%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU792^1 : 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.Mb1dtfEyKw true
% Computer : n027.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 19:17:42 EDT 2023
% Result : Theorem 65.31s 9.01s
% Output : Refutation 65.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 400
% Syntax : Number of formulae : 414 ( 81 unt; 322 typ; 0 def)
% Number of atoms : 1715 ( 105 equ; 0 cnn)
% Maximal formula atoms : 443 ( 18 avg)
% Number of connectives : 3985 ( 44 ~; 26 |; 8 &;2410 @)
% ( 0 <=>;1497 =>; 0 <=; 0 <~>)
% Maximal formula depth : 324 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 324 ( 322 usr; 314 con; 0-3 aty)
% Number of variables : 662 ( 0 ^; 658 !; 4 ?; 662 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setminusELneg_type,type,
setminusELneg: $o ).
thf(breln1unionEcases_type,type,
breln1unionEcases: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(woz1_1_type,type,
woz1_1: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(breln1unionI_type,type,
breln1unionI: $o ).
thf(complementSubsetComplementIntersect_type,type,
complementSubsetComplementIntersect: $o ).
thf(exuI1_type,type,
exuI1: $o ).
thf(exuI2_type,type,
exuI2: $o ).
thf(notequalI2_type,type,
notequalI2: $o ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(binunionTE_type,type,
binunionTE: $o ).
thf(binunionTEcontra_type,type,
binunionTEcontra: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(setukpairinjR2_type,type,
setukpairinjR2: $o ).
thf(singletonsuniq_type,type,
singletonsuniq: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(funcextLem_type,type,
funcextLem: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(eta1_type,type,
eta1: $o ).
thf(complementTnotintersectT_type,type,
complementTnotintersectT: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(apProp_type,type,
apProp: $o ).
thf(setextT_type,type,
setextT: $o ).
thf(inIntersectImpInIntersectUnions_type,type,
inIntersectImpInIntersectUnions: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(breln1invprop_type,type,
breln1invprop: $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(dpsetconstrSub_type,type,
dpsetconstrSub: $o ).
thf(ex1E1_type,type,
ex1E1: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(complementTcontraSubset_type,type,
complementTcontraSubset: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(binintersectTELcontra_type,type,
binintersectTELcontra: $o ).
thf(ubforcartprodlem1_type,type,
ubforcartprodlem1: $o ).
thf(iftrue_type,type,
iftrue: $o ).
thf(woz13rule4_type,type,
woz13rule4: $o ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(theprop_type,type,
theprop: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(demorgan1_type,type,
demorgan1: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(complementInPowersetComplementIntersect_type,type,
complementInPowersetComplementIntersect: $o ).
thf(inIntersectImpInUnion_type,type,
inIntersectImpInUnion: $o ).
thf(breln1SetBreln1_type,type,
breln1SetBreln1: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(ex1I2_type,type,
ex1I2: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(ap2apEq2_type,type,
ap2apEq2: $o ).
thf(ifSingleton_type,type,
ifSingleton: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(iftrueProp1_type,type,
iftrueProp1: $o ).
thf(complementTI1_type,type,
complementTI1: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(doubleComplementSub2_type,type,
doubleComplementSub2: $o ).
thf(complementUnionInPowersetComplement_type,type,
complementUnionInPowersetComplement: $o ).
thf(iffalse_type,type,
iffalse: $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(cartprodfstin_type,type,
cartprodfstin: $o ).
thf(lamp_type,type,
lamp: $o ).
thf(iffalseProp1_type,type,
iffalseProp1: $o ).
thf(breln1invI_type,type,
breln1invI: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(breln1unionE_type,type,
breln1unionE: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(lam2lamEq_type,type,
lam2lamEq: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(woz2Ex_type,type,
woz2Ex: $o ).
thf(eta2_type,type,
eta2: $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(powersetTE1_type,type,
powersetTE1: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(cartprodpairsurjEq_type,type,
cartprodpairsurjEq: $o ).
thf(sk__160_type,type,
sk__160: $i ).
thf(lam2p_type,type,
lam2p: $o ).
thf(contraSubsetComplement_type,type,
contraSubsetComplement: $o ).
thf(doubleComplementSub1_type,type,
doubleComplementSub1: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(setOfPairsIsBReln1_type,type,
setOfPairsIsBReln1: $o ).
thf(inCongP_type,type,
inCongP: $o ).
thf(setukpairinjR11_type,type,
setukpairinjR11: $o ).
thf(setadjoinSub_type,type,
setadjoinSub: $o ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(woz13rule2_type,type,
woz13rule2: $o ).
thf(binintersectSubset2_type,type,
binintersectSubset2: $o ).
thf(setunionI_type,type,
setunionI: $o ).
thf(breln1unionIR_type,type,
breln1unionIR: $o ).
thf(binintersectTERcontra_type,type,
binintersectTERcontra: $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(woz1_2_type,type,
woz1_2: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setukpairinjR12_type,type,
setukpairinjR12: $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(upairequniteq_type,type,
upairequniteq: $o ).
thf(dpsetconstrEL1_type,type,
dpsetconstrEL1: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(breln1compprop_type,type,
breln1compprop: $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(demorgan2b_type,type,
demorgan2b: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(breln1unionIL_type,type,
breln1unionIL: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(infuncsetfunc_type,type,
infuncsetfunc: $o ).
thf(kpairp_type,type,
kpairp: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(powersetTI1_type,type,
powersetTI1: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(sk__161_type,type,
sk__161: $i ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(contrasubsetT1_type,type,
contrasubsetT1: $o ).
thf(setunionsingleton1_type,type,
setunionsingleton1: $o ).
thf(breln1compE_type,type,
breln1compE: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(binintersectT_lem_type,type,
binintersectT_lem: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(doubleComplementEq_type,type,
doubleComplementEq: $o ).
thf(eqbreln1_type,type,
eqbreln1: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $o ).
thf(dpsetconstrER_type,type,
dpsetconstrER: $o ).
thf(doubleComplementE1_type,type,
doubleComplementE1: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $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(notinsingleton_type,type,
notinsingleton: $o ).
thf(intersectInPowersetIntersectUnions_type,type,
intersectInPowersetIntersectUnions: $o ).
thf(dpsetconstrEL2_type,type,
dpsetconstrEL2: $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(breln1invE_type,type,
breln1invE: $o ).
thf(breln1unionCommutes_type,type,
breln1unionCommutes: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(app_type,type,
app: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(powersetT_lem_type,type,
powersetT_lem: $o ).
thf(woz2W_type,type,
woz2W: $o ).
thf(iffalseProp2_type,type,
iffalseProp2: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(breln1all1_type,type,
breln1all1: $o ).
thf(choice2fnsingleton_type,type,
choice2fnsingleton: $o ).
thf(breln1compI_type,type,
breln1compI: $o ).
thf(demorgan2a1_type,type,
demorgan2a1: $o ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(complementTE1_type,type,
complementTE1: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(breln1all2_type,type,
breln1all2: $o ).
