TSTP Solution File: SEU634^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU634^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OaryxdMcQM true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:15:03 EDT 2023
% Result : Theorem 64.60s 8.94s
% Output : Refutation 64.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 250
% Syntax : Number of formulae : 262 ( 85 unt; 163 typ; 0 def)
% Number of atoms : 1109 ( 184 equ; 0 cnn)
% Maximal formula atoms : 198 ( 11 avg)
% Number of connectives : 2128 ( 50 ~; 28 |; 9 &;1209 @)
% ( 12 <=>; 820 =>; 0 <=; 0 <~>)
% Maximal formula depth : 159 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 163 ( 161 usr; 153 con; 0-3 aty)
% Number of variables : 516 ( 0 ^; 506 !; 10 ?; 516 :)
% 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(sk__100_type,type,
sk__100: $i > $i > $i ).
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(setukpairIR_type,type,
setukpairIR: $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(upairsubunion_type,type,
upairsubunion: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIL_type,type,
setukpairIL: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
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(upairset2E_type,type,
upairset2E: $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(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $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(singletoninpowunion_type,type,
singletoninpowunion: $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(ubforcartprodlem2_type,type,
ubforcartprodlem2: $o ).
thf(sk__102_type,type,
sk__102: $i ).
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(ubforcartprodlem1_type,type,
ubforcartprodlem1: $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(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(zip_tseitin_1_type,type,
zip_tseitin_1: $i > $i > $i > $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(singletonsubset_type,type,
singletonsubset: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(setunionE2_type,type,
setunionE2: $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(kpairp_type,type,
kpairp: $o ).
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(sk__101_type,type,
sk__101: $i > $i > $i ).
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(cartprodmempair_type,type,
cartprodmempair: $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(setunionE2,axiom,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ Xx @ X )
& ( in @ X @ A ) ) ) ) ) ).
thf('0',plain,
( setunionE2
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( setunion @ X4 ) )
=> ? [X8: $i] :
( ( in @ X6 @ X8 )
& ( in @ X8 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(upairset2E,axiom,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ) ).
thf('1',plain,
( upairset2E
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) )
=> ( ( X8 = X4 )
| ( X8 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(singletonsubset,axiom,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
thf('2',plain,
( singletonsubset
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ X4 )
=> ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) ) ),
define([status(thm)]) ).
thf(setukpairIR,axiom,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
thf('3',plain,
( setukpairIR
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairIL,axiom,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
thf('4',plain,
( setukpairIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
define([status(thm)]) ).
thf(secondinupair,axiom,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('5',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('6',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('7',plain,
( subsetemptysetimpeq
= ( ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(setextsub,axiom,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf('8',plain,
( setextsub
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X4 )
=> ( X4 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
thf('9',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('10',plain,
( setadjoinSub
= ( ! [X4: $i,X6: $i] : ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(subsetTrans,axiom,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ) ).
thf('11',plain,
( subsetTrans
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X8 )
=> ( subset @ X4 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetRefl,axiom,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
thf('12',plain,
( subsetRefl
= ( ! [X4: $i] : ( subset @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(notequalI1,axiom,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ) ).
thf('13',plain,
( notequalI1
= ( ! [X4: $i,X6: $i] :
( ~ ( subset @ X4 @ X6 )
=> ( X4 != X6 ) ) ) ),
define([status(thm)]) ).
thf(notsubsetI,axiom,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ) ).
thf('14',plain,
( notsubsetI
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ~ ( in @ X8 @ X6 )
=> ~ ( subset @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetE2,axiom,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ) ).
thf('15',plain,
( subsetE2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ~ ( in @ X8 @ X6 )
=> ~ ( in @ X8 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetE,axiom,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ) ).
thf('16',plain,
( subsetE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(emptysetsubset,axiom,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
thf('17',plain,
( emptysetsubset
= ( ! [X4: $i] : ( subset @ emptyset @ X4 ) ) ),
define([status(thm)]) ).
thf(subsetI2,axiom,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf('18',plain,
( subsetI2
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ) ).
