%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU709^1 : 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.feiMutqe0l true
% Computer : n017.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 19:16:27 EDT 2023
% Result : Theorem 2.35s 1.07s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 295
% Syntax : Number of formulae : 314 ( 67 unt; 235 typ; 0 def)
% Number of atoms : 1272 ( 215 equ; 0 cnn)
% Maximal formula atoms : 260 ( 16 avg)
% Number of connectives : 2403 ( 31 ~; 31 |; 0 &;1267 @)
% ( 6 <=>;1068 =>; 0 <=; 0 <~>)
% Maximal formula depth : 239 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 236 ( 234 usr; 231 con; 0-4 aty)
% Number of variables : 419 ( 0 ^; 419 !; 0 ?; 419 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setminusELneg_type,type,
setminusELneg: $o ).
thf(cartprodsndin_type,type,
cartprodsndin: $o ).
thf(ex1E1_type,type,
ex1E1: $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(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(iftrue_type,type,
iftrue: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(ifSingleton_type,type,
ifSingleton: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(dpsetconstrER_type,type,
dpsetconstrER: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(lam2p_type,type,
lam2p: $o ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(ubforcartprodlem1_type,type,
ubforcartprodlem1: $o ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(beta1_type,type,
beta1: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(iftrueProp2_type,type,
iftrueProp2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(iffalseProp2_type,type,
iffalseProp2: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $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(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(ap2apEq1_type,type,
ap2apEq1: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(singletoninpowunion_type,type,
singletoninpowunion: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(cartprodmempair_type,type,
cartprodmempair: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(lamp_type,type,
lamp: $o ).
thf(dpsetconstrEL1_type,type,
dpsetconstrEL1: $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(singletonsuniq_type,type,
singletonsuniq: $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(setukpairinjR11_type,type,
setukpairinjR11: $o ).
thf(ex1I_type,type,
ex1I: $o ).
thf(ex1E2_type,type,
ex1E2: $o ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
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(lam2lamEq_type,type,
lam2lamEq: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(kpairp_type,type,
kpairp: $o ).
thf(setukpairinjR12_type,type,
setukpairinjR12: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(dpsetconstrSub_type,type,
dpsetconstrSub: $o ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(sk__77_type,type,
sk__77: $i ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(beta2_type,type,
beta2: $o ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(setunionsingleton1_type,type,
setunionsingleton1: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(cartprodpairsurjEq_type,type,
cartprodpairsurjEq: $o ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(theeq_type,type,
theeq: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(infuncsetfunc_type,type,
infuncsetfunc: $o ).
thf(ap2apEq2_type,type,
ap2apEq2: $o ).
thf(ap2p_type,type,
ap2p: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(exuE1_type,type,
exuE1: $o ).
thf(ubforcartprodlem2_type,type,
ubforcartprodlem2: $o ).
thf(binintersectRsub_type,type,
binintersectRsub: $o ).
thf(setminusLsub_type,type,
setminusLsub: $o ).
thf(funcextLem_type,type,
funcextLem: $o ).
thf(setukpairinjR_type,type,
setukpairinjR: $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(sk__78_type,type,
sk__78: $o ).
thf(upairsetE_type,type,
upairsetE: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(iffalseProp1_type,type,
iffalseProp1: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $o ).
thf(sk__79_type,type,
sk__79: $i ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(ifp_type,type,
ifp: $o ).
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(eta2_type,type,
eta2: $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(binintersectI_type,type,
binintersectI: $o ).
thf(funcext_type,type,
funcext: $o ).
thf(funcGraphProp4_type,type,
funcGraphProp4: $o ).
thf(sk__80_type,type,
sk__80: $i ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(brelnall2_type,type,
brelnall2: $o ).
thf(ex1I2_type,type,
ex1I2: $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(setukpairinjR2_type,type,
setukpairinjR2: $o ).
thf(dpsetconstrEL2_type,type,
dpsetconstrEL2: $o ).
thf(theprop_type,type,
theprop: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(if_type,type,
if: $i > $o > $i > $i > $i ).