thf(contrasubsetT2_type,type,
contrasubsetT2: $o ).
thf(sk__162_type,type,
sk__162: $i ).
thf(inIntersectImpInUnion2_type,type,
inIntersectImpInUnion2: $o ).
thf(demorgan2b2_type,type,
demorgan2b2: $o ).
thf(binintersectLsub_type,type,
binintersectLsub: $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(symdiffE_type,type,
symdiffE: $o ).
thf(woz13rule1_type,type,
woz13rule1: $o ).
thf(breln1unionprop_type,type,
breln1unionprop: $o ).
thf(descrp_type,type,
descrp: $o ).
thf(dsetconstr__Cong_type,type,
dsetconstr__Cong: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(brelnall2_type,type,
brelnall2: $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(demorgan2a_type,type,
demorgan2a: $o ).
thf(woz1_3_type,type,
woz1_3: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(demorgan1a_type,type,
demorgan1a: $o ).
thf(ifp_type,type,
ifp: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(beta1_type,type,
beta1: $o ).
thf(funcext2_type,type,
funcext2: $o ).
thf(subbreln_type,type,
subbreln: $o ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(breln1compset_type,type,
breln1compset: $i > $i > $i > $i ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(subbreln1_type,type,
subbreln1: $o ).
thf(demorgan2a2_type,type,
demorgan2a2: $o ).
thf(subsetTI_type,type,
subsetTI: $o ).
thf(setminusT_lem_type,type,
setminusT_lem: $o ).
thf(ap2p_type,type,
ap2p: $o ).
thf(doubleComplementI1_type,type,
doubleComplementI1: $o ).
thf(binunionT_lem_type,type,
binunionT_lem: $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(woz1_4_type,type,
woz1_4: $o ).
thf(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(theeq_type,type,
theeq: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(binunionTIRcontra_type,type,
binunionTIRcontra: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(demorgan1b_type,type,
demorgan1b: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(inComplementUnionImpNotIn1_type,type,
inComplementUnionImpNotIn1: $o ).
thf(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(breln1compEex_type,type,
breln1compEex: $o ).
thf(contrasubsetT_type,type,
contrasubsetT: $o ).
thf(setminusSubset2_type,type,
setminusSubset2: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(breln1invset_type,type,
breln1invset: $i > $i > $i ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(woz2A_type,type,
woz2A: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(funcGraphProp4_type,type,
funcGraphProp4: $o ).
thf(woz1_5_type,type,
woz1_5: $o ).
thf(demorgan2_type,type,
demorgan2: $o ).
thf(setunionsingleton2_type,type,
setunionsingleton2: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(inComplementUnionImpInComplement1_type,type,
inComplementUnionImpInComplement1: $o ).
thf(funcext_type,type,
funcext: $o ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(notdallE_type,type,
notdallE: $o ).
thf(iftrueProp2_type,type,
iftrueProp2: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(woz13rule0_type,type,
woz13rule0: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(beta2_type,type,
beta2: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(cartprodsndin_type,type,
cartprodsndin: $o ).
thf(iftrueorfalse_type,type,
iftrueorfalse: $o ).
thf(sk__163_type,type,
sk__163: $i ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(ex1I_type,type,
ex1I: $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(ex1E2_type,type,
ex1E2: $o ).
thf(replAx_type,type,
replAx: $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(binunionTILcontra_type,type,
binunionTILcontra: $o ).
thf(ap2apEq1_type,type,
ap2apEq1: $o ).
thf(contrasubsetT3_type,type,
contrasubsetT3: $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(woz13rule3_type,type,
woz13rule3: $o ).
thf(complementImpComplementIntersect_type,type,
complementImpComplementIntersect: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(woz2A,axiom,
( woz2A
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
thf('0',plain,
( woz2A
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( breln1 @ X4 @ X10 )
=> ( ( breln1compset @ X4 @ ( binunion @ X6 @ X8 ) @ X10 )
= ( binunion @ ( breln1compset @ X4 @ X6 @ X10 ) @ ( breln1compset @ X4 @ X8 @ X10 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(woz2W,axiom,
( woz2W
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
thf('1',plain,
( woz2W
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( ( breln1invset @ X4 @ ( breln1compset @ X4 @ X6 @ X8 ) )
= ( breln1compset @ X4 @ ( breln1invset @ X4 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(woz2Ex,axiom,
( woz2Ex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
thf('2',plain,
( woz2Ex
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ( X6
= ( breln1invset @ X4 @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionCommutes,axiom,
( breln1unionCommutes
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) ) ) ) ).
thf('3',plain,
( breln1unionCommutes
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( ( binunion @ X6 @ X8 )
= ( binunion @ X8 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionEcases,axiom,
( breln1unionEcases
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ) ) ).
thf('4',plain,
( breln1unionEcases
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) )
=> ! [X14: $o] :
( ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> X14 )
=> ( ( ( in @ ( kpair @ X10 @ X12 ) @ X8 )
=> X14 )
=> X14 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionE,axiom,
( breln1unionE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
thf('5',plain,
( breln1unionE
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
| ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionI,axiom,
( breln1unionI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
thf('6',plain,
( breln1unionI
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
| ( in @ ( kpair @ X10 @ X12 ) @ X8 ) )
=> ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionIR,axiom,
( breln1unionIR
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
thf('7',plain,
( breln1unionIR
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X8 )
=> ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionIL,axiom,
( breln1unionIL
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
thf('8',plain,
( breln1unionIL
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1unionprop,axiom,
( breln1unionprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
thf('9',plain,
( breln1unionprop
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( breln1 @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1compEex,axiom,
( breln1compEex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) ) ) ).
thf('10',plain,
( breln1compEex
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) )
=> ! [X14: $o] :
( ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X16 ) @ X6 )
=> ( ( in @ ( kpair @ X16 @ X12 ) @ X8 )
=> X14 ) ) )
=> X14 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1compE,axiom,
( breln1compE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ ( kpair @ Xz @ Xy ) @ S )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ Xz @ A ) ) ) ) ) ) ) ) ) ).
thf('11',plain,
( breln1compE
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) )
=> ? [X14: $i] :
( ( in @ ( kpair @ X14 @ X12 ) @ X8 )
& ( in @ ( kpair @ X10 @ X14 ) @ X6 )
& ( in @ X14 @ X4 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1compI,axiom,
( breln1compI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
thf('12',plain,
( breln1compI
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X14 ) @ X6 )
=> ( ( in @ ( kpair @ X14 @ X12 ) @ X8 )
=> ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1compprop,axiom,
( breln1compprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
thf('13',plain,
( breln1compprop
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( breln1 @ X4 @ ( breln1compset @ X4 @ X6 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1invE,axiom,
( breln1invE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
thf('14',plain,
( breln1invE
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) )
=> ( in @ ( kpair @ X8 @ X10 ) @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1invI,axiom,
( breln1invI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
thf('15',plain,
( breln1invI
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X8 @ X10 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1invprop,axiom,
( breln1invprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
thf('16',plain,
( breln1invprop
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ( breln1 @ X4 @ ( breln1invset @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(eqbreln1,axiom,
( eqbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ) ).
