%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU760^1 : 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.qTiUW9wEil true
% Computer : n015.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 19:17:08 EDT 2023
% Result : Theorem 16.48s 3.02s
% Output : Refutation 16.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 388
% Syntax : Number of formulae : 396 ( 105 unt; 286 typ; 0 def)
% Number of atoms : 1597 ( 152 equ; 0 cnn)
% Maximal formula atoms : 392 ( 14 avg)
% Number of connectives : 3414 ( 62 ~; 3 |; 4 &;2065 @)
% ( 0 <=>;1280 =>; 0 <=; 0 <~>)
% Maximal formula depth : 290 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 288 ( 286 usr; 281 con; 0-2 aty)
% Number of variables : 616 ( 0 ^; 612 !; 4 ?; 616 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf(demorgan1a_type,type,
demorgan1a: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(doubleComplementI1_type,type,
doubleComplementI1: $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(woz13rule1_type,type,
woz13rule1: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(binunionTE_type,type,
binunionTE: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(binintersectTERcontra_type,type,
binintersectTERcontra: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(sk__151_type,type,
sk__151: $i ).
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(doubleComplementSub2_type,type,
doubleComplementSub2: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(inIntersectImpInUnion2_type,type,
inIntersectImpInUnion2: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(demorgan2b2_type,type,
demorgan2b2: $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(demorgan2_type,type,
demorgan2: $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(binintersectTELcontra_type,type,
binintersectTELcontra: $o ).
thf(doubleComplementEq_type,type,
doubleComplementEq: $o ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(inComplementUnionImpInComplement1_type,type,
inComplementUnionImpInComplement1: $o ).
thf(complementImpComplementIntersect_type,type,
complementImpComplementIntersect: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(binunionT_lem_type,type,
binunionT_lem: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(doubleComplementE1_type,type,
doubleComplementE1: $o ).
thf(beta1_type,type,
beta1: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(powersetTE1_type,type,
powersetTE1: $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(demorgan2a_type,type,
demorgan2a: $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(inComplementUnionImpNotIn1_type,type,
inComplementUnionImpNotIn1: $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(binunionTIRcontra_type,type,
binunionTIRcontra: $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(setminus_type,type,
setminus: $i > $i > $i ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(binunionTILcontra_type,type,
binunionTILcontra: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(contrasubsetT_type,type,
contrasubsetT: $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(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(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(demorgan2a2_type,type,
demorgan2a2: $o ).
thf(complementUnionInPowersetComplement_type,type,
complementUnionInPowersetComplement: $o ).
thf(sk__152_type,type,
sk__152: $i ).
thf(iftrueorfalse_type,type,
iftrueorfalse: $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(woz13rule0_type,type,
woz13rule0: $o ).
thf(powersetT_lem_type,type,
powersetT_lem: $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(doubleComplementSub1_type,type,
doubleComplementSub1: $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(inIntersectImpInIntersectUnions_type,type,
inIntersectImpInIntersectUnions: $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(subsetTI_type,type,
subsetTI: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(contraSubsetComplement_type,type,
contraSubsetComplement: $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(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(contrasubsetT3_type,type,
contrasubsetT3: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(complementTcontraSubset_type,type,
complementTcontraSubset: $o ).
thf(ifp_type,type,
ifp: $o ).
thf(inIntersectImpInUnion_type,type,
inIntersectImpInUnion: $o ).
thf(powersetTI1_type,type,
powersetTI1: $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(complementTI1_type,type,
complementTI1: $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(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(brelnall2_type,type,
brelnall2: $o ).
thf(setextT_type,type,
setextT: $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(complementInPowersetComplementIntersect_type,type,
complementInPowersetComplementIntersect: $o ).
thf(demorgan1_type,type,
demorgan1: $o ).
thf(setminusT_lem_type,type,
setminusT_lem: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(complementSubsetComplementIntersect_type,type,
complementSubsetComplementIntersect: $o ).
thf(demorgan2b_type,type,
demorgan2b: $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(complementTE1_type,type,
complementTE1: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(app_type,type,
app: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(demorgan2a1_type,type,
demorgan2a1: $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(complementTnotintersectT_type,type,
complementTnotintersectT: $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(powerset_type,type,
powerset: $i > $i ).
thf(binunionTEcontra_type,type,
binunionTEcontra: $o ).
thf(demorgan1b_type,type,
demorgan1b: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(binintersectT_lem_type,type,
binintersectT_lem: $o ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(intersectInPowersetIntersectUnions_type,type,
intersectInPowersetIntersectUnions: $o ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(contrasubsetT2_type,type,
contrasubsetT2: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(singletonprop_type,type,
singletonprop: $o ).
thf(singletonsubset_type,type,
singletonsubset: $o ).
thf(contrasubsetT1_type,type,
contrasubsetT1: $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(sk__153_type,type,
sk__153: $i ).
thf(subset_type,type,
subset: $i > $i > $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(woz13rule1,axiom,
( woz13rule1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
thf('0',plain,
( woz13rule1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X4 ) )
=> ( ( subset @ X6 @ X10 )
=> ( subset @ ( binintersect @ X6 @ X8 ) @ X10 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(woz13rule0,axiom,
( woz13rule0
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) ) ) ).