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(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(app_type,type,
app: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(eta1_type,type,
eta1: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(cartprodfstin_type,type,
cartprodfstin: $o ).
thf(setunionsingleton2_type,type,
setunionsingleton2: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(apProp_type,type,
apProp: $o ).
thf(notdallE_type,type,
notdallE: $o ).
thf(iftrueProp1_type,type,
iftrueProp1: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(singletonprop_type,type,
singletonprop: $o ).
thf(singletonsubset_type,type,
singletonsubset: $o ).
thf(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(replAx_type,type,
replAx: $o ).
thf(upairequniteq_type,type,
upairequniteq: $o ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(setukpairIL_type,type,
setukpairIL: $o ).
thf(setunionE2_type,type,
setunionE2: $o ).
thf(inPowerset_type,type,
inPowerset: $o ).
thf(iffalse_type,type,
iffalse: $o ).
thf(funcext2_type,type,
funcext2: $o ).
thf(subbreln_type,type,
subbreln: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(iffalse,axiom,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ) ).
thf('0',plain,
( iffalse
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ X6
=> ( ( if @ X4 @ X6 @ X8 @ X10 )
= X10 ) ) ) ) ) ),
define([status(thm)]) ).
thf(iftrue,axiom,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ) ).
thf('1',plain,
( iftrue
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( ( if @ X4 @ X6 @ X8 @ X10 )
= X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ifp,axiom,
( ifp
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
thf('2',plain,
( ifp
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( if @ X4 @ X6 @ X8 @ X10 ) @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ) ).
thf('3',plain,
( setukpairinjR2
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( X6 = X10 ) ) ) ),
define([status(thm)]) ).
thf(upairequniteq,axiom,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ).
thf('4',plain,
( upairequniteq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) )
= ( setadjoin @ X8 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ) ).
thf('5',plain,
( setukpairinjR1
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X8 = X10 )
=> ( X6 = X10 ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
thf('6',plain,
( setukpairinjR12
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
thf('7',plain,
( setukpairinjR11
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ) ).
thf('8',plain,
( setukpairinjL2
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X8 ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ) ).
thf('9',plain,
( setukpairinjL1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X8 ) ) ) ),
define([status(thm)]) ).
thf(singletonsuniq,axiom,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ).
thf('10',plain,
( singletonsuniq
= ( ! [X4: $i,X6: $i] :
( ( ( setadjoin @ X4 @ emptyset )
= ( setadjoin @ X6 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
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('11',plain,
( upairset2E
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) )
=> ( ( X8 = X4 )
| ( X8 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(secondinupair,axiom,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('12',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('13',plain,
( upairset2IR
= ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
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('14',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('15',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('16',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('17',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('18',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('19',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('20',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('21',plain,
( uniqinunit
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(setadjoinOr,axiom,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ) ).
thf('22',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('23',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('24',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('25',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).
thf('26',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(setadjoinIL,axiom,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
thf('27',plain,
( setadjoinIL
= ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(setadjoinAx,axiom,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ) ).
thf('28',plain,