thf('17',plain,
( eqbreln1
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) )
=> ( ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ( ( in @ ( kpair @ X14 @ X16 ) @ X8 )
=> ( in @ ( kpair @ X14 @ X16 ) @ X6 ) ) ) )
=> ( X6 = X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(subbreln1,axiom,
( subbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ) ).
thf('18',plain,
( subbreln1
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) )
=> ( subset @ X6 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1all1,axiom,
( breln1all1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ) ).
thf('19',plain,
( breln1all1
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i > $o] :
( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( X8 @ ( kpair @ X10 @ X12 ) ) ) ) )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( X8 @ X14 ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1all2,axiom,
( breln1all2
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ) ).
thf('20',plain,
( breln1all2
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i > $o] :
( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( X8 @ ( kpair @ X10 @ X12 ) ) ) ) )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( X8 @ X14 ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionTEcontra,axiom,
( binunionTEcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
thf('21',plain,
( binunionTEcontra
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ ( in @ X10 @ X6 )
=> ( ~ ( in @ X10 @ X8 )
=> ~ ( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionTE,axiom,
( binunionTE
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ) ).
thf('22',plain,
( binunionTE
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $o,X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ X12 @ ( binunion @ X6 @ X8 ) )
=> ( ( ( in @ X12 @ X6 )
=> X10 )
=> ( ( ( in @ X12 @ X8 )
=> X10 )
=> X10 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
thf('23',plain,
( binunionTIRcontra
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ ( in @ X10 @ ( binunion @ X6 @ X8 ) )
=> ~ ( in @ X10 @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
thf('24',plain,
( binunionTILcontra
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ ( in @ X10 @ ( binunion @ X6 @ X8 ) )
=> ~ ( in @ X10 @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionT_lem,axiom,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
thf('25',plain,
( binunionT_lem
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
thf('26',plain,
( ubforcartprodlem3
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
thf('27',plain,
( ubforcartprodlem2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
thf('28',plain,
( ubforcartprodlem1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(upairinpowunion,axiom,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
thf('29',plain,
( upairinpowunion
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(upairsubunion,axiom,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
thf('30',plain,
( upairsubunion
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( subset @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ ( binunion @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
thf('31',plain,
( singletoninpowunion
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ ( setadjoin @ X8 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(binunionRsub,axiom,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
thf('32',plain,
( binunionRsub
= ( ! [X4: $i,X6: $i] : ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(binunionLsub,axiom,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
thf('33',plain,
( binunionLsub
= ( ! [X4: $i,X6: $i] : ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(binunionE,axiom,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ) ).
thf('34',plain,
( binunionE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( binunion @ X4 @ X6 ) )
=> ( ( in @ X8 @ X4 )
| ( in @ X8 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(binunionEcases,axiom,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ) ).
thf('35',plain,
( binunionEcases
= ( ! [X4: $i,X6: $i,X8: $i,X10: $o] :
( ( in @ X8 @ ( binunion @ X4 @ X6 ) )
=> ( ( ( in @ X8 @ X4 )
=> X10 )
=> ( ( ( in @ X8 @ X6 )
=> X10 )
=> X10 ) ) ) ) ),
define([status(thm)]) ).
thf(binunionIR,axiom,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
thf('36',plain,
( binunionIR
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X6 )
=> ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(binunionIL,axiom,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
thf('37',plain,
( binunionIL
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(woz2B,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
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,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