thf('19',plain,
( eqimpsubset1
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ) ).
thf('20',plain,
( eqimpsubset2
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(subsetI1,axiom,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf('21',plain,
( subsetI1
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(setunion__Cong,axiom,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ) ).
thf('22',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('23',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(upairsetIR,axiom,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('24',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('25',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('26',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('27',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('28',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('29',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('30',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('31',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('32',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('33',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('34',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('35',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('36',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('37',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).
thf('38',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(setadjoinIL,axiom,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
thf('39',plain,
( setadjoinIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ 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('40',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('41',plain,
( setadjoinAx
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( ( X8 = X4 )
| ( in @ X8 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(setunionsingleton1,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
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( ( in @ X8 @ X6 )
| ( X8 = X4 ) ) )
=> ( powersetAx
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( setunion @ X10 ) )
<=> ? [X14: $i] :
( ( in @ X12 @ X14 )
& ( in @ X14 @ X10 ) ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X16: $i,X18: $i] : ( in @ X16 @ ( setadjoin @ X16 @ X18 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X22 )
=> ( in @ X24 @ ( setadjoin @ X20 @ X22 ) ) )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( in @ X30 @ ( setadjoin @ X26 @ X28 ) )
=> ! [X32: $o] :
( ( ( X30 = X26 )
=> X32 )
=> ( ( ( in @ X30 @ X28 )
=> X32 )
=> X32 ) ) )
=> ( ! [X34: $i,X36: $i,X38: $i] :
( ( in @ X38 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( in @ X38 @ X36 )
| ( X38 = X34 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X40: $i,X42: $i,X44: $i] :
( ( in @ X42 @ X44 )
=> ( ( in @ X44 @ X40 )
=> ( in @ X42 @ ( setunion @ X40 ) ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X48 @ ( setunion @ X46 ) )
=> ! [X50: $o] :
( ! [X52: $i] :
( ( in @ X48 @ X52 )
=> ( ( in @ X52 @ X46 )
=> X50 ) )
=> X50 ) )
=> ( ! [X54: $i,X56: $i] :
( ( in @ X56 @ X54 )
=> ( in @ X56 @ ( powerset @ ( setunion @ X54 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X58: $i,X60: $i] :
( ( in @ X58 @ ( setadjoin @ X60 @ emptyset ) )
=> ( X58 = X60 ) )
=> ( ! [X62: $i,X64: $i] :
( ( X62 != X64 )
=> ~ ( in @ X64 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( ! [X66: $i,X68: $i] :
( ( X66 = X68 )
=> ( in @ X66 @ ( setadjoin @ X68 @ emptyset ) ) )
=> ( ! [X70: $i,X72: $i] :
( ( in @ X70 @ ( setadjoin @ X72 @ emptyset ) )
=> ( in @ X72 @ ( setadjoin @ X70 @ emptyset ) ) )
=> ( ! [X74: $i,X76: $i,X78: $i] :