( setadjoinAx
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( ( X8 = X4 )
| ( in @ X8 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(iftrueorfalse,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
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( ( in @ X8 @ X6 )
| ( X8 = X4 ) ) )
=> ( 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
=> ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( in @ X18 @ X16 )
=> ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
=> ! [X26: $o] :
( ( ( X24 = X20 )
=> X26 )
=> ( ( ( in @ X24 @ X22 )
=> X26 )
=> X26 ) ) )
=> ( ! [X28: $i,X30: $i,X32: $i] :
( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
=> ( ( in @ X32 @ X30 )
| ( X32 = X28 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X34: $i,X36: $i] :
( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
=> ( X34 = X36 ) )
=> ( ! [X38: $i,X40: $i] :
( ( X38 != X40 )
=> ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
=> ( ! [X42: $i,X44: $i] :
( ( X42 = X44 )
=> ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
=> ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
=> ( ! [X50: $i,X52: $i,X54: $i] :
( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
=> ( ( X54 = X52 )
| ( X54 = X50 ) ) )
=> ( ! [X56: $i,X58: $i] : ( in @ X56 @ ( setadjoin @ X56 @ ( setadjoin @ X58 @ emptyset ) ) )
=> ( ! [X60: $i,X62: $i] : ( in @ X62 @ ( setadjoin @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X64: $i,X66: $i] :
( ( X64 = X66 )
=> ! [X68: $i,X70: $i] :
( ( X68 = X70 )
=> ( ( setadjoin @ X64 @ X68 )
= ( setadjoin @ X66 @ X70 ) ) ) )
=> ( 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
=> ( ! [X72: $i,X74: $i] : ( in @ X74 @ ( setadjoin @ X72 @ ( setadjoin @ X74 @ 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
=> ( ! [X76: $i,X78: $i] : ( in @ X78 @ ( setadjoin @ X76 @ ( setadjoin @ X78 @ emptyset ) ) )
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X80: $i,X82: $i,X84: $i] :
( ( in @ X84 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ( X84 = X82 )
| ( X84 = X80 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( ! [X86: $i,X88: $i] :
( ( ( setadjoin @ X86 @ emptyset )
= ( setadjoin @ X88 @ emptyset ) )
=> ( X86 = X88 ) )
=> ( ! [X90: $i,X92: $i,X94: $i] :
( ( in @ ( setadjoin @ X94 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ ( setadjoin @ X92 @ emptyset ) ) @ emptyset ) ) )
=> ( X90 = X94 ) )
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( ! [X96: $i,X98: $i,X100: $i,X102: $i] :
( ( ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X98 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X100 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X100 @ ( setadjoin @ X102 @ emptyset ) ) @ emptyset ) ) )
=> ( X96 = X100 ) )
=> ( setukpairinjL
=> ( ! [X104: $i,X106: $i] :
( ( X104 = X106 )
=> ( ( setadjoin @ X104 @ ( setadjoin @ X106 @ emptyset ) )
= ( setadjoin @ X104 @ emptyset ) ) )
=> ( ! [X108: $i,X110: $i] :
( ( X108 = X110 )
=> ( ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ emptyset ) ) )
=> ( ! [X112: $i,X114: $i,X116: $i,X118: $i] :
( ( ( setadjoin @ ( setadjoin @ X112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X116 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X116 @ ( setadjoin @ X118 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X116 = X118 )
=> ( X114 = X118 ) ) )
=> ( ! [X120: $i,X122: $i,X124: $i] :
( ( ( setadjoin @ X120 @ ( setadjoin @ X122 @ emptyset ) )
= ( setadjoin @ X124 @ emptyset ) )
=> ( X120 = X122 ) )
=> ( ! [X126: $i,X128: $i,X130: $i,X132: $i] :
( ( ( setadjoin @ ( setadjoin @ X126 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X126 @ ( setadjoin @ X128 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X130 @ ( setadjoin @ X132 @ emptyset ) ) @ emptyset ) ) )
=> ( X128 = X132 ) )
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ! [X134: $i,X136: $o,X138: $i] :
( ( in @ X138 @ X134 )
=> ! [X140: $i] :
( ( in @ X140 @ X134 )
=> ( in @ ( if @ X134 @ X136 @ X138 @ X140 ) @ X134 ) ) )
=> ( theeq
=> ( ! [X142: $i,X144: $o,X146: $i] :
( ( in @ X146 @ X142 )
=> ! [X148: $i] :
( ( in @ X148 @ X142 )
=> ( X144
=> ( ( if @ X142 @ X144 @ X146 @ X148 )
= X146 ) ) ) )
=> ( ! [X150: $i,X152: $o,X154: $i] :
( ( in @ X154 @ X150 )
=> ! [X156: $i] :
( ( in @ X156 @ X150 )
=> ( ~ X152
=> ( ( if @ X150 @ X152 @ X154 @ X156 )
= X156 ) ) ) )
=> ! [X158: $i,X160: $o,X162: $i] :
( ( in @ X162 @ X158 )
=> ! [X164: $i] :
( ( in @ X164 @ X158 )
=> ( in @ ( if @ X158 @ X160 @ X162 @ X164 ) @ ( setadjoin @ X162 @ ( setadjoin @ X164 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [X8: $i,X6: $i,X4: $i] :
( ( zip_tseitin_0 @ X8 @ X6 @ X4 )
<=> ( ( X8 = X4 )
| ( in @ X8 @ X6 ) ) ) ).