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ ( binunion @ X4 @ X6 ) ) )
=> ( upairset2IR
=> ( ! [X10: $i,X12: $i,X14: $i] :
( ( in @ X14 @ X12 )
=> ( in @ X14 @ ( binunion @ X10 @ X12 ) ) )
=> ( ! [X16: $i,X18: $i,X20: $i,X22: $o] :
( ( in @ X20 @ ( binunion @ X16 @ X18 ) )
=> ( ( ( in @ X20 @ X16 )
=> X22 )
=> ( ( ( in @ X20 @ X18 )
=> X22 )
=> X22 ) ) )
=> ( ! [X24: $i,X26: $i,X28: $i] :
( ( in @ X28 @ ( binunion @ X24 @ X26 ) )
=> ( ( in @ X28 @ X24 )
| ( in @ X28 @ X26 ) ) )
=> ( ! [X30: $i,X32: $i] : ( subset @ X30 @ ( binunion @ X30 @ X32 ) )
=> ( ! [X34: $i,X36: $i] : ( subset @ X36 @ ( binunion @ X34 @ X36 ) )
=> ( 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
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X38 )
=> ( in @ ( setadjoin @ X42 @ emptyset ) @ ( powerset @ ( binunion @ X38 @ X40 ) ) ) )
=> ( upairset2E
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( in @ X48 @ X44 )
=> ! [X50: $i] :
( ( in @ X50 @ X46 )
=> ( subset @ ( setadjoin @ X48 @ ( setadjoin @ X50 @ emptyset ) ) @ ( binunion @ X44 @ X46 ) ) ) )
=> ( ! [X52: $i,X54: $i,X56: $i] :
( ( in @ X56 @ X52 )
=> ! [X58: $i] :
( ( in @ X58 @ X54 )
=> ( in @ ( setadjoin @ X56 @ ( setadjoin @ X58 @ emptyset ) ) @ ( powerset @ ( binunion @ X52 @ X54 ) ) ) ) )
=> ( ! [X60: $i,X62: $i,X64: $i] :
( ( in @ X64 @ X60 )
=> ! [X66: $i] :
( ( in @ X66 @ X62 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X64 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X64 @ ( setadjoin @ X66 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X60 @ X62 ) ) ) ) )
=> ( ! [X68: $i,X70: $i,X72: $i] :
( ( in @ X72 @ X68 )
=> ! [X74: $i] :
( ( in @ X74 @ X70 )
=> ( in @ ( setadjoin @ ( setadjoin @ X72 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X72 @ ( setadjoin @ X74 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X68 @ X70 ) ) ) ) ) )
=> ( ! [X76: $i,X78: $i,X80: $i] :
( ( in @ X80 @ X76 )
=> ! [X82: $i] :
( ( in @ X82 @ X78 )
=> ( in @ ( kpair @ X80 @ X82 ) @ ( powerset @ ( powerset @ ( binunion @ X76 @ X78 ) ) ) ) ) )
=> ( 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
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( ! [X84: $i,X86: $i] :
( ( in @ X86 @ ( powerset @ X84 ) )
=> ! [X88: $i] :
( ( in @ X88 @ ( powerset @ X84 ) )
=> ( in @ ( binunion @ X86 @ X88 ) @ ( powerset @ X84 ) ) ) )
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( ! [X90: $i,X92: $i] :
( ( in @ X92 @ ( powerset @ X90 ) )
=> ! [X94: $i] :
( ( in @ X94 @ ( powerset @ X90 ) )
=> ! [X96: $i] :
( ( in @ X96 @ X90 )
=> ( ~ ( in @ X96 @ ( binunion @ X92 @ X94 ) )
=> ~ ( in @ X96 @ X92 ) ) ) ) )
=> ( ! [X98: $i,X100: $i] :
( ( in @ X100 @ ( powerset @ X98 ) )
=> ! [X102: $i] :
( ( in @ X102 @ ( powerset @ X98 ) )
=> ! [X104: $i] :
( ( in @ X104 @ X98 )
=> ( ~ ( in @ X104 @ ( binunion @ X100 @ X102 ) )
=> ~ ( in @ X104 @ X102 ) ) ) ) )
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( ! [X106: $i,X108: $i] :
( ( in @ X108 @ ( powerset @ X106 ) )
=> ! [X110: $i] :
( ( in @ X110 @ ( powerset @ X106 ) )
=> ! [X112: $o,X114: $i] :
( ( in @ X114 @ X106 )
=> ( ( in @ X114 @ ( binunion @ X108 @ X110 ) )
=> ( ( ( in @ X114 @ X108 )
=> X112 )
=> ( ( ( in @ X114 @ X110 )
=> X112 )
=> X112 ) ) ) ) ) )
=> ( ! [X116: $i,X118: $i] :
( ( in @ X118 @ ( powerset @ X116 ) )
=> ! [X120: $i] :
( ( in @ X120 @ ( powerset @ X116 ) )
=> ! [X122: $i] :
( ( in @ X122 @ X116 )
=> ( ~ ( in @ X122 @ X118 )
=> ( ~ ( in @ X122 @ X120 )
=> ~ ( in @ X122 @ ( binunion @ X118 @ X120 ) ) ) ) ) ) )
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( ! [X124: $i,X126: $i] :
( ( breln1 @ X124 @ X126 )
=> ! [X128: $i > $o] :
( ! [X130: $i] :
( ( in @ X130 @ X124 )
=> ! [X132: $i] :
( ( in @ X132 @ X124 )
=> ( ( in @ ( kpair @ X130 @ X132 ) @ X126 )
=> ( X128 @ ( kpair @ X130 @ X132 ) ) ) ) )
=> ! [X134: $i] :
( ( in @ X134 @ X126 )
=> ( X128 @ X134 ) ) ) )
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( ! [X136: $i,X138: $i] :
( ( breln1 @ X136 @ X138 )
=> ! [X140: $i > $o] :
( ! [X142: $i] :
( ( in @ X142 @ X136 )
=> ! [X144: $i] :
( ( in @ X144 @ X136 )
=> ( ( in @ ( kpair @ X142 @ X144 ) @ X138 )
=> ( X140 @ ( kpair @ X142 @ X144 ) ) ) ) )
=> ! [X146: $i] :
( ( in @ X146 @ X138 )
=> ( X140 @ X146 ) ) ) )
=> ( ! [X148: $i,X150: $i] :
( ( breln1 @ X148 @ X150 )
=> ! [X152: $i] :
( ( breln1 @ X148 @ X152 )
=> ( ! [X154: $i] :
( ( in @ X154 @ X148 )
=> ! [X156: $i] :
( ( in @ X156 @ X148 )
=> ( ( in @ ( kpair @ X154 @ X156 ) @ X150 )
=> ( in @ ( kpair @ X154 @ X156 ) @ X152 ) ) ) )
=> ( subset @ X150 @ X152 ) ) ) )
=> ( ! [X158: $i,X160: $i] :
( ( breln1 @ X158 @ X160 )
=> ! [X162: $i] :
( ( breln1 @ X158 @ X162 )
=> ( ! [X164: $i] :
( ( in @ X164 @ X158 )
=> ! [X166: $i] :
( ( in @ X166 @ X158 )
=> ( ( in @ ( kpair @ X164 @ X166 ) @ X160 )