thf('1',plain,
( woz13rule0
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( binintersect @ X6 @ X8 ) )
=> ( in @ X10 @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan2,axiom,
( demorgan2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
thf('2',plain,
( demorgan2
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binunion @ X6 @ X8 ) )
= ( binintersect @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan2b,axiom,
( demorgan2b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
thf('3',plain,
( demorgan2b
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( binintersect @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) )
=> ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan2a,axiom,
( demorgan2a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
thf('4',plain,
( demorgan2a
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) )
=> ( in @ X10 @ ( binintersect @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan1,axiom,
( demorgan1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
thf('5',plain,
( demorgan1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) )
= ( binunion @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan1b,axiom,
( demorgan1b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
thf('6',plain,
( demorgan1b
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( binunion @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) )
=> ( in @ X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(demorgan1a,axiom,
( demorgan1a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
thf('7',plain,
( demorgan1a
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) )
=> ( in @ X10 @ ( binunion @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(intersectInPowersetIntersectUnions,axiom,
( intersectInPowersetIntersectUnions
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
thf('8',plain,
( intersectInPowersetIntersectUnions
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ ( binintersect @ ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
thf('9',plain,
( inIntersectImpInIntersectUnions
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X4 ) )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) )
=> ( in @ X12 @ ( binintersect @ ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
thf('10',plain,
( inIntersectImpInUnion2
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X4 ) )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) )
=> ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
thf('11',plain,
( inIntersectImpInUnion
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( powerset @ X4 ) )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) )
=> ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
thf('12',plain,
( complementInPowersetComplementIntersect
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
thf('13',plain,
( complementSubsetComplementIntersect
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
thf('14',plain,
( complementImpComplementIntersect
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( setminus @ X4 @ X6 ) )
=> ( in @ X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
thf('15',plain,
( complementTnotintersectT
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ X10 @ ( setminus @ X4 @ X6 ) )
=> ~ ( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ Y )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
thf('16',plain,
( contrasubsetT1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( subset @ X6 @ X8 )
=> ( ~ ( in @ X10 @ X8 )
=> ~ ( in @ X10 @ X6 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
thf('17',plain,
( binintersectTERcontra
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ ( in @ X10 @ X8 )
=> ~ ( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
thf('18',plain,
( binintersectTELcontra
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ ( in @ X10 @ X6 )
=> ~ ( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(subsetTI,axiom,
( subsetTI
= ( ! [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 ) ) )
=> ( subset @ X @ Y ) ) ) ) ) ) ).
thf('19',plain,
( subsetTI
= ( ! [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 ) ) )
=> ( subset @ X6 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
thf('20',plain,
( binintersectT_lem
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ! [X8: $i] :
( ( in @ X8 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(bs114d,axiom,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
thf('21',plain,
( bs114d
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) )
= ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ) ).
thf('22',plain,
( binintersectSubset1
= ( ! [X4: $i,X6: $i] :
( ( ( binintersect @ X4 @ X6 )
= X4 )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ) ).
thf('23',plain,
( binintersectSubset4
= ( ! [X4: $i,X6: $i] :
( ( subset @ X6 @ X4 )
=> ( ( binintersect @ X4 @ X6 )
= X6 ) ) ) ),
define([status(thm)]) ).
thf(binintersectRsub,axiom,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
thf('24',plain,
( binintersectRsub
= ( ! [X4: $i,X6: $i] : ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) ) ),
define([status(thm)]) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) ).
thf('25',plain,
( disjointsetsI1
= ( ! [X4: $i,X6: $i] :
( ~ ? [X8: $i] :
( ( in @ X8 @ X6 )
& ( in @ X8 @ X4 ) )
=> ( ( binintersect @ X4 @ X6 )
= emptyset ) ) ) ),
define([status(thm)]) ).
thf(binintersectER,axiom,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ) ).
thf('26',plain,
( binintersectER
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( binintersect @ X4 @ X6 ) )
=> ( in @ X8 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ) ).
thf('27',plain,
( binintersectSubset3
= ( ! [X4: $i,X6: $i] :
( ( ( binintersect @ X4 @ X6 )
= X6 )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ) ).
thf('28',plain,
( binintersectSubset2
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( binintersect @ X4 @ X6 )
= X4 ) ) ) ),
define([status(thm)]) ).
thf(binintersectLsub,axiom,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
thf('29',plain,
( binintersectLsub
= ( ! [X4: $i,X6: $i] : ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) ) ),
define([status(thm)]) ).
thf(binintersectEL,axiom,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ) ).
thf('30',plain,
( binintersectEL
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( binintersect @ X4 @ X6 ) )
=> ( in @ X8 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
thf('31',plain,
( binintersectSubset5
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X8 @ X4 )
=> ( ( subset @ X8 @ X6 )
=> ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(binintersectI,axiom,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
thf('32',plain,
( binintersectI
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( in @ X8 @ X6 )
=> ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(powersetsubset,axiom,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
thf('33',plain,
( powersetsubset
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(powersetE1,axiom,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ) ).
thf('34',plain,
( powersetE1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(powersetI1,axiom,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf('35',plain,
( powersetI1
= ( ! [X4: $i,X6: $i] :
( ( subset @ X6 @ X4 )
=> ( in @ X6 @ ( powerset @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf('36',plain,
( subsetemptysetimpeq
= ( ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(setextsub,axiom,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf('37',plain,
( setextsub
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X4 )
=> ( X4 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subset2powerset,axiom,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ) ).
thf('38',plain,
( subset2powerset
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( in @ X4 @ ( powerset @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetTrans,axiom,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ) ).
thf('39',plain,
( subsetTrans
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X8 )
=> ( subset @ X4 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetRefl,axiom,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
thf('40',plain,
( subsetRefl
= ( ! [X4: $i] : ( subset @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(notequalI1,axiom,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ) ).
thf('41',plain,
( notequalI1
= ( ! [X4: $i,X6: $i] :
( ~ ( subset @ X4 @ X6 )
=> ( X4 != X6 ) ) ) ),
define([status(thm)]) ).
