSubset2_type,type,
binintersectSubset2: $o ).
thf(setunionI_type,type,
setunionI: $o ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(prop2setI_type,type,
prop2setI: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf(setminusER_type,type,
setminusER: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(exuE1_type,type,
exuE1: $o ).
thf(binintersectRsub_type,type,
binintersectRsub: $o ).
thf(setminusLsub_type,type,
setminusLsub: $o ).
thf(notinsingleton_type,type,
notinsingleton: $o ).
thf(eqimpsubset2_type,type,
eqimpsubset2: $o ).
thf(exuEu_type,type,
exuEu: $o ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(upairsetE_type,type,
upairsetE: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(binintersectLsub_type,type,
binintersectLsub: $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(symdiffE_type,type,
symdiffE: $o ).
thf(descrp_type,type,
descrp: $o ).
thf(dsetconstr__Cong_type,type,
dsetconstr__Cong: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyI_type,type,
emptyI: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(binintersectEL_type,type,
binintersectEL: $o ).
thf(emptyE1_type,type,
emptyE1: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(sk__76_type,type,
sk__76: $i ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(setminusSubset2_type,type,
setminusSubset2: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(notdallE_type,type,
notdallE: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(replAx_type,type,
replAx: $o ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(inPowerset_type,type,
inPowerset: $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(secondinupair,axiom,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('0',plain,
( secondinupair
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(upairset2IR,axiom,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('1',plain,
( upairset2IR
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf('2',plain,
( subsetemptysetimpeq
= ( ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
thf('3',plain,
( setadjoinSub2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X8 )
=> ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(setadjoinSub,axiom,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
thf('4',plain,
( setadjoinSub
= ( ! [X4: $i,X6: $i] : ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(emptysetsubset,axiom,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
thf('5',plain,
( emptysetsubset
= ( ! [X4: $i] : ( subset @ emptyset @ X4 ) ) ),
define([status(thm)]) ).
thf(setunion__Cong,axiom,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ) ).
thf('6',plain,
( setunion__Cong
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( ( setunion @ X4 )
= ( setunion @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
thf('7',plain,
( setadjoin__Cong
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ! [X8: $i,X10: $i] :
( ( X8 = X10 )
=> ( ( setadjoin @ X4 @ X8 )
= ( setadjoin @ X6 @ X10 ) ) ) ) ) ),
define([status(thm)]) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
= ( emptyset = emptyset ) ) ).
thf('8',plain,
( emptyset__Cong
= ( emptyset = emptyset ) ),
define([status(thm)]) ).
thf(vacuousDall,axiom,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ) ).
thf('9',plain,
( vacuousDall
= ( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(upairsetIR,axiom,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('10',plain,
( upairsetIR
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(upairsetIL,axiom,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('11',plain,
( upairsetIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(upairsetE,axiom,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ).
thf('12',plain,
( upairsetE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) )
=> ( ( X8 = X4 )
| ( X8 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(singletonsswitch,axiom,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
thf('13',plain,
( singletonsswitch
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(eqinunit,axiom,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('14',plain,
( eqinunit
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(notinsingleton,axiom,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
thf('15',plain,
( notinsingleton
= ( ! [X4: $i,X6: $i] :
( ( X4 != X6 )
=> ~ ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(uniqinunit,axiom,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ).
thf('16',plain,
( uniqinunit
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(subPowSU,axiom,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
thf('17',plain,
( subPowSU
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ X4 )
=> ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setunionE,axiom,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ) ).
thf('18',plain,
( setunionE
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( setunion @ X4 ) )
=> ! [X8: $o] :
( ! [X10: $i] :
( ( in @ X6 @ X10 )
=> ( ( in @ X10 @ X4 )
=> X8 ) )
=> X8 ) ) ) ),
define([status(thm)]) ).
thf(setunionI,axiom,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
thf('19',plain,
( setunionI
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X6 @ X8 )
=> ( ( in @ X8 @ X4 )
=> ( in @ X6 @ ( setunion @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setadjoinOr,axiom,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ) ).
thf('20',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('21',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('22',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('23',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).
thf('24',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(setadjoinIL,axiom,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
thf('25',plain,
( setadjoinIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ) ).
thf('26',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('27',plain,
( emptyI
= ( ! [X4: $i] :
( ! [X6: $i] :
~ ( in @ X6 @ X4 )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(notinemptyset,axiom,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ) ).
thf('28',plain,
( notinemptyset
= ( ! [X4: $i] :
~ ( in @ X4 @ emptyset ) ) ),
define([status(thm)]) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ) ).