=> ( in @ ( kpair @ X164 @ X166 ) @ X162 ) ) ) )
=> ( ! [X168: $i] :
( ( in @ X168 @ X158 )
=> ! [X170: $i] :
( ( in @ X170 @ X158 )
=> ( ( in @ ( kpair @ X168 @ X170 ) @ X162 )
=> ( in @ ( kpair @ X168 @ X170 ) @ X160 ) ) ) )
=> ( X160 = X162 ) ) ) ) )
=> ( ! [X172: $i,X174: $i] :
( ( breln1 @ X172 @ X174 )
=> ( breln1 @ X172 @ ( breln1invset @ X172 @ X174 ) ) )
=> ( ! [X176: $i,X178: $i] :
( ( breln1 @ X176 @ X178 )
=> ! [X180: $i] :
( ( in @ X180 @ X176 )
=> ! [X182: $i] :
( ( in @ X182 @ X176 )
=> ( ( in @ ( kpair @ X180 @ X182 ) @ X178 )
=> ( in @ ( kpair @ X182 @ X180 ) @ ( breln1invset @ X176 @ X178 ) ) ) ) ) )
=> ( ! [X184: $i,X186: $i] :
( ( breln1 @ X184 @ X186 )
=> ! [X188: $i] :
( ( in @ X188 @ X184 )
=> ! [X190: $i] :
( ( in @ X190 @ X184 )
=> ( ( in @ ( kpair @ X190 @ X188 ) @ ( breln1invset @ X184 @ X186 ) )
=> ( in @ ( kpair @ X188 @ X190 ) @ X186 ) ) ) ) )
=> ( ! [X192: $i,X194: $i] :
( ( breln1 @ X192 @ X194 )
=> ! [X196: $i] :
( ( breln1 @ X192 @ X196 )
=> ( breln1 @ X192 @ ( breln1compset @ X192 @ X194 @ X196 ) ) ) )
=> ( ! [X198: $i,X200: $i] :
( ( breln1 @ X198 @ X200 )
=> ! [X202: $i] :
( ( breln1 @ X198 @ X202 )
=> ! [X204: $i] :
( ( in @ X204 @ X198 )
=> ! [X206: $i] :
( ( in @ X206 @ X198 )
=> ! [X208: $i] :
( ( in @ X208 @ X198 )
=> ( ( in @ ( kpair @ X204 @ X208 ) @ X200 )
=> ( ( in @ ( kpair @ X208 @ X206 ) @ X202 )
=> ( in @ ( kpair @ X204 @ X206 ) @ ( breln1compset @ X198 @ X200 @ X202 ) ) ) ) ) ) ) ) )
=> ( ! [X210: $i,X212: $i] :
( ( breln1 @ X210 @ X212 )
=> ! [X214: $i] :
( ( breln1 @ X210 @ X214 )
=> ! [X216: $i] :
( ( in @ X216 @ X210 )
=> ! [X218: $i] :
( ( in @ X218 @ X210 )
=> ( ( in @ ( kpair @ X216 @ X218 ) @ ( breln1compset @ X210 @ X212 @ X214 ) )
=> ? [X220: $i] :
( ( in @ ( kpair @ X220 @ X218 ) @ X214 )
& ( in @ ( kpair @ X216 @ X220 ) @ X212 )
& ( in @ X220 @ X210 ) ) ) ) ) ) )
=> ( ! [X222: $i,X224: $i] :
( ( breln1 @ X222 @ X224 )
=> ! [X226: $i] :
( ( breln1 @ X222 @ X226 )
=> ! [X228: $i] :
( ( in @ X228 @ X222 )
=> ! [X230: $i] :
( ( in @ X230 @ X222 )
=> ( ( in @ ( kpair @ X228 @ X230 ) @ ( breln1compset @ X222 @ X224 @ X226 ) )
=> ! [X232: $o] :
( ! [X234: $i] :
( ( in @ X234 @ X222 )
=> ( ( in @ ( kpair @ X228 @ X234 ) @ X224 )
=> ( ( in @ ( kpair @ X234 @ X230 ) @ X226 )
=> X232 ) ) )
=> X232 ) ) ) ) ) )
=> ( ! [X236: $i,X238: $i] :
( ( breln1 @ X236 @ X238 )
=> ! [X240: $i] :
( ( breln1 @ X236 @ X240 )
=> ( breln1 @ X236 @ ( binunion @ X238 @ X240 ) ) ) )
=> ( ! [X242: $i,X244: $i] :
( ( breln1 @ X242 @ X244 )
=> ! [X246: $i] :
( ( breln1 @ X242 @ X246 )
=> ! [X248: $i] :
( ( in @ X248 @ X242 )
=> ! [X250: $i] :
( ( in @ X250 @ X242 )
=> ( ( in @ ( kpair @ X248 @ X250 ) @ X244 )
=> ( in @ ( kpair @ X248 @ X250 ) @ ( binunion @ X244 @ X246 ) ) ) ) ) ) )
=> ( ! [X252: $i,X254: $i] :
( ( breln1 @ X252 @ X254 )
=> ! [X256: $i] :
( ( breln1 @ X252 @ X256 )
=> ! [X258: $i] :
( ( in @ X258 @ X252 )
=> ! [X260: $i] :
( ( in @ X260 @ X252 )
=> ( ( in @ ( kpair @ X258 @ X260 ) @ X256 )
=> ( in @ ( kpair @ X258 @ X260 ) @ ( binunion @ X254 @ X256 ) ) ) ) ) ) )
=> ( ! [X262: $i,X264: $i] :
( ( breln1 @ X262 @ X264 )
=> ! [X266: $i] :
( ( breln1 @ X262 @ X266 )
=> ! [X268: $i] :
( ( in @ X268 @ X262 )
=> ! [X270: $i] :
( ( in @ X270 @ X262 )
=> ( ( ( in @ ( kpair @ X268 @ X270 ) @ X264 )
| ( in @ ( kpair @ X268 @ X270 ) @ X266 ) )
=> ( in @ ( kpair @ X268 @ X270 ) @ ( binunion @ X264 @ X266 ) ) ) ) ) ) )
=> ( ! [X272: $i,X274: $i] :
( ( breln1 @ X272 @ X274 )
=> ! [X276: $i] :
( ( breln1 @ X272 @ X276 )
=> ! [X278: $i] :
( ( in @ X278 @ X272 )
=> ! [X280: $i] :
( ( in @ X280 @ X272 )
=> ( ( in @ ( kpair @ X278 @ X280 ) @ ( binunion @ X274 @ X276 ) )
=> ( ( in @ ( kpair @ X278 @ X280 ) @ X274 )
| ( in @ ( kpair @ X278 @ X280 ) @ X276 ) ) ) ) ) ) )
=> ( ! [X282: $i,X284: $i] :
( ( breln1 @ X282 @ X284 )
=> ! [X286: $i] :
( ( breln1 @ X282 @ X286 )
=> ! [X288: $i] :
( ( in @ X288 @ X282 )
=> ! [X290: $i] :
( ( in @ X290 @ X282 )
=> ( ( in @ ( kpair @ X288 @ X290 ) @ ( binunion @ X284 @ X286 ) )
=> ! [X292: $o] :
( ( ( in @ ( kpair @ X288 @ X290 ) @ X284 )
=> X292 )
=> ( ( ( in @ ( kpair @ X288 @ X290 ) @ X286 )
=> X292 )
=> X292 ) ) ) ) ) ) )
=> ( ! [X294: $i,X296: $i] :
( ( breln1 @ X294 @ X296 )
=> ! [X298: $i] :
( ( breln1 @ X294 @ X298 )
=> ( ( binunion @ X296 @ X298 )
= ( binunion @ X298 @ X296 ) ) ) )
=> ( ! [X300: $i,X302: $i] :
( ( breln1 @ X300 @ X302 )
=> ( X302
= ( breln1invset @ X300 @ ( breln1invset @ X300 @ X302 ) ) ) )
=> ( ! [X304: $i,X306: $i] :
( ( breln1 @ X304 @ X306 )
=> ! [X308: $i] :
( ( breln1 @ X304 @ X308 )
=> ( ( breln1invset @ X304 @ ( breln1compset @ X304 @ X306 @ X308 ) )
= ( breln1compset @ X304 @ ( breln1invset @ X304 @ X308 ) @ ( breln1invset @ X304 @ X306 ) ) ) ) )
=> ( ! [X310: $i,X312: $i] :
( ( breln1 @ X310 @ X312 )
=> ! [X314: $i] :
( ( breln1 @ X310 @ X314 )