thf(notsubsetI,axiom,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ) ).
thf('42',plain,
( notsubsetI
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ~ ( in @ X8 @ X6 )
=> ~ ( subset @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetE2,axiom,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ) ).
thf('43',plain,
( subsetE2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ~ ( in @ X8 @ X6 )
=> ~ ( in @ X8 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(subsetE,axiom,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ) ).
thf('44',plain,
( subsetE
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X4 @ X6 )
=> ( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(emptysetsubset,axiom,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
thf('45',plain,
( emptysetsubset
= ( ! [X4: $i] : ( subset @ emptyset @ X4 ) ) ),
define([status(thm)]) ).
thf(subsetI2,axiom,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf('46',plain,
( subsetI2
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ) ).
thf('47',plain,
( eqimpsubset1
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ) ).
thf('48',plain,
( eqimpsubset2
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(subsetI1,axiom,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf('49',plain,
( subsetI1
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(woz13rule2,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
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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
=> ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) )
=> ( ! [X10: $i,X12: $i] :
( ( X10 = X12 )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X14: $i,X16: $i] :
( ( X14 = X16 )
=> ( subset @ X14 @ X16 ) )
=> ( ! [X18: $i,X20: $i] :
( ! [X22: $i] :
( ( in @ X22 @ X18 )
=> ( in @ X22 @ X20 ) )
=> ( subset @ X18 @ X20 ) )
=> ( ! [X24: $i] : ( subset @ emptyset @ X24 )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( subset @ X26 @ X28 )
=> ( ( in @ X30 @ X26 )
=> ( in @ X30 @ X28 ) ) )
=> ( ! [X32: $i,X34: $i,X36: $i] :
( ( subset @ X32 @ X34 )
=> ( ~ ( in @ X36 @ X34 )
=> ~ ( in @ X36 @ X32 ) ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X38 )
=> ( ~ ( in @ X42 @ X40 )
=> ~ ( subset @ X38 @ X40 ) ) )
=> ( ! [X44: $i,X46: $i] :
( ~ ( subset @ X44 @ X46 )
=> ( X44 != X46 ) )
=> ( notequalI2
=> ( ! [X48: $i] : ( subset @ X48 @ X48 )
=> ( ! [X50: $i,X52: $i,X54: $i] :
( ( subset @ X50 @ X52 )
=> ( ( subset @ X52 @ X54 )
=> ( subset @ X50 @ X54 ) ) )
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( ! [X56: $i,X58: $i] :
( ( subset @ X56 @ X58 )
=> ( in @ X56 @ ( powerset @ X58 ) ) )
=> ( ! [X60: $i,X62: $i] :
( ( subset @ X60 @ X62 )
=> ( ( subset @ X62 @ X60 )
=> ( X60 = X62 ) ) )
=> ( ! [X64: $i] :
( ( subset @ X64 @ emptyset )
=> ( X64 = emptyset ) )
=> ( ! [X66: $i,X68: $i] :
( ( subset @ X68 @ X66 )
=> ( in @ X68 @ ( powerset @ X66 ) ) )
=> ( ! [X70: $i,X72: $i] :
( ( in @ X72 @ ( powerset @ X70 ) )
=> ( subset @ X72 @ X70 ) )
=> ( inPowerset
=> ( ! [X74: $i,X76: $i] :
( ( subset @ X74 @ X76 )
=> ( subset @ ( powerset @ X74 ) @ ( powerset @ X76 ) ) )
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( ! [X78: $i,X80: $i,X82: $i] :
( ( in @ X82 @ X78 )
=> ( ( in @ X82 @ X80 )
=> ( in @ X82 @ ( binintersect @ X78 @ X80 ) ) ) )
=> ( ! [X84: $i,X86: $i,X88: $i] :
( ( subset @ X88 @ X84 )
=> ( ( subset @ X88 @ X86 )
=> ( subset @ X88 @ ( binintersect @ X84 @ X86 ) ) ) )
=> ( ! [X90: $i,X92: $i,X94: $i] :
( ( in @ X94 @ ( binintersect @ X90 @ X92 ) )
=> ( in @ X94 @ X90 ) )
=> ( ! [X96: $i,X98: $i] : ( subset @ ( binintersect @ X96 @ X98 ) @ X96 )
=> ( ! [X100: $i,X102: $i] :
( ( subset @ X100 @ X102 )
=> ( ( binintersect @ X100 @ X102 )
= X100 ) )
=> ( ! [X104: $i,X106: $i] :