thf('29',plain,
( emptysetimpfalse
= ( ! [X4: $i] :
( ( in @ X4 @ emptyset )
=> $false ) ) ),
define([status(thm)]) ).
thf(emptysetE,axiom,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ) ).
thf('30',plain,
( emptysetE
= ( ! [X4: $i] :
( ( in @ X4 @ emptyset )
=> ! [X6: $o] : X6 ) ) ),
define([status(thm)]) ).
thf(setunionAx,axiom,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ B @ A )
& ( in @ Xx @ B ) ) ) ) ) ).
thf('31',plain,
( setunionAx
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( setunion @ X4 ) )
<=> ? [X8: $i] :
( ( in @ X8 @ X4 )
& ( in @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(setadjoinAx,axiom,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ) ).
thf('32',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('33',plain,
( emptysetAx
= ( ! [X4: $i] :
~ ( in @ X4 @ emptyset ) ) ),
define([status(thm)]) ).
thf(setukpairIL,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( setextAx
=> ( ! [X4: $i] :
~ ( in @ X4 @ emptyset )
=> ( ! [X6: $i,X8: $i,X10: $i] :
( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
<=> ( ( in @ X10 @ X8 )
| ( X10 = X6 ) ) )
=> ( powersetAx
=> ( ! [X12: $i,X14: $i] :
( ( in @ X14 @ ( setunion @ X12 ) )
<=> ? [X16: $i] :
( ( in @ X14 @ X16 )
& ( in @ X16 @ X12 ) ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $o] : X20 )
=> ( ! [X22: $i] :
( ( in @ X22 @ emptyset )
=> $false )
=> ( ! [X24: $i] :
~ ( in @ X24 @ emptyset )
=> ( exuE3e
=> ( setext
=> ( ! [X26: $i] :
( ! [X28: $i] :
~ ( in @ X28 @ X26 )
=> ( X26 = emptyset ) )
=> ( ! [X30: $i] :
( ! [X32: $i] :
~ ( in @ X32 @ X30 )
=> ( X30 = emptyset ) )
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X34: $i,X36: $i] : ( in @ X34 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X40 )
=> ( in @ X42 @ ( setadjoin @ X38 @ X40 ) ) )
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( in @ X48 @ ( setadjoin @ X44 @ X46 ) )
=> ! [X50: $o] :
( ( ( X48 = X44 )
=> X50 )
=> ( ( ( in @ X48 @ X46 )
=> X50 )
=> X50 ) ) )
=> ( ! [X52: $i,X54: $i,X56: $i] :
( ( in @ X56 @ ( setadjoin @ X52 @ X54 ) )
=> ( ( in @ X56 @ X54 )
| ( X56 = X52 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X58: $i,X60: $i,X62: $i] :
( ( in @ X60 @ X62 )
=> ( ( in @ X62 @ X58 )
=> ( in @ X60 @ ( setunion @ X58 ) ) ) )
=> ( ! [X64: $i,X66: $i] :
( ( in @ X66 @ ( setunion @ X64 ) )
=> ! [X68: $o] :
( ! [X70: $i] :
( ( in @ X66 @ X70 )
=> ( ( in @ X70 @ X64 )
=> X68 ) )
=> X68 ) )
=> ( ! [X72: $i,X74: $i] :
( ( in @ X74 @ X72 )
=> ( in @ X74 @ ( powerset @ ( setunion @ X72 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X76: $i,X78: $i] :
( ( in @ X76 @ ( setadjoin @ X78 @ emptyset ) )
=> ( X76 = X78 ) )
=> ( ! [X80: $i,X82: $i] :
( ( X80 != X82 )
=> ~ ( in @ X82 @ ( setadjoin @ X80 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] :
( ( X84 = X86 )
=> ( in @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( ! [X88: $i,X90: $i] :
( ( in @ X88 @ ( setadjoin @ X90 @ emptyset ) )
=> ( in @ X90 @ ( setadjoin @ X88 @ emptyset ) ) )
=> ( ! [X92: $i,X94: $i,X96: $i] :
( ( in @ X96 @ ( setadjoin @ X92 @ ( setadjoin @ X94 @ emptyset ) ) )
=> ( ( X96 = X94 )
| ( X96 = X92 ) ) )
=> ( ! [X98: $i,X100: $i] : ( in @ X98 @ ( setadjoin @ X98 @ ( setadjoin @ X100 @ emptyset ) ) )
=> ( ! [X102: $i,X104: $i] : ( in @ X104 @ ( setadjoin @ X102 @ ( setadjoin @ X104 @ emptyset ) ) )
=> ( emptyE1
=> ( ! [X106: $i > $o,X108: $i] :
( ( in @ X108 @ emptyset )
=> ( X106 @ X108 ) )
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( ( emptyset = emptyset )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ! [X114: $i,X116: $i] :