=> ! [X316: $i] :
( ( breln1 @ X310 @ X316 )
=> ( ( breln1compset @ X310 @ ( binunion @ X312 @ X314 ) @ X316 )
= ( binunion @ ( breln1compset @ X310 @ X312 @ X316 ) @ ( breln1compset @ X310 @ X314 @ X316 ) ) ) ) ) )
=> ! [X318: $i,X320: $i] :
( ( breln1 @ X318 @ X320 )
=> ! [X322: $i] :
( ( breln1 @ X318 @ X322 )
=> ! [X324: $i] :
( ( breln1 @ X318 @ X324 )
=> ( ( breln1compset @ X318 @ ( binunion @ X320 @ X322 ) @ X324 )
= ( binunion @ ( breln1invset @ X318 @ ( breln1compset @ X318 @ ( breln1invset @ X318 @ X324 ) @ ( breln1invset @ X318 @ X322 ) ) ) @ ( breln1invset @ X318 @ ( breln1compset @ X318 @ ( breln1invset @ X318 @ X324 ) @ ( breln1invset @ X318 @ X320 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_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
=> ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ ( binunion @ X4 @ X6 ) ) )
=> ( upairset2IR
=> ( ! [X10: $i,X12: $i,X14: $i] :
( ( in @ X14 @ X12 )
=> ( in @ X14 @ ( binunion @ X10 @ X12 ) ) )
=> ( ! [X16: $i,X18: $i,X20: $i,X22: $o] :
( ( in @ X20 @ ( binunion @ X16 @ X18 ) )
=> ( ( ( in @ X20 @ X16 )
=> X22 )
=> ( ( ( in @ X20 @ X18 )
=> X22 )
=> X22 ) ) )
=> ( ! [X24: $i,X26: $i,X28: $i] :
( ( in @ X28 @ ( binunion @ X24 @ X26 ) )
=> ( ( in @ X28 @ X24 )
| ( in @ X28 @ X26 ) ) )
=> ( ! [X30: $i,X32: $i] : ( subset @ X30 @ ( binunion @ X30 @ X32 ) )
=> ( ! [X34: $i,X36: $i] : ( subset @ X36 @ ( binunion @ X34 @ X36 ) )
=> ( 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
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X38 )
=> ( in @ ( setadjoin @ X42 @ emptyset ) @ ( powerset @ ( binunion @ X38 @ X40 ) ) ) )
=> ( upairset2E
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( in @ X48 @ X44 )
=> ! [X50: $i] :
( ( in @ X50 @ X46 )
=> ( subset @ ( setadjoin @ X48 @ ( setadjoin @ X50 @ emptyset ) ) @ ( binunion @ X44 @ X46 ) ) ) )
=> ( ! [X52: $i,X54: $i,X56: $i] :
( ( in @ X56 @ X52 )
=> ! [X58: $i] :
( ( in @ X58 @ X54 )
=> ( in @ ( setadjoin @ X56 @ ( setadjoin @ X58 @ emptyset ) ) @ ( powerset @ ( binunion @ X52 @ X54 ) ) ) ) )
=> ( ! [X60: $i,X62: $i,X64: $i] :
( ( in @ X64 @ X60 )
=> ! [X66: $i] :
( ( in @ X66 @ X62 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X64 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X64 @ ( setadjoin @ X66 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X60 @ X62 ) ) ) ) )
=> ( ! [X68: $i,X70: $i,X72: $i] :
( ( in @ X72 @ X68 )
=> ! [X74: $i] :
( ( in @ X74 @ X70 )
=> ( in @ ( setadjoin @ ( setadjoin @ X72 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X72 @ ( setadjoin @ X74 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X68 @ X70 ) ) ) ) ) )
=> ( ! [X76: $i,X78: $i,X80: $i] :
( ( in @ X80 @ X76 )
=> ! [X82: $i] :
( ( in @ X82 @ X78 )
=> ( in @ ( kpair @ X80 @ X82 ) @ ( powerset @ ( powerset @ ( binunion @ X76 @ X78 ) ) ) ) ) )
=> ( 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
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( ! [X84: $i,X86: $i] :
( ( in @ X86 @ ( powerset @ X84 ) )
=> ! [X88: $i] :
( ( in @ X88 @ ( powerset @ X84 ) )
=> ( in @ ( binunion @ X86 @ X88 ) @ ( powerset @ X84 ) ) ) )
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( ! [X90: $i,X92: $i] :
( ( in @ X92 @ ( powerset @ X90 ) )
=> ! [X94: $i] :
( ( in @ X94 @ ( powerset @ X90 ) )
=> ! [X96: $i] :
( ( in @ X96 @ X90 )
=> ( ~ ( in @ X96 @ ( binunion @ X92 @ X94 ) )
=> ~ ( in @ X96 @ X92 ) ) ) ) )
=> ( ! [X98: $i,X100: $i] :
( ( in @ X100 @ ( powerset @ X98 ) )
=> ! [X102: $i] :
( ( in @ X102 @ ( powerset @ X98 ) )
=> ! [X104: $i] :
( ( in @ X104 @ X98 )
=> ( ~ ( in @ X104 @ ( binunion @ X100 @ X102 ) )
=> ~ ( in @ X104 @ X102 ) ) ) ) )
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( ! [X106: $i,X108: $i] :
( ( in @ X108 @ ( powerset @ X106 ) )
=> ! [X110: $i] :
( ( in @ X110 @ ( powerset @ X106 ) )
=> ! [X112: $o,X114: $i] :
( ( in @ X114 @ X106 )
=> ( ( in @ X114 @ ( binunion @ X108 @ X110 ) )
=> ( ( ( in @ X114 @ X108 )
=> X112 )
=> ( ( ( in @ X114 @ X110 )
=> X112 )
=> X112 ) ) ) ) ) )
=> ( ! [X116: $i,X118: $i] :
( ( in @ X118 @ ( powerset @ X116 ) )
=> ! [X120: $i] :
( ( in @ X120 @ ( powerset @ X116 ) )
=> ! [X122: $i] :
( ( in @ X122 @ X116 )
=> ( ~ ( in @ X122 @ X118 )
=> ( ~ ( in @ X122 @ X120 )
=> ~ ( in @ X122 @ ( binunion @ X118 @ X120 ) ) ) ) ) ) )
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( ! [X124: $i,X126: $i] :
( ( breln1 @ X124 @ X126 )
=> ! [X128: $i > $o] :
( ! [X130: $i] :
( ( in @ X130 @ X124 )
=> ! [X132: $i] :
( ( in @ X132 @ X124 )
=> ( ( in @ ( kpair @ X130 @ X132 ) @ X126 )
=> ( X128 @ ( kpair @ X130 @ X132 ) ) ) ) )
=> ! [X134: $i] :
( ( in @ X134 @ X126 )
=> ( X128 @ X134 ) ) ) )
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( ! [X136: $i,X138: $i] :
( ( breln1 @ X136 @ X138 )
=> ! [X140: $i > $o] :
( ! [X142: $i] :
( ( in @ X142 @ X136 )