( ( ( binintersect @ X104 @ X106 )
= X106 )
=> ( subset @ X106 @ X104 ) )
=> ( ! [X108: $i,X110: $i,X112: $i] :
( ( in @ X112 @ ( binintersect @ X108 @ X110 ) )
=> ( in @ X112 @ X110 ) )
=> ( ! [X114: $i,X116: $i] :
( ~ ? [X118: $i] :
( ( in @ X118 @ X116 )
& ( in @ X118 @ X114 ) )
=> ( ( binintersect @ X114 @ X116 )
= emptyset ) )
=> ( ! [X120: $i,X122: $i] : ( subset @ ( binintersect @ X120 @ X122 ) @ X122 )
=> ( ! [X124: $i,X126: $i] :
( ( subset @ X126 @ X124 )
=> ( ( binintersect @ X124 @ X126 )
= X126 ) )
=> ( ! [X128: $i,X130: $i] :
( ( ( binintersect @ X128 @ X130 )
= X128 )
=> ( subset @ X128 @ X130 ) )
=> ( ! [X132: $i,X134: $i,X136: $i] :
( ( binintersect @ X132 @ ( binunion @ X134 @ X136 ) )
= ( binunion @ ( binintersect @ X132 @ X134 ) @ ( binintersect @ X132 @ X136 ) ) )
=> ( 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
=> ( ! [X138: $i,X140: $i] :
( ( in @ X140 @ ( powerset @ X138 ) )
=> ! [X142: $i] :
( ( in @ X142 @ ( powerset @ X138 ) )
=> ( in @ ( binintersect @ X140 @ X142 ) @ ( powerset @ X138 ) ) ) )
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( ! [X144: $i,X146: $i] :
( ( in @ X146 @ ( powerset @ X144 ) )
=> ! [X148: $i] :
( ( in @ X148 @ ( powerset @ X144 ) )
=> ( ! [X150: $i] :
( ( in @ X150 @ X144 )
=> ( ( in @ X150 @ X146 )
=> ( in @ X150 @ X148 ) ) )
=> ( subset @ X146 @ X148 ) ) ) )
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( ! [X152: $i,X154: $i] :
( ( in @ X154 @ ( powerset @ X152 ) )
=> ! [X156: $i] :
( ( in @ X156 @ ( powerset @ X152 ) )
=> ! [X158: $i] :
( ( in @ X158 @ X152 )
=> ( ~ ( in @ X158 @ X154 )
=> ~ ( in @ X158 @ ( binintersect @ X154 @ X156 ) ) ) ) ) )
=> ( ! [X160: $i,X162: $i] :
( ( in @ X162 @ ( powerset @ X160 ) )
=> ! [X164: $i] :
( ( in @ X164 @ ( powerset @ X160 ) )
=> ! [X166: $i] :
( ( in @ X166 @ X160 )
=> ( ~ ( in @ X166 @ X164 )
=> ~ ( in @ X166 @ ( binintersect @ X162 @ X164 ) ) ) ) ) )
=> ( contrasubsetT
=> ( ! [X168: $i,X170: $i] :
( ( in @ X170 @ ( powerset @ X168 ) )
=> ! [X172: $i] :
( ( in @ X172 @ ( powerset @ X168 ) )
=> ! [X174: $i] :
( ( in @ X174 @ X168 )
=> ( ( subset @ X170 @ X172 )
=> ( ~ ( in @ X174 @ X172 )
=> ~ ( in @ X174 @ X170 ) ) ) ) ) )
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( ! [X176: $i,X178: $i] :
( ( in @ X178 @ ( powerset @ X176 ) )
=> ! [X180: $i] :
( ( in @ X180 @ ( powerset @ X176 ) )
=> ! [X182: $i] :
( ( in @ X182 @ X176 )
=> ( ( in @ X182 @ ( setminus @ X176 @ X178 ) )
=> ~ ( in @ X182 @ ( binintersect @ X178 @ X180 ) ) ) ) ) )
=> ( ! [X184: $i,X186: $i] :
( ( in @ X186 @ ( powerset @ X184 ) )
=> ! [X188: $i] :
( ( in @ X188 @ ( powerset @ X184 ) )
=> ! [X190: $i] :
( ( in @ X190 @ X184 )
=> ( ( in @ X190 @ ( setminus @ X184 @ X186 ) )
=> ( in @ X190 @ ( setminus @ X184 @ ( binintersect @ X186 @ X188 ) ) ) ) ) ) )
=> ( ! [X192: $i,X194: $i] :
( ( in @ X194 @ ( powerset @ X192 ) )
=> ! [X196: $i] :
( ( in @ X196 @ ( powerset @ X192 ) )
=> ( subset @ ( setminus @ X192 @ X194 ) @ ( setminus @ X192 @ ( binintersect @ X194 @ X196 ) ) ) ) )
=> ( ! [X198: $i,X200: $i] :
( ( in @ X200 @ ( powerset @ X198 ) )
=> ! [X202: $i] :
( ( in @ X202 @ ( powerset @ X198 ) )
=> ( in @ ( setminus @ X198 @ X200 ) @ ( powerset @ ( setminus @ X198 @ ( binintersect @ X200 @ X202 ) ) ) ) ) )
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( ! [X204: $i,X206: $i] :
( ( in @ X206 @ ( powerset @ X204 ) )
=> ! [X208: $i] :
( ( in @ X208 @ ( powerset @ X204 ) )
=> ! [X210: $i] :
( ( in @ X210 @ ( powerset @ X204 ) )
=> ! [X212: $i] :
( ( in @ X212 @ X204 )
=> ( ( in @ X212 @ ( binintersect @ X206 @ X208 ) )
=> ( in @ X212 @ ( binunion @ X206 @ X210 ) ) ) ) ) ) )
=> ( ! [X214: $i,X216: $i] :
( ( in @ X216 @ ( powerset @ X214 ) )
=> ! [X218: $i] :
( ( in @ X218 @ ( powerset @ X214 ) )