( ( X114 = X116 )
=> ( ( setadjoin @ X110 @ X114 )
= ( setadjoin @ X112 @ X116 ) ) ) )
=> ( powerset__Cong
=> ( ! [X118: $i,X120: $i] :
( ( X118 = X120 )
=> ( ( setunion @ X118 )
= ( setunion @ X120 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( ! [X122: $i] : ( subset @ emptyset @ X122 )
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( ! [X124: $i,X126: $i] : ( subset @ X126 @ ( setadjoin @ X124 @ X126 ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X132 )
=> ( subset @ X128 @ ( setadjoin @ X130 @ X132 ) ) )
=> ( subset2powerset
=> ( setextsub
=> ( ! [X134: $i] :
( ( subset @ X134 @ emptyset )
=> ( X134 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X136: $i,X138: $i] : ( in @ X138 @ ( setadjoin @ X136 @ ( setadjoin @ X138 @ emptyset ) ) )
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( ! [X140: $i,X142: $i] : ( in @ X142 @ ( setadjoin @ X140 @ ( setadjoin @ X142 @ emptyset ) ) )
=> ! [X144: $i,X146: $i] : ( in @ X144 @ ( setunion @ ( setadjoin @ ( setadjoin @ X144 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X144 @ ( setadjoin @ X146 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [X16: $i,X14: $i,X12: $i] :
( ( zip_tseitin_1 @ X16 @ X14 @ X12 )
<=> ( ( in @ X16 @ X12 )
& ( in @ X14 @ X16 ) ) ) ).
thf(zf_stmt_3,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(zf_stmt_4,axiom,
! [X10: $i,X8: $i,X6: $i] :
( ( zip_tseitin_0 @ X10 @ X8 @ X6 )
<=> ( ( X10 = X6 )
| ( in @ X10 @ X8 ) ) ) ).
thf(zf_stmt_5,conjecture,
( setextAx
=> ( ! [X4: $i] :
~ ( in @ X4 @ emptyset )
=> ( ! [X6: $i,X8: $i,X10: $i] :
( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
<=> ( zip_tseitin_0 @ X10 @ X8 @ X6 ) )
=> ( powersetAx
=> ( ! [X12: $i,X14: $i] :
( ( in @ X14 @ ( setunion @ X12 ) )
<=> ? [X16: $i] : ( zip_tseitin_1 @ X16 @ X14 @ X12 ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $o] : X20 )
=> ( ! [X22: $i] :
~ ( in @ X22 @ emptyset )
=> ( ! [X24: $i] :
~ ( in @ X24 @ emptyset )
=> ( exuE3e
=> ( setext
=> ( ! [X26: $i] :
( ! [X28: $i] :
~ ( in @ X28 @ X26 )
=> ( X26 = emptyset ) )
=> ( ! [X30: $i] :
( ! [X32: $i] :
~ ( in @ X32 @ X30 )
=> ( X30 = emptyset ) )
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X34: $i,X36: $i] : ( in @ X34 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X40 )
=> ( in @ X42 @ ( setadjoin @ X38 @ X40 ) ) )
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( in @ X48 @ ( setadjoin @ X44 @ X46 ) )
=> ! [X50: $o] :
( ( ( X48 = X44 )
=> X50 )
=> ( ( ( in @ X48 @ X46 )
=> X50 )
=> X50 ) ) )
=> ( ! [X52: $i,X54: $i,X56: $i] :
( ( in @ X56 @ ( setadjoin @ X52 @ X54 ) )
=> ( ( X56 = X52 )
| ( in @ X56 @ X54 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X58: $i,X60: $i,X62: $i] :
( ( in @ X60 @ X62 )
=> ( ( in @ X62 @ X58 )
=> ( in @ X60 @ ( setunion @ X58 ) ) ) )
=> ( ! [X64: $i,X66: $i] :
( ( in @ X66 @ ( setunion @ X64 ) )
=> ! [X68: $o] :
( ! [X70: $i] :
( ( in @ X66 @ X70 )
=> ( ( in @ X70 @ X64 )
=> X68 ) )
=> X68 ) )
=> ( ! [X72: $i,X74: $i] :
( ( in @ X74 @ X72 )
=> ( in @ X74 @ ( powerset @ ( setunion @ X72 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X76: $i,X78: $i] :
( ( in @ X76 @ ( setadjoin @ X78 @ emptyset ) )
=> ( X76 = X78 ) )
=> ( ! [X80: $i,X82: $i] :
( ( X80 != X82 )
=> ~ ( in @ X82 @ ( setadjoin @ X80 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] :
( ( X84 = X86 )
=> ( in @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( ! [X88: $i,X90: $i] :
( ( in @ X88 @ ( setadjoin @ X90 @ emptyset ) )
=> ( in @ X90 @ ( setadjoin @ X88 @ emptyset ) ) )