( ( in @ X78 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
=> ( ( X78 = X76 )
| ( X78 = X74 ) ) )
=> ( ! [X80: $i,X82: $i] : ( in @ X80 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] : ( in @ X86 @ ( setadjoin @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X88: $i,X90: $i] :
( ( X88 = X90 )
=> ! [X92: $i,X94: $i] :
( ( X92 = X94 )
=> ( ( setadjoin @ X88 @ X92 )
= ( setadjoin @ X90 @ X94 ) ) ) )
=> ( powerset__Cong
=> ( ! [X96: $i,X98: $i] :
( ( X96 = X98 )
=> ( ( setunion @ X96 )
= ( setunion @ X98 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( ! [X100: $i,X102: $i] :
( ! [X104: $i] :
( ( in @ X104 @ X100 )
=> ( in @ X104 @ X102 ) )
=> ( subset @ X100 @ X102 ) )
=> ( ! [X106: $i,X108: $i] :
( ( X106 = X108 )
=> ( subset @ X108 @ X106 ) )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ( subset @ X110 @ X112 ) )
=> ( ! [X114: $i,X116: $i] :
( ! [X118: $i] :
( ( in @ X118 @ X114 )
=> ( in @ X118 @ X116 ) )
=> ( subset @ X114 @ X116 ) )
=> ( ! [X120: $i] : ( subset @ emptyset @ X120 )
=> ( ! [X122: $i,X124: $i,X126: $i] :
( ( subset @ X122 @ X124 )
=> ( ( in @ X126 @ X122 )
=> ( in @ X126 @ X124 ) ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X130 )
=> ( ~ ( in @ X132 @ X130 )
=> ~ ( in @ X132 @ X128 ) ) )
=> ( ! [X134: $i,X136: $i,X138: $i] :
( ( in @ X138 @ X134 )
=> ( ~ ( in @ X138 @ X136 )
=> ~ ( subset @ X134 @ X136 ) ) )
=> ( ! [X140: $i,X142: $i] :
( ~ ( subset @ X140 @ X142 )
=> ( X140 != X142 ) )
=> ( notequalI2
=> ( ! [X144: $i] : ( subset @ X144 @ X144 )
=> ( ! [X146: $i,X148: $i,X150: $i] :
( ( subset @ X146 @ X148 )
=> ( ( subset @ X148 @ X150 )
=> ( subset @ X146 @ X150 ) ) )
=> ( ! [X152: $i,X154: $i] : ( subset @ X154 @ ( setadjoin @ X152 @ X154 ) )
=> ( ! [X156: $i,X158: $i,X160: $i] :
( ( subset @ X156 @ X160 )
=> ( subset @ X156 @ ( setadjoin @ X158 @ X160 ) ) )
=> ( subset2powerset
=> ( ! [X162: $i,X164: $i] :
( ( subset @ X162 @ X164 )
=> ( ( subset @ X164 @ X162 )
=> ( X162 = X164 ) ) )
=> ( ! [X166: $i] :
( ( subset @ X166 @ emptyset )
=> ( X166 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X168: $i,X170: $i] : ( in @ X170 @ ( setadjoin @ X168 @ ( setadjoin @ X170 @ 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
=> ( ! [X172: $i,X174: $i] : ( in @ X174 @ ( setadjoin @ X172 @ ( setadjoin @ X174 @ emptyset ) ) )
=> ( ! [X176: $i,X178: $i] : ( in @ X176 @ ( setunion @ ( setadjoin @ ( setadjoin @ X176 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X176 @ ( setadjoin @ X178 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X180: $i,X182: $i] : ( in @ X182 @ ( setunion @ ( setadjoin @ ( setadjoin @ X180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X180 @ ( setadjoin @ X182 @ emptyset ) ) @ emptyset ) ) ) )
=> ( kpairiskpair
=> ( kpairp
=> ( ! [X184: $i,X186: $i] :
( ( in @ X186 @ X184 )
=> ( subset @ ( setadjoin @ X186 @ emptyset ) @ X184 ) )
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X188: $i,X190: $i,X192: $i] :
( ( in @ X192 @ ( setadjoin @ X188 @ ( setadjoin @ X190 @ emptyset ) ) )
=> ( ( X192 = X190 )
| ( X192 = X188 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( ! [X194: $i,X196: $i] :
( ( in @ X196 @ ( setunion @ X194 ) )
=> ? [X198: $i] :
( ( in @ X198 @ X194 )
& ( in @ X196 @ X198 ) ) )
=> ! [X200: $i] : ( subset @ ( setunion @ ( setadjoin @ X200 @ emptyset ) ) @ X200 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [X14: $i,X12: $i,X10: $i] :
( ( zip_tseitin_1 @ X14 @ X12 @ X10 )
<=> ( ( in @ X14 @ X10 )
& ( in @ X12 @ X14 ) ) ) ).
thf(zf_stmt_3,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(zf_stmt_4,axiom,
! [X8: $i,X6: $i,X4: $i] :
( ( zip_tseitin_0 @ X8 @ X6 @ X4 )
<=> ( ( X8 = X4 )
| ( in @ X8 @ X6 ) ) ) ).