=> ! [X220: $i] :
( ( in @ X220 @ ( powerset @ X214 ) )
=> ! [X222: $i] :
( ( in @ X222 @ X214 )
=> ( ( in @ X222 @ ( binintersect @ X216 @ X218 ) )
=> ( in @ X222 @ ( binunion @ X218 @ X220 ) ) ) ) ) ) )
=> ( ! [X224: $i,X226: $i] :
( ( in @ X226 @ ( powerset @ X224 ) )
=> ! [X228: $i] :
( ( in @ X228 @ ( powerset @ X224 ) )
=> ! [X230: $i] :
( ( in @ X230 @ ( powerset @ X224 ) )
=> ! [X232: $i] :
( ( in @ X232 @ X224 )
=> ( ( in @ X232 @ ( binintersect @ X226 @ X228 ) )
=> ( in @ X232 @ ( binintersect @ ( binunion @ X226 @ X230 ) @ ( binunion @ X228 @ X230 ) ) ) ) ) ) ) )
=> ( ! [X234: $i,X236: $i] :
( ( in @ X236 @ ( powerset @ X234 ) )
=> ! [X238: $i] :
( ( in @ X238 @ ( powerset @ X234 ) )
=> ! [X240: $i] :
( ( in @ X240 @ ( powerset @ X234 ) )
=> ( in @ ( binintersect @ X236 @ X238 ) @ ( powerset @ ( binintersect @ ( binunion @ X236 @ X240 ) @ ( binunion @ X238 @ X240 ) ) ) ) ) ) )
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( ! [X242: $i,X244: $i] :
( ( in @ X244 @ ( powerset @ X242 ) )
=> ! [X246: $i] :
( ( in @ X246 @ ( powerset @ X242 ) )
=> ! [X248: $i] :
( ( in @ X248 @ X242 )
=> ( ( in @ X248 @ ( setminus @ X242 @ ( binintersect @ X244 @ X246 ) ) )
=> ( in @ X248 @ ( binunion @ ( setminus @ X242 @ X244 ) @ ( setminus @ X242 @ X246 ) ) ) ) ) ) )
=> ( ! [X250: $i,X252: $i] :
( ( in @ X252 @ ( powerset @ X250 ) )
=> ! [X254: $i] :
( ( in @ X254 @ ( powerset @ X250 ) )
=> ! [X256: $i] :
( ( in @ X256 @ X250 )
=> ( ( in @ X256 @ ( binunion @ ( setminus @ X250 @ X252 ) @ ( setminus @ X250 @ X254 ) ) )
=> ( in @ X256 @ ( setminus @ X250 @ ( binintersect @ X252 @ X254 ) ) ) ) ) ) )
=> ( ! [X258: $i,X260: $i] :
( ( in @ X260 @ ( powerset @ X258 ) )
=> ! [X262: $i] :
( ( in @ X262 @ ( powerset @ X258 ) )
=> ( ( setminus @ X258 @ ( binintersect @ X260 @ X262 ) )
= ( binunion @ ( setminus @ X258 @ X260 ) @ ( setminus @ X258 @ X262 ) ) ) ) )
=> ( ! [X264: $i,X266: $i] :
( ( in @ X266 @ ( powerset @ X264 ) )
=> ! [X268: $i] :
( ( in @ X268 @ ( powerset @ X264 ) )
=> ! [X270: $i] :
( ( in @ X270 @ X264 )
=> ( ( in @ X270 @ ( setminus @ X264 @ ( binunion @ X266 @ X268 ) ) )
=> ( in @ X270 @ ( binintersect @ ( setminus @ X264 @ X266 ) @ ( setminus @ X264 @ X268 ) ) ) ) ) ) )
=> ( demorgan2b2
=> ( ! [X272: $i,X274: $i] :
( ( in @ X274 @ ( powerset @ X272 ) )
=> ! [X276: $i] :
( ( in @ X276 @ ( powerset @ X272 ) )
=> ! [X278: $i] :
( ( in @ X278 @ X272 )
=> ( ( in @ X278 @ ( binintersect @ ( setminus @ X272 @ X274 ) @ ( setminus @ X272 @ X276 ) ) )
=> ( in @ X278 @ ( setminus @ X272 @ ( binunion @ X274 @ X276 ) ) ) ) ) ) )
=> ( ! [X280: $i,X282: $i] :
( ( in @ X282 @ ( powerset @ X280 ) )
=> ! [X284: $i] :
( ( in @ X284 @ ( powerset @ X280 ) )
=> ( ( setminus @ X280 @ ( binunion @ X282 @ X284 ) )
= ( binintersect @ ( setminus @ X280 @ X282 ) @ ( setminus @ X280 @ X284 ) ) ) ) )
=> ( ! [X286: $i,X288: $i] :
( ( in @ X288 @ ( powerset @ X286 ) )
=> ! [X290: $i] :
( ( in @ X290 @ ( powerset @ X286 ) )
=> ! [X292: $i] :
( ( in @ X292 @ ( binintersect @ X288 @ X290 ) )
=> ( in @ X292 @ X286 ) ) ) )
=> ( ! [X294: $i,X296: $i] :
( ( in @ X296 @ ( powerset @ X294 ) )
=> ! [X298: $i] :
( ( in @ X298 @ ( powerset @ X294 ) )
=> ! [X300: $i] :
( ( in @ X300 @ ( powerset @ X294 ) )
=> ( ( subset @ X296 @ X300 )
=> ( subset @ ( binintersect @ X296 @ X298 ) @ X300 ) ) ) ) )
=> ! [X302: $i,X304: $i] :
( ( in @ X304 @ ( powerset @ X302 ) )
=> ! [X306: $i] :
( ( in @ X306 @ ( powerset @ X302 ) )
=> ! [X308: $i] :
( ( in @ X308 @ ( powerset @ X302 ) )
=> ( ( subset @ X306 @ X308 )
=> ( subset @ ( binintersect @ X304 @ X306 ) @ X308 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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
=> ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) )
=> ( ! [X10: $i,X12: $i] :