thf(zf_stmt_3,conjecture,
( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
=> ( 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
=> ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( in @ X18 @ X16 )
=> ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
=> ! [X26: $o] :
( ( ( X24 = X20 )
=> X26 )
=> ( ( ( in @ X24 @ X22 )
=> X26 )
=> X26 ) ) )
=> ( ! [X28: $i,X30: $i,X32: $i] :
( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
=> ( ( X32 = X28 )
| ( in @ X32 @ X30 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X34: $i,X36: $i] :
( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
=> ( X34 = X36 ) )
=> ( ! [X38: $i,X40: $i] :
( ( X38 != X40 )
=> ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
=> ( ! [X42: $i,X44: $i] :
( ( X42 = X44 )
=> ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
=> ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
=> ( ! [X50: $i,X52: $i,X54: $i] :
( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
=> ( ( X54 = X50 )
| ( X54 = X52 ) ) )
=> ( ! [X56: $i,X58: $i] : ( in @ X56 @ ( setadjoin @ X56 @ ( setadjoin @ X58 @ emptyset ) ) )
=> ( ! [X60: $i,X62: $i] : ( in @ X62 @ ( setadjoin @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X64: $i,X66: $i] :
( ( X64 = X66 )
=> ! [X68: $i,X70: $i] :
( ( X68 = X70 )
=> ( ( setadjoin @ X64 @ X68 )
= ( setadjoin @ X66 @ X70 ) ) ) )
=> ( 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
=> ( ! [X72: $i,X74: $i] : ( in @ X74 @ ( setadjoin @ X72 @ ( setadjoin @ X74 @ 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
=> ( ! [X76: $i,X78: $i] : ( in @ X78 @ ( setadjoin @ X76 @ ( setadjoin @ X78 @ emptyset ) ) )
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X80: $i,X82: $i,X84: $i] :
( ( in @ X84 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ( X84 = X80 )
| ( X84 = X82 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( ! [X86: $i,X88: $i] :
( ( ( setadjoin @ X86 @ emptyset )
= ( setadjoin @ X88 @ emptyset ) )
=> ( X86 = X88 ) )
=> ( ! [X90: $i,X92: $i,X94: $i] :
( ( in @ ( setadjoin @ X94 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ ( setadjoin @ X92 @ emptyset ) ) @ emptyset ) ) )
=> ( X90 = X94 ) )
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( ! [X96: $i,X98: $i,X100: $i,X102: $i] :
( ( ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X98 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X100 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X100 @ ( setadjoin @ X102 @ emptyset ) ) @ emptyset ) ) )
=> ( X96 = X100 ) )
=> ( setukpairinjL
=> ( ! [X104: $i,X106: $i] :
( ( X104 = X106 )
=> ( ( setadjoin @ X104 @ ( setadjoin @ X106 @ emptyset ) )
= ( setadjoin @ X104 @ emptyset ) ) )
=> ( ! [X108: $i,X110: $i] :
( ( X108 = X110 )
=> ( ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ emptyset ) ) )
=> ( ! [X112: $i,X114: $i,X116: $i,X118: $i] :
( ( ( setadjoin @ ( setadjoin @ X112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X116 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X116 @ ( setadjoin @ X118 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X116 = X118 )
=> ( X114 = X118 ) ) )
=> ( ! [X120: $i,X122: $i,X124: $i] :
( ( ( setadjoin @ X120 @ ( setadjoin @ X122 @ emptyset ) )
= ( setadjoin @ X124 @ emptyset ) )
=> ( X120 = X122 ) )
=> ( ! [X126: $i,X128: $i,X130: $i,X132: $i] :
( ( ( setadjoin @ ( setadjoin @ X126 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X126 @ ( setadjoin @ X128 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X130 @ ( setadjoin @ X132 @ emptyset ) ) @ emptyset ) ) )
=> ( X128 = X132 ) )
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ! [X134: $i,X136: $o,X138: $i] :
( ( in @ X138 @ X134 )
=> ! [X140: $i] :
( ( in @ X140 @ X134 )
=> ( in @ ( if @ X134 @ X136 @ X138 @ X140 ) @ X134 ) ) )
=> ( theeq
=> ( ! [X142: $i,X144: $o,X146: $i] :
( ( in @ X146 @ X142 )
=> ! [X148: $i] :
( ( in @ X148 @ X142 )
=> ( X144
=> ( ( if @ X142 @ X144 @ X146 @ X148 )
= X146 ) ) ) )
=> ( ! [X150: $i,X152: $o,X154: $i] :
( ( in @ X154 @ X150 )
=> ! [X156: $i] :
( ( in @ X156 @ X150 )
=> ( ~ X152
=> ( ( if @ X150 @ X152 @ X154 @ X156 )
= X156 ) ) ) )
=> ! [X158: $i,X160: $o,X162: $i] :
( ( in @ X162 @ X158 )
=> ! [X164: $i] :
( ( in @ X164 @ X158 )
=> ( in @ ( if @ X158 @ X160 @ X162 @ X164 ) @ ( setadjoin @ X162 @ ( setadjoin @ X164 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_4,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
<=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
=> ( 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
=> ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( in @ X18 @ X16 )
=> ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
=> ! [X26: $o] :
( ( ( X24 = X20 )
=> X26 )