thf(zf_stmt_5,conjecture,
( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
=> ( powersetAx
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( setunion @ X10 ) )
<=> ? [X14: $i] : ( zip_tseitin_1 @ X14 @ X12 @ X10 ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X16: $i,X18: $i] : ( in @ X16 @ ( setadjoin @ X16 @ X18 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X22 )
=> ( in @ X24 @ ( setadjoin @ X20 @ X22 ) ) )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( in @ X30 @ ( setadjoin @ X26 @ X28 ) )
=> ! [X32: $o] :
( ( ( X30 = X26 )
=> X32 )
=> ( ( ( in @ X30 @ X28 )
=> X32 )
=> X32 ) ) )
=> ( ! [X34: $i,X36: $i,X38: $i] :
( ( in @ X38 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( X38 = X34 )
| ( in @ X38 @ X36 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X40: $i,X42: $i,X44: $i] :
( ( in @ X42 @ X44 )
=> ( ( in @ X44 @ X40 )
=> ( in @ X42 @ ( setunion @ X40 ) ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X48 @ ( setunion @ X46 ) )
=> ! [X50: $o] :
( ! [X52: $i] :
( ( in @ X48 @ X52 )
=> ( ( in @ X52 @ X46 )
=> X50 ) )
=> X50 ) )
=> ( ! [X54: $i,X56: $i] :
( ( in @ X56 @ X54 )
=> ( in @ X56 @ ( powerset @ ( setunion @ X54 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X58: $i,X60: $i] :
( ( in @ X58 @ ( setadjoin @ X60 @ emptyset ) )
=> ( X58 = X60 ) )
=> ( ! [X62: $i,X64: $i] :
( ( X62 != X64 )
=> ~ ( in @ X64 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( ! [X66: $i,X68: $i] :
( ( X66 = X68 )
=> ( in @ X66 @ ( setadjoin @ X68 @ emptyset ) ) )
=> ( ! [X70: $i,X72: $i] :
( ( in @ X70 @ ( setadjoin @ X72 @ emptyset ) )
=> ( in @ X72 @ ( setadjoin @ X70 @ emptyset ) ) )
=> ( ! [X74: $i,X76: $i,X78: $i] :
( ( in @ X78 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
=> ( ( X78 = X74 )
| ( X78 = X76 ) ) )
=> ( ! [X80: $i,X82: $i] : ( in @ X80 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] : ( in @ X86 @ ( setadjoin @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X88: $i,X90: $i] :
( ( X88 = X90 )
=> ! [X92: $i,X94: $i] :
( ( X92 = X94 )
=> ( ( setadjoin @ X88 @ X92 )
= ( setadjoin @ X90 @ X94 ) ) ) )
=> ( powerset__Cong
=> ( ! [X96: $i,X98: $i] :
( ( X96 = X98 )
=> ( ( setunion @ X96 )
= ( setunion @ X98 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( ! [X100: $i,X102: $i] :
( ! [X104: $i] :
( ( in @ X104 @ X100 )
=> ( in @ X104 @ X102 ) )
=> ( subset @ X100 @ X102 ) )
=> ( ! [X106: $i,X108: $i] :
( ( X106 = X108 )
=> ( subset @ X108 @ X106 ) )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ( subset @ X110 @ X112 ) )
=> ( ! [X114: $i,X116: $i] :
( ! [X118: $i] :
( ( in @ X118 @ X114 )
=> ( in @ X118 @ X116 ) )
=> ( subset @ X114 @ X116 ) )
=> ( ! [X120: $i] : ( subset @ emptyset @ X120 )
=> ( ! [X122: $i,X124: $i,X126: $i] :
( ( subset @ X122 @ X124 )
=> ( ( in @ X126 @ X122 )
=> ( in @ X126 @ X124 ) ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X130 )
=> ( ~ ( in @ X132 @ X130 )
=> ~ ( in @ X132 @ X128 ) ) )
=> ( ! [X134: $i,X136: $i,X138: $i] :
( ( in @ X138 @ X134 )
=> ( ~ ( in @ X138 @ X136 )
=> ~ ( subset @ X134 @ X136 ) ) )
=> ( ! [X140: $i,X142: $i] :