( ( X10 = X12 )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X14: $i,X16: $i] :
( ( X14 = X16 )
=> ( subset @ X14 @ X16 ) )
=> ( ! [X18: $i,X20: $i] :
( ! [X22: $i] :
( ( in @ X22 @ X18 )
=> ( in @ X22 @ X20 ) )
=> ( subset @ X18 @ X20 ) )
=> ( ! [X24: $i] : ( subset @ emptyset @ X24 )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( subset @ X26 @ X28 )
=> ( ( in @ X30 @ X26 )
=> ( in @ X30 @ X28 ) ) )
=> ( ! [X32: $i,X34: $i,X36: $i] :
( ( subset @ X32 @ X34 )
=> ( ~ ( in @ X36 @ X34 )
=> ~ ( in @ X36 @ X32 ) ) )
=> ( ! [X38: $i,X40: $i,X42: $i] :
( ( in @ X42 @ X38 )
=> ( ~ ( in @ X42 @ X40 )
=> ~ ( subset @ X38 @ X40 ) ) )
=> ( ! [X44: $i,X46: $i] :
( ~ ( subset @ X44 @ X46 )
=> ( X44 != X46 ) )
=> ( notequalI2
=> ( ! [X48: $i] : ( subset @ X48 @ X48 )
=> ( ! [X50: $i,X52: $i,X54: $i] :
( ( subset @ X50 @ X52 )
=> ( ( subset @ X52 @ X54 )
=> ( subset @ X50 @ X54 ) ) )
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( ! [X56: $i,X58: $i] :
( ( subset @ X56 @ X58 )
=> ( in @ X56 @ ( powerset @ X58 ) ) )
=> ( ! [X60: $i,X62: $i] :
( ( subset @ X60 @ X62 )
=> ( ( subset @ X62 @ X60 )
=> ( X60 = X62 ) ) )
=> ( ! [X64: $i] :
( ( subset @ X64 @ emptyset )
=> ( X64 = emptyset ) )
=> ( ! [X66: $i,X68: $i] :
( ( subset @ X68 @ X66 )
=> ( in @ X68 @ ( powerset @ X66 ) ) )
=> ( ! [X70: $i,X72: $i] :
( ( in @ X72 @ ( powerset @ X70 ) )
=> ( subset @ X72 @ X70 ) )
=> ( inPowerset
=> ( ! [X74: $i,X76: $i] :
( ( subset @ X74 @ X76 )
=> ( subset @ ( powerset @ X74 ) @ ( powerset @ X76 ) ) )
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( ! [X78: $i,X80: $i,X82: $i] :
( ( in @ X82 @ X78 )
=> ( ( in @ X82 @ X80 )
=> ( in @ X82 @ ( binintersect @ X78 @ X80 ) ) ) )
=> ( ! [X84: $i,X86: $i,X88: $i] :
( ( subset @ X88 @ X84 )
=> ( ( subset @ X88 @ X86 )
=> ( subset @ X88 @ ( binintersect @ X84 @ X86 ) ) ) )
=> ( ! [X90: $i,X92: $i,X94: $i] :
( ( in @ X94 @ ( binintersect @ X90 @ X92 ) )
=> ( in @ X94 @ X90 ) )
=> ( ! [X96: $i,X98: $i] : ( subset @ ( binintersect @ X96 @ X98 ) @ X96 )
=> ( ! [X100: $i,X102: $i] :
( ( subset @ X100 @ X102 )
=> ( ( binintersect @ X100 @ X102 )
= X100 ) )
=> ( ! [X104: $i,X106: $i] :
( ( ( binintersect @ X104 @ X106 )
= X106 )
=> ( subset @ X106 @ X104 ) )
=> ( ! [X108: $i,X110: $i,X112: $i] :
( ( in @ X112 @ ( binintersect @ X108 @ X110 ) )
=> ( in @ X112 @ X110 ) )
=> ( ! [X114: $i,X116: $i] :
( ~ ? [X118: $i] :
( ( in @ X118 @ X116 )
& ( in @ X118 @ X114 ) )
=> ( ( binintersect @ X114 @ X116 )
= emptyset ) )
=> ( ! [X120: $i,X122: $i] : ( subset @ ( binintersect @ X120 @ X122 ) @ X122 )
=> ( ! [X124: $i,X126: $i] :
( ( subset @ X126 @ X124 )
=> ( ( binintersect @ X124 @ X126 )
= X126 ) )
=> ( ! [X128: $i,X130: $i] :
( ( ( binintersect @ X128 @ X130 )
= X128 )
=> ( subset @ X128 @ X130 ) )
=> ( ! [X132: $i,X134: $i,X136: $i] :
( ( binintersect @ X132 @ ( binunion @ X134 @ X136 ) )
= ( binunion @ ( binintersect @ X132 @ X134 ) @ ( binintersect @ X132 @ X136 ) ) )
=> ( 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
=> ( ! [X138: $i,X140: $i] :
( ( in @ X140 @ ( powerset @ X138 ) )
=> ! [X142: $i] :
( ( in @ X142 @ ( powerset @ X138 ) )
=> ( in @ ( binintersect @ X140 @ X142 ) @ ( powerset @ X138 ) ) ) )
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( ! [X144: $i,X146: $i] :
( ( in @ X146 @ ( powerset @ X144 ) )
=> ! [X148: $i] :
( ( in @ X148 @ ( powerset @ X144 ) )
=> ( ! [X150: $i] :
( ( in @ X150 @ X144 )
=> ( ( in @ X150 @ X146 )
=> ( in @ X150 @ X148 ) ) )
=> ( subset @ X146 @ X148 ) ) ) )
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( ! [X152: $i,X154: $i] :
( ( in @ X154 @ ( powerset @ X152 ) )
=> ! [X156: $i] :
( ( in @ X156 @ ( powerset @ X152 ) )
=> ! [X158: $i] :
( ( in @ X158 @ X152 )
=> ( ~ ( in @ X158 @ X154 )