=> ( ( ( in @ X24 @ X22 )
=> X26 )
=> X26 ) ) )
=> ( ! [X28: $i,X30: $i,X32: $i] :
( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
=> ( ( X32 = X28 )
| ( in @ X32 @ X30 ) ) )
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( ! [X34: $i,X36: $i] :
( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
=> ( X34 = X36 ) )
=> ( ! [X38: $i,X40: $i] :
( ( X38 != X40 )
=> ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
=> ( ! [X42: $i,X44: $i] :
( ( X42 = X44 )
=> ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
=> ( ! [X46: $i,X48: $i] :
( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
=> ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
=> ( ! [X50: $i,X52: $i,X54: $i] :
( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
=> ( ( X54 = X50 )
| ( X54 = X52 ) ) )
=> ( ! [X56: $i,X58: $i] : ( in @ X56 @ ( setadjoin @ X56 @ ( setadjoin @ X58 @ emptyset ) ) )
=> ( ! [X60: $i,X62: $i] : ( in @ X62 @ ( setadjoin @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( ! [X64: $i,X66: $i] :
( ( X64 = X66 )
=> ! [X68: $i,X70: $i] :
( ( X68 = X70 )
=> ( ( setadjoin @ X64 @ X68 )
= ( setadjoin @ X66 @ X70 ) ) ) )
=> ( 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
=> ( ! [X72: $i,X74: $i] : ( in @ X74 @ ( setadjoin @ X72 @ ( setadjoin @ X74 @ 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
=> ( ! [X76: $i,X78: $i] : ( in @ X78 @ ( setadjoin @ X76 @ ( setadjoin @ X78 @ emptyset ) ) )
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( ! [X80: $i,X82: $i,X84: $i] :
( ( in @ X84 @ ( setadjoin @ X80 @ ( setadjoin @ X82 @ emptyset ) ) )
=> ( ( X84 = X80 )
| ( X84 = X82 ) ) )
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( ! [X86: $i,X88: $i] :
( ( ( setadjoin @ X86 @ emptyset )
= ( setadjoin @ X88 @ emptyset ) )
=> ( X86 = X88 ) )
=> ( ! [X90: $i,X92: $i,X94: $i] :
( ( in @ ( setadjoin @ X94 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ ( setadjoin @ X92 @ emptyset ) ) @ emptyset ) ) )
=> ( X90 = X94 ) )
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( ! [X96: $i,X98: $i,X100: $i,X102: $i] :
( ( ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X98 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X100 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X100 @ ( setadjoin @ X102 @ emptyset ) ) @ emptyset ) ) )
=> ( X96 = X100 ) )
=> ( setukpairinjL
=> ( ! [X104: $i,X106: $i] :
( ( X104 = X106 )
=> ( ( setadjoin @ X104 @ ( setadjoin @ X106 @ emptyset ) )
= ( setadjoin @ X104 @ emptyset ) ) )
=> ( ! [X108: $i,X110: $i] :
( ( X108 = X110 )
=> ( ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X108 @ emptyset ) @ emptyset ) ) )
=> ( ! [X112: $i,X114: $i,X116: $i,X118: $i] :
( ( ( setadjoin @ ( setadjoin @ X112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X116 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X116 @ ( setadjoin @ X118 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X116 = X118 )
=> ( X114 = X118 ) ) )
=> ( ! [X120: $i,X122: $i,X124: $i] :
( ( ( setadjoin @ X120 @ ( setadjoin @ X122 @ emptyset ) )
= ( setadjoin @ X124 @ emptyset ) )
=> ( X120 = X122 ) )
=> ( ! [X126: $i,X128: $i,X130: $i,X132: $i] :
( ( ( setadjoin @ ( setadjoin @ X126 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X126 @ ( setadjoin @ X128 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X130 @ ( setadjoin @ X132 @ emptyset ) ) @ emptyset ) ) )
=> ( X128 = X132 ) )
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ! [X134: $i,X136: $o,X138: $i] :
( ( in @ X138 @ X134 )
=> ! [X140: $i] :
( ( in @ X140 @ X134 )
=> ( in @ ( if @ X134 @ X136 @ X138 @ X140 ) @ X134 ) ) )
=> ( theeq
=> ( ! [X142: $i,X144: $o,X146: $i] :
( ( in @ X146 @ X142 )
=> ! [X148: $i] :
( ( in @ X148 @ X142 )
=> ( X144
=> ( ( if @ X142 @ X144 @ X146 @ X148 )
= X146 ) ) ) )
=> ( ! [X150: $i,X152: $o,X154: $i] :
( ( in @ X154 @ X150 )
=> ! [X156: $i] :
( ( in @ X156 @ X150 )
=> ( ~ X152
=> ( ( if @ X150 @ X152 @ X154 @ X156 )
= X156 ) ) ) )
=> ! [X158: $i,X160: $o,X162: $i] :
( ( in @ X162 @ X158 )
=> ! [X164: $i] :
( ( in @ X164 @ X158 )
=> ( in @ ( if @ X158 @ X160 @ X162 @ X164 ) @ ( setadjoin @ X162 @ ( setadjoin @ X164 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl119,plain,
in @ sk__79 @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl117,plain,
in @ sk__80 @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl116,plain,
! [X35: $i,X36: $i,X37: $o,X38: $i] :
( ~ ( in @ X35 @ X36 )
| ( ( if @ X36 @ X37 @ X38 @ X35 )
= X35 )
| X37
| ~ ( in @ X38 @ X36 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl672,plain,
! [X0: $i,X1: $o] :
( ~ ( in @ X0 @ sk__77 )
| X1
| ( ( if @ sk__77 @ X1 @ X0 @ sk__80 )
= sk__80 ) ),
inference('sup-',[status(thm)],[zip_derived_cl117,zip_derived_cl116]) ).