( ~ ( subset @ X140 @ X142 )
=> ( X140 != X142 ) )
=> ( notequalI2
=> ( ! [X144: $i] : ( subset @ X144 @ X144 )
=> ( ! [X146: $i,X148: $i,X150: $i] :
( ( subset @ X146 @ X148 )
=> ( ( subset @ X148 @ X150 )
=> ( subset @ X146 @ X150 ) ) )
=> ( ! [X152: $i,X154: $i] : ( subset @ X154 @ ( setadjoin @ X152 @ X154 ) )
=> ( ! [X156: $i,X158: $i,X160: $i] :
( ( subset @ X156 @ X160 )
=> ( subset @ X156 @ ( setadjoin @ X158 @ X160 ) ) )
=> ( subset2powerset
=> ( ! [X162: $i,X164: $i] :
( ( subset @ X162 @ X164 )
=> ( ( subset @ X164 @ X162 )
=> ( X162 = X164 ) ) )
=> ( ! [X166: $i] :
( ( subset @ X166 @ emptyset )
=> ( X166 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X168: $i,X170: $i] : ( in @ X170 @ ( setadjoin @ X168 @ ( setadjoin @ X170 @ 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
=> ( ! [X172: $i,X174: $i] : ( in @ X174 @ ( setadjoin @ X172 @ ( setadjoin @ X174 @ emptyset ) ) )
=> ( ! [X176: $i,X178: $i] : ( in @ X176 @ ( setunion @ ( setadjoin @ ( setadjoin @ X176 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X176 @ ( setadjoin @ X178 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X180: $i,X182: $i] : ( in @ X182 @ ( setunion @ ( setadjoin @ ( setadjoin @ X180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X180 @ ( setadjoin @ X182 @ emptyset ) ) @ emptyset ) ) ) )
=> ( kpairiskpair
=> ( kpairp
=> ( ! [X184: $i,X186: $i] :
( ( in @ X186 @ X184 )
=> ( subset @ ( setadjoin @ X186 @ emptyset ) @ X184 ) )
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X188: $i,X190: $i,X192: $i] :
( ( in @ X192 @ ( setadjoin @ X188 @ ( setadjoin @ X190 @ emptyset ) ) )
=> ( ( X192 = X188 )
| ( X192 = X190 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( ! [X194: $i,X196: $i] :
( ( in @ X196 @ ( setunion @ X194 ) )
=> ? [X198: $i] :
( ( in @ X196 @ X198 )
& ( in @ X198 @ X194 ) ) )
=> ! [X200: $i] : ( subset @ ( setunion @ ( setadjoin @ X200 @ emptyset ) ) @ X200 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_6,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
=> ( powersetAx
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( setunion @ X10 ) )
<=> ? [X14: $i] : ( zip_tseitin_1 @ X14 @ X12 @ X10 ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( ! [X16: $i,X18: $i] : ( in @ X16 @ ( setadjoin @ X16 @ X18 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X22 )
=> ( in @ X24 @ ( setadjoin @ X20 @ X22 ) ) )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( in @ X30 @ ( setadjoin @ X26 @ X28 ) )
=> ! [X32: $o] :
( ( ( X30 = X26 )
=> X32 )
=> ( ( ( in @ X30 @ X28 )
=> X32 )
=> X32 ) ) )
=> ( ! [X34: $i,X36: $i,X38: $i] :
( ( in @ X38 @ ( setadjoin @ X34 @ X36 ) )
=> ( ( X38 = X34 )
| ( in @ X38 @ X36 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X40: $i,X42: $i,X44: $i] :
( ( in @ X42 @ X44 )
=> ( ( in @ X44 @ X40 )
=> ( in @ X42 @ ( setunion @ X40 ) ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X48 @ ( setunion @ X46 ) )
=> ! [X50: $o] :
( ! [X52: $i] :
( ( in @ X48 @ X52 )
=> ( ( in @ X52 @ X46 )
=> X50 ) )
=> X50 ) )
=> ( ! [X54: $i,X56: $i] :
( ( in @ X56 @ X54 )