=> ~ ( in @ X158 @ ( binintersect @ X154 @ X156 ) ) ) ) ) )
=> ( ! [X160: $i,X162: $i] :
( ( in @ X162 @ ( powerset @ X160 ) )
=> ! [X164: $i] :
( ( in @ X164 @ ( powerset @ X160 ) )
=> ! [X166: $i] :
( ( in @ X166 @ X160 )
=> ( ~ ( in @ X166 @ X164 )
=> ~ ( in @ X166 @ ( binintersect @ X162 @ X164 ) ) ) ) ) )
=> ( contrasubsetT
=> ( ! [X168: $i,X170: $i] :
( ( in @ X170 @ ( powerset @ X168 ) )
=> ! [X172: $i] :
( ( in @ X172 @ ( powerset @ X168 ) )
=> ! [X174: $i] :
( ( in @ X174 @ X168 )
=> ( ( subset @ X170 @ X172 )
=> ( ~ ( in @ X174 @ X172 )
=> ~ ( in @ X174 @ X170 ) ) ) ) ) )
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( ! [X176: $i,X178: $i] :
( ( in @ X178 @ ( powerset @ X176 ) )
=> ! [X180: $i] :
( ( in @ X180 @ ( powerset @ X176 ) )
=> ! [X182: $i] :
( ( in @ X182 @ X176 )
=> ( ( in @ X182 @ ( setminus @ X176 @ X178 ) )
=> ~ ( in @ X182 @ ( binintersect @ X178 @ X180 ) ) ) ) ) )
=> ( ! [X184: $i,X186: $i] :
( ( in @ X186 @ ( powerset @ X184 ) )
=> ! [X188: $i] :
( ( in @ X188 @ ( powerset @ X184 ) )
=> ! [X190: $i] :
( ( in @ X190 @ X184 )
=> ( ( in @ X190 @ ( setminus @ X184 @ X186 ) )
=> ( in @ X190 @ ( setminus @ X184 @ ( binintersect @ X186 @ X188 ) ) ) ) ) ) )
=> ( ! [X192: $i,X194: $i] :
( ( in @ X194 @ ( powerset @ X192 ) )
=> ! [X196: $i] :
( ( in @ X196 @ ( powerset @ X192 ) )
=> ( subset @ ( setminus @ X192 @ X194 ) @ ( setminus @ X192 @ ( binintersect @ X194 @ X196 ) ) ) ) )
=> ( ! [X198: $i,X200: $i] :
( ( in @ X200 @ ( powerset @ X198 ) )
=> ! [X202: $i] :
( ( in @ X202 @ ( powerset @ X198 ) )
=> ( in @ ( setminus @ X198 @ X200 ) @ ( powerset @ ( setminus @ X198 @ ( binintersect @ X200 @ X202 ) ) ) ) ) )
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( ! [X204: $i,X206: $i] :
( ( in @ X206 @ ( powerset @ X204 ) )
=> ! [X208: $i] :
( ( in @ X208 @ ( powerset @ X204 ) )
=> ! [X210: $i] :
( ( in @ X210 @ ( powerset @ X204 ) )
=> ! [X212: $i] :
( ( in @ X212 @ X204 )
=> ( ( in @ X212 @ ( binintersect @ X206 @ X208 ) )
=> ( in @ X212 @ ( binunion @ X206 @ X210 ) ) ) ) ) ) )
=> ( ! [X214: $i,X216: $i] :
( ( in @ X216 @ ( powerset @ X214 ) )
=> ! [X218: $i] :
( ( in @ X218 @ ( powerset @ X214 ) )
=> ! [X220: $i] :
( ( in @ X220 @ ( powerset @ X214 ) )
=> ! [X222: $i] :
( ( in @ X222 @ X214 )
=> ( ( in @ X222 @ ( binintersect @ X216 @ X218 ) )
=> ( in @ X222 @ ( binunion @ X218 @ X220 ) ) ) ) ) ) )
=> ( ! [X224: $i,X226: $i] :
( ( in @ X226 @ ( powerset @ X224 ) )
=> ! [X228: $i] :
( ( in @ X228 @ ( powerset @ X224 ) )
=> ! [X230: $i] :
( ( in @ X230 @ ( powerset @ X224 ) )
=> ! [X232: $i] :
( ( in @ X232 @ X224 )
=> ( ( in @ X232 @ ( binintersect @ X226 @ X228 ) )
=> ( in @ X232 @ ( binintersect @ ( binunion @ X226 @ X230 ) @ ( binunion @ X228 @ X230 ) ) ) ) ) ) ) )
=> ( ! [X234: $i,X236: $i] :
( ( in @ X236 @ ( powerset @ X234 ) )
=> ! [X238: $i] :
( ( in @ X238 @ ( powerset @ X234 ) )
=> ! [X240: $i] :
( ( in @ X240 @ ( powerset @ X234 ) )
=> ( in @ ( binintersect @ X236 @ X238 ) @ ( powerset @ ( binintersect @ ( binunion @ X236 @ X240 ) @ ( binunion @ X238 @ X240 ) ) ) ) ) ) )
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( ! [X242: $i,X244: $i] :
( ( in @ X244 @ ( powerset @ X242 ) )
=> ! [X246: $i] :
( ( in @ X246 @ ( powerset @ X242 ) )
=> ! [X248: $i] :
( ( in @ X248 @ X242 )
=> ( ( in @ X248 @ ( setminus @ X242 @ ( binintersect @ X244 @ X246 ) ) )
=> ( in @ X248 @ ( binunion @ ( setminus @ X242 @ X244 ) @ ( setminus @ X242 @ X246 ) ) ) ) ) ) )
=> ( ! [X250: $i,X252: $i] :
( ( in @ X252 @ ( powerset @ X250 ) )
=> ! [X254: $i] :
( ( in @ X254 @ ( powerset @ X250 ) )
=> ! [X256: $i] :
( ( in @ X256 @ X250 )
=> ( ( in @ X256 @ ( binunion @ ( setminus @ X250 @ X252 ) @ ( setminus @ X250 @ X254 ) ) )
=> ( in @ X256 @ ( setminus @ X250 @ ( binintersect @ X252 @ X254 ) ) ) ) ) ) )