=> ! [X144: $i] :
( ( in @ X144 @ X136 )
=> ( ( in @ ( kpair @ X142 @ X144 ) @ X138 )
=> ( X140 @ ( kpair @ X142 @ X144 ) ) ) ) )
=> ! [X146: $i] :
( ( in @ X146 @ X138 )
=> ( X140 @ X146 ) ) ) )
=> ( ! [X148: $i,X150: $i] :
( ( breln1 @ X148 @ X150 )
=> ! [X152: $i] :
( ( breln1 @ X148 @ X152 )
=> ( ! [X154: $i] :
( ( in @ X154 @ X148 )
=> ! [X156: $i] :
( ( in @ X156 @ X148 )
=> ( ( in @ ( kpair @ X154 @ X156 ) @ X150 )
=> ( in @ ( kpair @ X154 @ X156 ) @ X152 ) ) ) )
=> ( subset @ X150 @ X152 ) ) ) )
=> ( ! [X158: $i,X160: $i] :
( ( breln1 @ X158 @ X160 )
=> ! [X162: $i] :
( ( breln1 @ X158 @ X162 )
=> ( ! [X164: $i] :
( ( in @ X164 @ X158 )
=> ! [X166: $i] :
( ( in @ X166 @ X158 )
=> ( ( in @ ( kpair @ X164 @ X166 ) @ X160 )
=> ( in @ ( kpair @ X164 @ X166 ) @ X162 ) ) ) )
=> ( ! [X168: $i] :
( ( in @ X168 @ X158 )
=> ! [X170: $i] :
( ( in @ X170 @ X158 )
=> ( ( in @ ( kpair @ X168 @ X170 ) @ X162 )
=> ( in @ ( kpair @ X168 @ X170 ) @ X160 ) ) ) )
=> ( X160 = X162 ) ) ) ) )
=> ( ! [X172: $i,X174: $i] :
( ( breln1 @ X172 @ X174 )
=> ( breln1 @ X172 @ ( breln1invset @ X172 @ X174 ) ) )
=> ( ! [X176: $i,X178: $i] :
( ( breln1 @ X176 @ X178 )
=> ! [X180: $i] :
( ( in @ X180 @ X176 )
=> ! [X182: $i] :
( ( in @ X182 @ X176 )
=> ( ( in @ ( kpair @ X180 @ X182 ) @ X178 )
=> ( in @ ( kpair @ X182 @ X180 ) @ ( breln1invset @ X176 @ X178 ) ) ) ) ) )
=> ( ! [X184: $i,X186: $i] :
( ( breln1 @ X184 @ X186 )
=> ! [X188: $i] :
( ( in @ X188 @ X184 )
=> ! [X190: $i] :
( ( in @ X190 @ X184 )
=> ( ( in @ ( kpair @ X190 @ X188 ) @ ( breln1invset @ X184 @ X186 ) )
=> ( in @ ( kpair @ X188 @ X190 ) @ X186 ) ) ) ) )
=> ( ! [X192: $i,X194: $i] :
( ( breln1 @ X192 @ X194 )
=> ! [X196: $i] :
( ( breln1 @ X192 @ X196 )
=> ( breln1 @ X192 @ ( breln1compset @ X192 @ X194 @ X196 ) ) ) )
=> ( ! [X198: $i,X200: $i] :
( ( breln1 @ X198 @ X200 )
=> ! [X202: $i] :
( ( breln1 @ X198 @ X202 )
=> ! [X204: $i] :
( ( in @ X204 @ X198 )
=> ! [X206: $i] :
( ( in @ X206 @ X198 )
=> ! [X208: $i] :
( ( in @ X208 @ X198 )
=> ( ( in @ ( kpair @ X204 @ X208 ) @ X200 )
=> ( ( in @ ( kpair @ X208 @ X206 ) @ X202 )
=> ( in @ ( kpair @ X204 @ X206 ) @ ( breln1compset @ X198 @ X200 @ X202 ) ) ) ) ) ) ) ) )
=> ( ! [X210: $i,X212: $i] :
( ( breln1 @ X210 @ X212 )
=> ! [X214: $i] :
( ( breln1 @ X210 @ X214 )
=> ! [X216: $i] :
( ( in @ X216 @ X210 )
=> ! [X218: $i] :
( ( in @ X218 @ X210 )
=> ( ( in @ ( kpair @ X216 @ X218 ) @ ( breln1compset @ X210 @ X212 @ X214 ) )
=> ? [X220: $i] :
( ( in @ ( kpair @ X220 @ X218 ) @ X214 )
& ( in @ ( kpair @ X216 @ X220 ) @ X212 )
& ( in @ X220 @ X210 ) ) ) ) ) ) )
=> ( ! [X222: $i,X224: $i] :
( ( breln1 @ X222 @ X224 )
=> ! [X226: $i] :
( ( breln1 @ X222 @ X226 )
=> ! [X228: $i] :
( ( in @ X228 @ X222 )
=> ! [X230: $i] :
( ( in @ X230 @ X222 )
=> ( ( in @ ( kpair @ X228 @ X230 ) @ ( breln1compset @ X222 @ X224 @ X226 ) )
=> ! [X232: $o] :
( ! [X234: $i] :
( ( in @ X234 @ X222 )
=> ( ( in @ ( kpair @ X228 @ X234 ) @ X224 )
=> ( ( in @ ( kpair @ X234 @ X230 ) @ X226 )
=> X232 ) ) )
=> X232 ) ) ) ) ) )
=> ( ! [X236: $i,X238: $i] :
( ( breln1 @ X236 @ X238 )
=> ! [X240: $i] :
( ( breln1 @ X236 @ X240 )
=> ( breln1 @ X236 @ ( binunion @ X238 @ X240 ) ) ) )
=> ( ! [X242: $i,X244: $i] :
( ( breln1 @ X242 @ X244 )
=> ! [X246: $i] :
( ( breln1 @ X242 @ X246 )
=> ! [X248: $i] :
( ( in @ X248 @ X242 )
=> ! [X250: $i] :
( ( in @ X250 @ X242 )
=> ( ( in @ ( kpair @ X248 @ X250 ) @ X244 )
=> ( in @ ( kpair @ X248 @ X250 ) @ ( binunion @ X244 @ X246 ) ) ) ) ) ) )
=> ( ! [X252: $i,X254: $i] :
( ( breln1 @ X252 @ X254 )
=> ! [X256: $i] :
( ( breln1 @ X252 @ X256 )
=> ! [X258: $i] :
( ( in @ X258 @ X252 )
=> ! [X260: $i] :
( ( in @ X260 @ X252 )
=> ( ( in @ ( kpair @ X258 @ X260 ) @ X256 )
=> ( in @ ( kpair @ X258 @ X260 ) @ ( binunion @ X254 @ X256 ) ) ) ) ) ) )
=> ( ! [X262: $i,X264: $i] :
( ( breln1 @ X262 @ X264 )
=> ! [X266: $i] :
( ( breln1 @ X262 @ X266 )
=> ! [X268: $i] :
( ( in @ X268 @ X262 )
=> ! [X270: $i] :
( ( in @ X270 @ X262 )
=> ( ( ( in @ ( kpair @ X268 @ X270 ) @ X264 )
| ( in @ ( kpair @ X268 @ X270 ) @ X266 ) )
=> ( in @ ( kpair @ X268 @ X270 ) @ ( binunion @ X264 @ X266 ) ) ) ) ) ) )
=> ( ! [X272: $i,X274: $i] :
( ( breln1 @ X272 @ X274 )
=> ! [X276: $i] :
( ( breln1 @ X272 @ X276 )
=> ! [X278: $i] :
( ( in @ X278 @ X272 )
=> ! [X280: $i] :
( ( in @ X280 @ X272 )
=> ( ( in @ ( kpair @ X278 @ X280 ) @ ( binunion @ X274 @ X276 ) )
=> ( ( in @ ( kpair @ X278 @ X280 ) @ X274 )
| ( in @ ( kpair @ X278 @ X280 ) @ X276 ) ) ) ) ) ) )
=> ( ! [X282: $i,X284: $i] :
( ( breln1 @ X282 @ X284 )
=> ! [X286: $i] :
( ( breln1 @ X282 @ X286 )
=> ! [X288: $i] :
( ( in @ X288 @ X282 )
=> ! [X290: $i] :
( ( in @ X290 @ X282 )
=> ( ( in @ ( kpair @ X288 @ X290 ) @ ( binunion @ X284 @ X286 ) )
=> ! [X292: $o] :
( ( ( in @ ( kpair @ X288 @ X290 ) @ X284 )