=> ( in @ X56 @ ( powerset @ ( setunion @ X54 ) ) ) )
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X58: $i,X60: $i] :
( ( in @ X58 @ ( setadjoin @ X60 @ emptyset ) )
=> ( X58 = X60 ) )
=> ( ! [X62: $i,X64: $i] :
( ( X62 != X64 )
=> ~ ( in @ X64 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( ! [X66: $i,X68: $i] :
( ( X66 = X68 )
=> ( in @ X66 @ ( setadjoin @ X68 @ emptyset ) ) )
=> ( ! [X70: $i,X72: $i] :
( ( in @ X70 @ ( setadjoin @ X72 @ emptyset ) )
=> ( in @ X72 @ ( setadjoin @ X70 @ emptyset ) ) )
=> ( ! [X74: $i,X76: $i,X78: $i] :
( ( in @ X78 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
=> ( ( X78 = X74 )
| ( X78 = X76 ) ) )
=> ( ! [X80: $i,X82: $i] : ( in @ X80 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ! [X84: $i,X86: $i] : ( in @ X86 @ ( setadjoin @ X84 @ ( setadjoin @ X86 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X88: $i,X90: $i] :
( ( X88 = X90 )
=> ! [X92: $i,X94: $i] :
( ( X92 = X94 )
=> ( ( setadjoin @ X88 @ X92 )
= ( setadjoin @ X90 @ X94 ) ) ) )
=> ( powerset__Cong
=> ( ! [X96: $i,X98: $i] :
( ( X96 = X98 )
=> ( ( setunion @ X96 )
= ( setunion @ X98 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( ! [X100: $i,X102: $i] :
( ! [X104: $i] :
( ( in @ X104 @ X100 )
=> ( in @ X104 @ X102 ) )
=> ( subset @ X100 @ X102 ) )
=> ( ! [X106: $i,X108: $i] :
( ( X106 = X108 )
=> ( subset @ X108 @ X106 ) )
=> ( ! [X110: $i,X112: $i] :
( ( X110 = X112 )
=> ( subset @ X110 @ X112 ) )
=> ( ! [X114: $i,X116: $i] :
( ! [X118: $i] :
( ( in @ X118 @ X114 )
=> ( in @ X118 @ X116 ) )
=> ( subset @ X114 @ X116 ) )
=> ( ! [X120: $i] : ( subset @ emptyset @ X120 )
=> ( ! [X122: $i,X124: $i,X126: $i] :
( ( subset @ X122 @ X124 )
=> ( ( in @ X126 @ X122 )
=> ( in @ X126 @ X124 ) ) )
=> ( ! [X128: $i,X130: $i,X132: $i] :
( ( subset @ X128 @ X130 )
=> ( ~ ( in @ X132 @ X130 )
=> ~ ( in @ X132 @ X128 ) ) )
=> ( ! [X134: $i,X136: $i,X138: $i] :
( ( in @ X138 @ X134 )
=> ( ~ ( in @ X138 @ X136 )
=> ~ ( subset @ X134 @ X136 ) ) )
=> ( ! [X140: $i,X142: $i] :
( ~ ( subset @ X140 @ X142 )
=> ( X140 != X142 ) )
=> ( notequalI2
=> ( ! [X144: $i] : ( subset @ X144 @ X144 )
=> ( ! [X146: $i,X148: $i,X150: $i] :
( ( subset @ X146 @ X148 )
=> ( ( subset @ X148 @ X150 )
=> ( subset @ X146 @ X150 ) ) )
=> ( ! [X152: $i,X154: $i] : ( subset @ X154 @ ( setadjoin @ X152 @ X154 ) )
=> ( ! [X156: $i,X158: $i,X160: $i] :
( ( subset @ X156 @ X160 )
=> ( subset @ X156 @ ( setadjoin @ X158 @ X160 ) ) )
=> ( subset2powerset
=> ( ! [X162: $i,X164: $i] :
( ( subset @ X162 @ X164 )
=> ( ( subset @ X164 @ X162 )
=> ( X162 = X164 ) ) )
=> ( ! [X166: $i] :
( ( subset @ X166 @ emptyset )
=> ( X166 = emptyset ) )
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( ! [X168: $i,X170: $i] : ( in @ X170 @ ( setadjoin @ X168 @ ( setadjoin @ X170 @ 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
=> ( ! [X172: $i,X174: $i] : ( in @ X174 @ ( setadjoin @ X172 @ ( setadjoin @ X174 @ emptyset ) ) )