thf(zip_derived_cl707,plain,
! [X0: $o] :
( ( ( if @ sk__77 @ X0 @ sk__79 @ sk__80 )
= sk__80 )
| X0 ),
inference('sup-',[status(thm)],[zip_derived_cl119,zip_derived_cl672]) ).
thf(zip_derived_cl118,plain,
~ ( in @ ( if @ sk__77 @ sk__78 @ sk__79 @ sk__80 ) @ ( setadjoin @ sk__79 @ ( setadjoin @ sk__80 @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl120,plain,
! [X39: $i,X40: $i,X41: $i,X42: $o] :
( ~ ( in @ X39 @ X40 )
| ( ( if @ X40 @ X42 @ X41 @ X39 )
= X41 )
| ~ X42
| ~ ( in @ X41 @ X40 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl118_001,plain,
~ ( in @ ( if @ sk__77 @ sk__78 @ sk__79 @ sk__80 ) @ ( setadjoin @ sk__79 @ ( setadjoin @ sk__80 @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl655,plain,
( ~ ( in @ sk__79 @ ( setadjoin @ sk__79 @ ( setadjoin @ sk__80 @ emptyset ) ) )
| ~ ( in @ sk__79 @ sk__77 )
| ~ sk__78
| ~ ( in @ sk__80 @ sk__77 ) ),
inference('sup-',[status(thm)],[zip_derived_cl120,zip_derived_cl118]) ).
thf(zip_derived_cl18,plain,
! [X4: $i,X5: $i] : ( in @ X4 @ ( setadjoin @ X4 @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl119_002,plain,
in @ sk__79 @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl117_003,plain,
in @ sk__80 @ sk__77,
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl669,plain,
~ sk__78,
inference(demod,[status(thm)],[zip_derived_cl655,zip_derived_cl18,zip_derived_cl119,zip_derived_cl117]) ).
thf(zip_derived_cl671,plain,
~ ( in @ ( if @ sk__77 @ $false @ sk__79 @ sk__80 ) @ ( setadjoin @ sk__79 @ ( setadjoin @ sk__80 @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl118,zip_derived_cl669]) ).
thf(zip_derived_cl750,plain,
~ ( in @ sk__80 @ ( setadjoin @ sk__79 @ ( setadjoin @ sk__80 @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl707,zip_derived_cl671]) ).
thf(zip_derived_cl70,plain,
! [X22: $i,X23: $i] : ( in @ X22 @ ( setadjoin @ X23 @ ( setadjoin @ X22 @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl766,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl750,zip_derived_cl70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU709^1 : 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.feiMutqe0l true
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 15:34:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.23/0.68 % Total configuration time : 828
% 0.23/0.68 % Estimated wc time : 1656
% 0.23/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.41/0.81 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.41/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.41/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 2.35/1.07 % Solved by lams/40_c_ic.sh.
% 2.35/1.07 % done 317 iterations in 0.244s
% 2.35/1.07 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.35/1.07 % SZS output start Refutation
% See solution above
% 2.35/1.08
% 2.35/1.08
% 2.35/1.08 % Terminating...
% 2.52/1.21 % Runner terminated.
% 2.52/1.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------