=> ( ! [X258: $i,X260: $i] :
( ( in @ X260 @ ( powerset @ X258 ) )
=> ! [X262: $i] :
( ( in @ X262 @ ( powerset @ X258 ) )
=> ( ( setminus @ X258 @ ( binintersect @ X260 @ X262 ) )
= ( binunion @ ( setminus @ X258 @ X260 ) @ ( setminus @ X258 @ X262 ) ) ) ) )
=> ( ! [X264: $i,X266: $i] :
( ( in @ X266 @ ( powerset @ X264 ) )
=> ! [X268: $i] :
( ( in @ X268 @ ( powerset @ X264 ) )
=> ! [X270: $i] :
( ( in @ X270 @ X264 )
=> ( ( in @ X270 @ ( setminus @ X264 @ ( binunion @ X266 @ X268 ) ) )
=> ( in @ X270 @ ( binintersect @ ( setminus @ X264 @ X266 ) @ ( setminus @ X264 @ X268 ) ) ) ) ) ) )
=> ( demorgan2b2
=> ( ! [X272: $i,X274: $i] :
( ( in @ X274 @ ( powerset @ X272 ) )
=> ! [X276: $i] :
( ( in @ X276 @ ( powerset @ X272 ) )
=> ! [X278: $i] :
( ( in @ X278 @ X272 )
=> ( ( in @ X278 @ ( binintersect @ ( setminus @ X272 @ X274 ) @ ( setminus @ X272 @ X276 ) ) )
=> ( in @ X278 @ ( setminus @ X272 @ ( binunion @ X274 @ X276 ) ) ) ) ) ) )
=> ( ! [X280: $i,X282: $i] :
( ( in @ X282 @ ( powerset @ X280 ) )
=> ! [X284: $i] :
( ( in @ X284 @ ( powerset @ X280 ) )
=> ( ( setminus @ X280 @ ( binunion @ X282 @ X284 ) )
= ( binintersect @ ( setminus @ X280 @ X282 ) @ ( setminus @ X280 @ X284 ) ) ) ) )
=> ( ! [X286: $i,X288: $i] :
( ( in @ X288 @ ( powerset @ X286 ) )
=> ! [X290: $i] :
( ( in @ X290 @ ( powerset @ X286 ) )
=> ! [X292: $i] :
( ( in @ X292 @ ( binintersect @ X288 @ X290 ) )
=> ( in @ X292 @ X286 ) ) ) )
=> ( ! [X294: $i,X296: $i] :
( ( in @ X296 @ ( powerset @ X294 ) )
=> ! [X298: $i] :
( ( in @ X298 @ ( powerset @ X294 ) )
=> ! [X300: $i] :
( ( in @ X300 @ ( powerset @ X294 ) )
=> ( ( subset @ X296 @ X300 )
=> ( subset @ ( binintersect @ X296 @ X298 ) @ X300 ) ) ) ) )
=> ! [X302: $i,X304: $i] :
( ( in @ X304 @ ( powerset @ X302 ) )
=> ! [X306: $i] :
( ( in @ X306 @ ( powerset @ X302 ) )
=> ! [X308: $i] :
( ( in @ X308 @ ( powerset @ X302 ) )
=> ( ( subset @ X306 @ X308 )
=> ( subset @ ( binintersect @ X304 @ X306 ) @ X308 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl228,plain,
! [X114: $i,X115: $i] : ( subset @ ( binintersect @ X114 @ X115 ) @ X115 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl44,plain,
! [X10: $i,X11: $i,X12: $i] :
( ~ ( subset @ X10 @ X11 )
| ( subset @ X10 @ X12 )
| ~ ( subset @ X11 @ X12 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( subset @ X0 @ X2 )
| ( subset @ ( binintersect @ X1 @ X0 ) @ X2 ) ),
inference('sup-',[status(thm)],[zip_derived_cl228,zip_derived_cl44]) ).
thf(zip_derived_cl144,plain,
~ ( subset @ ( binintersect @ sk__151 @ sk__152 ) @ sk__153 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4963,plain,
~ ( subset @ sk__152 @ sk__153 ),
inference('sup-',[status(thm)],[zip_derived_cl435,zip_derived_cl144]) ).
thf(zip_derived_cl143,plain,
subset @ sk__152 @ sk__153,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5067,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl4963,zip_derived_cl143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU760^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qTiUW9wEil true
% 0.14/0.35 % Computer : n015.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 13:49:19 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
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.20/0.67 % Total configuration time : 828
% 0.20/0.67 % Estimated wc time : 1656
% 0.20/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 16.48/3.02 % Solved by lams/40_c_ic.sh.
% 16.48/3.02 % done 1308 iterations in 2.179s
% 16.48/3.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.48/3.02 % SZS output start Refutation
% See solution above
% 16.48/3.04
% 16.48/3.04
% 16.48/3.04 % Terminating...
% 18.13/3.10 % Runner terminated.
% 18.13/3.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------