=> ( ! [X176: $i,X178: $i] : ( in @ X176 @ ( setunion @ ( setadjoin @ ( setadjoin @ X176 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X176 @ ( setadjoin @ X178 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X180: $i,X182: $i] : ( in @ X182 @ ( setunion @ ( setadjoin @ ( setadjoin @ X180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X180 @ ( setadjoin @ X182 @ emptyset ) ) @ emptyset ) ) ) )
=> ( kpairiskpair
=> ( kpairp
=> ( ! [X184: $i,X186: $i] :
( ( in @ X186 @ X184 )
=> ( subset @ ( setadjoin @ X186 @ emptyset ) @ X184 ) )
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X188: $i,X190: $i,X192: $i] :
( ( in @ X192 @ ( setadjoin @ X188 @ ( setadjoin @ X190 @ emptyset ) ) )
=> ( ( X192 = X188 )
| ( X192 = X190 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( ! [X194: $i,X196: $i] :
( ( in @ X196 @ ( setunion @ X194 ) )
=> ? [X198: $i] :
( ( in @ X196 @ X198 )
& ( in @ X198 @ X194 ) ) )
=> ! [X200: $i] : ( subset @ ( setunion @ ( setadjoin @ X200 @ emptyset ) ) @ X200 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl84,plain,
~ ( subset @ ( setunion @ ( setadjoin @ sk__102 @ emptyset ) ) @ sk__102 ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl124,plain,
! [X78: $i,X79: $i] :
( ( subset @ X78 @ X79 )
| ( in @ ( sk__100 @ X79 @ X78 ) @ X78 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl123,plain,
! [X78: $i,X79: $i] :
( ( subset @ X78 @ X79 )
| ~ ( in @ ( sk__100 @ X79 @ X78 ) @ X79 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl86,plain,
! [X58: $i,X59: $i] :
( ( in @ ( sk__101 @ X58 @ X59 ) @ X59 )
| ~ ( in @ X58 @ ( setunion @ X59 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl30,plain,
! [X21: $i,X22: $i] :
( ~ ( in @ X21 @ ( setadjoin @ X22 @ emptyset ) )
| ( X22 = X21 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl970,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0
= ( sk__101 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl30]) ).
thf(zip_derived_cl85,plain,
! [X58: $i,X59: $i] :
( ( in @ X58 @ ( sk__101 @ X58 @ X59 ) )
| ~ ( in @ X58 @ ( setunion @ X59 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl11481,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl970,zip_derived_cl85]) ).
thf(zip_derived_cl11496,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
| ( in @ X1 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl11481]) ).
thf(zip_derived_cl26939,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl84,zip_derived_cl124,zip_derived_cl123,zip_derived_cl11496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU634^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OaryxdMcQM true
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:45:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.60 % Total configuration time : 828
% 0.21/0.60 % Estimated wc time : 1656
% 0.21/0.60 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 64.60/8.94 % Solved by lams/40_c_ic.sh.
% 64.60/8.94 % done 3038 iterations in 8.151s
% 64.60/8.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 64.60/8.94 % SZS output start Refutation
% See solution above
% 64.60/8.95
% 64.60/8.95
% 64.60/8.95 % Terminating...
% 64.60/9.08 % Runner terminated.
% 64.60/9.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------