=> ( ! [X92: $i,X94: $i,X96: $i] :
( ( in @ X96 @ ( setadjoin @ X92 @ ( setadjoin @ X94 @ emptyset ) ) )
=> ( ( X96 = X92 )
| ( X96 = X94 ) ) )
=> ( ! [X98: $i,X100: $i] : ( in @ X98 @ ( setadjoin @ X98 @ ( setadjoin @ X100 @ emptyset ) ) )
=> ( ! [X102: $i,X104: $i] : ( in @ X104 @ ( setadjoin @ X102 @ ( setadjoin @ X104 @ emptyset ) ) )
=> ( emptyE1
=> ( ! [X106: $i > $o,X108: $i] :
( ( in @ X108 @ emptyset )
=> ( X106 @ X108 ) )
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( ( emptyset = emptyset )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ! [X114: $i,X116: $i] :
( ( X114 = X116 )
=> ( ( setadjoin @ X110 @ X114 )
= ( setadjoin @ X112 @ X116 ) ) ) )
=> ( powerset__Cong
=> ( ! [X118: $i,X120: $i] :
( ( X118 = X120 )
=> ( ( setunion @ X118 )
= ( setunion @ X120 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( ! [X122: $i] : ( subset @ emptyset @ X122 )
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( ! [X124: $i,X126: $i] : ( subset @ X126 @ ( setadjoin @ X124 @ X126 ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X132 )
=> ( subset @ X128 @ ( setadjoin @ X130 @ X132 ) ) )
=> ( subset2powerset
=> ( setextsub
=> ( ! [X134: $i] :
( ( subset @ X134 @ emptyset )
=> ( X134 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X136: $i,X138: $i] : ( in @ X138 @ ( setadjoin @ X136 @ ( setadjoin @ X138 @ emptyset ) ) )
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( ! [X140: $i,X142: $i] : ( in @ X142 @ ( setadjoin @ X140 @ ( setadjoin @ X142 @ emptyset ) ) )
=> ! [X144: $i,X146: $i] : ( in @ X144 @ ( setunion @ ( setadjoin @ ( setadjoin @ X144 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X144 @ ( setadjoin @ X146 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_6,negated_conjecture,
~ ( setextAx
=> ( ! [X4: $i] :
~ ( in @ X4 @ emptyset )
=> ( ! [X6: $i,X8: $i,X10: $i] :
( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
<=> ( zip_tseitin_0 @ X10 @ X8 @ X6 ) )
=> ( powersetAx
=> ( ! [X12: $i,X14: $i] :
( ( in @ X14 @ ( setunion @ X12 ) )
<=> ? [X16: $i] : ( zip_tseitin_1 @ X16 @ X14 @ X12 ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $o] : X20 )
=> ( ! [X22: $i] :
~ ( in @ X22 @ emptyset )
=> ( ! [X24: $i] :
~ ( in @ X24 @ emptyset )
=> ( exuE3e
=> ( setext
=> ( ! [X26: $i] :
( ! [X28: $i] :
~ ( in @ X28 @ X26 )
=> ( X26 = emptyset ) )
=> ( ! [X30: $i] :
( ! [X32: $i] :
~ ( in @ X32 @ X30 )
=> ( X30 = emptyset ) )
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X34: $i,X36: $i] : ( in @ X34 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X40 )
=> ( in @ X42 @ ( setadjoin @ X38 @ X40 ) ) )
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( in @ X48 @ ( setadjoin @ X44 @ X46 ) )
=> ! [X50: $o] :
( ( ( X48 = X44 )
=> X50 )
=> ( ( ( in @ X48 @ X46 )
=> X50 )
=> X50 ) ) )
=> ( ! [X52: $i,X54: $i,X56: $i] :
( ( in @ X56 @ ( setadjoin @ X52 @ X54 ) )
=> ( ( X56 = X52 )
| ( in @ X56 @ X54 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X58: $i,X60: $i,X62: $i] :
( ( in @ X60 @ X62 )
=> ( ( in @ X62 @ X58 )
=> ( in @ X60 @ ( setunion @ X58 ) ) ) )
=> ( ! [X64: $i,X66: $i] :
( ( in @ X66 @ ( setunion @ X64 ) )
=> ! [X68: $o] :
( ! [X70: $i] :
( ( in @ X66 @ X70 )
=> ( ( in @ X70 @ X64 )
=> X68 ) )
=> X68 ) )
=> ( ! [X72: $i,X74: $i] :
( ( in @ X74 @ X72 )
=> ( in @ X74 @ ( powerset @ ( setunion @ X72 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X76: $i,X78: $i] :
( ( in @ X76 @ ( setadjoin @ X78 @ emptyset ) )
=> ( X76 = X78 ) )
=> ( ! [X80: $i,X82: $i] :
( ( X80 != X82 )
=> ~ ( in @ X82 @ ( setadjoin @ X80 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] :