=> X292 )
=> ( ( ( in @ ( kpair @ X288 @ X290 ) @ X286 )
=> X292 )
=> X292 ) ) ) ) ) ) )
=> ( ! [X294: $i,X296: $i] :
( ( breln1 @ X294 @ X296 )
=> ! [X298: $i] :
( ( breln1 @ X294 @ X298 )
=> ( ( binunion @ X296 @ X298 )
= ( binunion @ X298 @ X296 ) ) ) )
=> ( ! [X300: $i,X302: $i] :
( ( breln1 @ X300 @ X302 )
=> ( X302
= ( breln1invset @ X300 @ ( breln1invset @ X300 @ X302 ) ) ) )
=> ( ! [X304: $i,X306: $i] :
( ( breln1 @ X304 @ X306 )
=> ! [X308: $i] :
( ( breln1 @ X304 @ X308 )
=> ( ( breln1invset @ X304 @ ( breln1compset @ X304 @ X306 @ X308 ) )
= ( breln1compset @ X304 @ ( breln1invset @ X304 @ X308 ) @ ( breln1invset @ X304 @ X306 ) ) ) ) )
=> ( ! [X310: $i,X312: $i] :
( ( breln1 @ X310 @ X312 )
=> ! [X314: $i] :
( ( breln1 @ X310 @ X314 )
=> ! [X316: $i] :
( ( breln1 @ X310 @ X316 )
=> ( ( breln1compset @ X310 @ ( binunion @ X312 @ X314 ) @ X316 )
= ( binunion @ ( breln1compset @ X310 @ X312 @ X316 ) @ ( breln1compset @ X310 @ X314 @ X316 ) ) ) ) ) )
=> ! [X318: $i,X320: $i] :
( ( breln1 @ X318 @ X320 )
=> ! [X322: $i] :
( ( breln1 @ X318 @ X322 )
=> ! [X324: $i] :
( ( breln1 @ X318 @ X324 )
=> ( ( breln1compset @ X318 @ ( binunion @ X320 @ X322 ) @ X324 )
= ( binunion @ ( breln1invset @ X318 @ ( breln1compset @ X318 @ ( breln1invset @ X318 @ X324 ) @ ( breln1invset @ X318 @ X322 ) ) ) @ ( breln1invset @ X318 @ ( breln1compset @ X318 @ ( breln1invset @ X318 @ X324 ) @ ( breln1invset @ X318 @ X320 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl171,plain,
! [X43: $i,X44: $i,X45: $i] :
( ~ ( breln1 @ X43 @ X44 )
| ( breln1 @ X43 @ ( breln1compset @ X43 @ X45 @ X44 ) )
| ~ ( breln1 @ X43 @ X45 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl184,plain,
! [X70: $i,X71: $i,X72: $i,X73: $i] :
( ~ ( breln1 @ X70 @ X71 )
| ( ( breln1compset @ X70 @ ( binunion @ X72 @ X71 ) @ X73 )
= ( binunion @ ( breln1compset @ X70 @ X72 @ X73 ) @ ( breln1compset @ X70 @ X71 @ X73 ) ) )
| ~ ( breln1 @ X70 @ X73 )
| ~ ( breln1 @ X70 @ X72 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl199,plain,
! [X108: $i,X109: $i] :
( ( breln1 @ X108 @ ( breln1invset @ X108 @ X109 ) )
| ~ ( breln1 @ X108 @ X109 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl199_001,plain,
! [X108: $i,X109: $i] :
( ( breln1 @ X108 @ ( breln1invset @ X108 @ X109 ) )
| ~ ( breln1 @ X108 @ X109 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl178,plain,
! [X64: $i,X65: $i,X66: $i] :
( ~ ( breln1 @ X64 @ X65 )
| ( ( binunion @ X66 @ X65 )
= ( binunion @ X65 @ X66 ) )
| ~ ( breln1 @ X64 @ X66 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( breln1 @ X1 @ X0 )
| ~ ( breln1 @ X1 @ X2 )
| ( ( binunion @ X2 @ ( breln1invset @ X1 @ X0 ) )
= ( binunion @ ( breln1invset @ X1 @ X0 ) @ X2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl199,zip_derived_cl178]) ).
thf(zip_derived_cl183,plain,
breln1 @ sk__160 @ sk__161,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl185,plain,
! [X74: $i,X75: $i] :
( ( X75
= ( breln1invset @ X74 @ ( breln1invset @ X74 @ X75 ) ) )
| ~ ( breln1 @ X74 @ X75 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl182,plain,
breln1 @ sk__160 @ sk__163,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl180,plain,
breln1 @ sk__160 @ sk__162,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl181,plain,
( ( breln1compset @ sk__160 @ ( binunion @ sk__161 @ sk__162 ) @ sk__163 )
!= ( binunion @ ( breln1invset @ sk__160 @ ( breln1compset @ sk__160 @ ( breln1invset @ sk__160 @ sk__163 ) @ ( breln1invset @ sk__160 @ sk__162 ) ) ) @ ( breln1invset @ sk__160 @ ( breln1compset @ sk__160 @ ( breln1invset @ sk__160 @ sk__163 ) @ ( breln1invset @ sk__160 @ sk__161 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl179,plain,
! [X67: $i,X68: $i,X69: $i] :
( ~ ( breln1 @ X67 @ X68 )
| ( ( breln1invset @ X67 @ ( breln1compset @ X67 @ X69 @ X68 ) )
= ( breln1compset @ X67 @ ( breln1invset @ X67 @ X68 ) @ ( breln1invset @ X67 @ X69 ) ) )
| ~ ( breln1 @ X67 @ X69 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13457,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl171,zip_derived_cl184,zip_derived_cl199,zip_derived_cl406,zip_derived_cl183,zip_derived_cl185,zip_derived_cl182,zip_derived_cl180,zip_derived_cl181,zip_derived_cl179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU792^1 : 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.Mb1dtfEyKw true
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:33:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 65.31/9.01 % Solved by lams/40_c_ic.sh.
% 65.31/9.01 % done 1701 iterations in 8.152s
% 65.31/9.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 65.31/9.01 % SZS output start Refutation
% See solution above
% 65.31/9.03
% 65.31/9.03
% 65.31/9.03 % Terminating...
% 65.81/9.11 % Runner terminated.
% 65.81/9.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------