( ( X84 = X86 )
=> ( in @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( ! [X88: $i,X90: $i] :
( ( in @ X88 @ ( setadjoin @ X90 @ emptyset ) )
=> ( in @ X90 @ ( setadjoin @ X88 @ emptyset ) ) )
=> ( ! [X92: $i,X94: $i,X96: $i] :
( ( in @ X96 @ ( setadjoin @ X92 @ ( setadjoin @ X94 @ emptyset ) ) )
=> ( ( X96 = X92 )
| ( X96 = X94 ) ) )
=> ( ! [X98: $i,X100: $i] : ( in @ X98 @ ( setadjoin @ X98 @ ( setadjoin @ X100 @ emptyset ) ) )
=> ( ! [X102: $i,X104: $i] : ( in @ X104 @ ( setadjoin @ X102 @ ( setadjoin @ X104 @ emptyset ) ) )
=> ( emptyE1
=> ( ! [X106: $i > $o,X108: $i] :
( ( in @ X108 @ emptyset )
=> ( X106 @ X108 ) )
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( ( emptyset = emptyset )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ! [X114: $i,X116: $i] :
( ( X114 = X116 )
=> ( ( setadjoin @ X110 @ X114 )
= ( setadjoin @ X112 @ X116 ) ) ) )
=> ( powerset__Cong
=> ( ! [X118: $i,X120: $i] :
( ( X118 = X120 )
=> ( ( setunion @ X118 )
= ( setunion @ X120 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( ! [X122: $i] : ( subset @ emptyset @ X122 )
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( ! [X124: $i,X126: $i] : ( subset @ X126 @ ( setadjoin @ X124 @ X126 ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X132 )
=> ( subset @ X128 @ ( setadjoin @ X130 @ X132 ) ) )
=> ( subset2powerset
=> ( setextsub
=> ( ! [X134: $i] :
( ( subset @ X134 @ emptyset )
=> ( X134 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X136: $i,X138: $i] : ( in @ X138 @ ( setadjoin @ X136 @ ( setadjoin @ X138 @ emptyset ) ) )
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( ! [X140: $i,X142: $i] : ( in @ X142 @ ( setadjoin @ X140 @ ( setadjoin @ X142 @ emptyset ) ) )
=> ! [X144: $i,X146: $i] : ( in @ X144 @ ( setunion @ ( setadjoin @ ( setadjoin @ X144 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X144 @ ( setadjoin @ X146 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl75,plain,
~ ( in @ sk__75 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk__75 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__75 @ ( setadjoin @ sk__76 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl74,plain,
! [X38: $i,X39: $i] : ( in @ X38 @ ( setadjoin @ X39 @ ( setadjoin @ X38 @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl22,plain,
! [X10: $i,X11: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X11 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl27,plain,
! [X18: $i,X19: $i,X20: $i] :
( ( in @ X18 @ ( setunion @ X19 ) )
| ~ ( in @ X18 @ X20 )
| ~ ( in @ X20 @ X19 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( setadjoin @ X1 @ X0 ) @ X2 )
| ( in @ X1 @ ( setunion @ X2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl27]) ).
thf(zip_derived_cl225,plain,
! [X0: $i,X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ ( setadjoin @ X1 @ X0 ) @ emptyset ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl198]) ).
thf(zip_derived_cl352,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU617^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ci8iYljcNj true
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 22:35:46 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 2.14/0.91 % Solved by lams/40_c_ic.sh.
% 2.14/0.91 % done 186 iterations in 0.101s
% 2.14/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.14/0.91 % SZS output start Refutation
% See solution above
% 2.14/0.92
% 2.14/0.92
% 2.14/0.93 % Terminating...
% 2.29/1.01 % Runner terminated.
% 2.29/1.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------