%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU781^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hjryeDVtnX true
% Computer : n026.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 19:17:33 EDT 2023
% Result : Theorem 177.26s 23.65s
% Output : Refutation 177.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 334
% Syntax : Number of formulae : 347 ( 30 unt; 310 typ; 0 def)
% Number of atoms : 1189 ( 47 equ; 0 cnn)
% Maximal formula atoms : 349 ( 32 avg)
% Number of connectives : 1977 ( 20 ~; 18 |; 8 &; 829 @)
% ( 0 <=>;1102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 319 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 312 ( 310 usr; 304 con; 0-5 aty)
% Number of variables : 247 ( 6 ^; 237 !; 4 ?; 247 :)
% 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(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(beta1_type,type,
beta1: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(doubleComplementE1_type,type,
doubleComplementE1: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(doubleComplementI1_type,type,
doubleComplementI1: $o ).
thf(exuI1_type,type,
exuI1: $o ).
thf(binunionTEcontra_type,type,
binunionTEcontra: $o ).
thf(exuI2_type,type,
exuI2: $o ).
thf(notequalI2_type,type,
notequalI2: $o ).
thf(sk__55_type,type,
sk__55: $i ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(demorgan1b_type,type,
demorgan1b: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(demorgan2a_type,type,
demorgan2a: $o ).
thf(subsetTI_type,type,
subsetTI: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(binintersectT_lem_type,type,
binintersectT_lem: $o ).
thf(funcGraphProp4_type,type,
funcGraphProp4: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(complementImpComplementIntersect_type,type,
complementImpComplementIntersect: $o ).
thf(sk__54_type,type,
sk__54: $i ).
thf(setukpairinjR2_type,type,
setukpairinjR2: $o ).
thf(singletonsuniq_type,type,
singletonsuniq: $o ).
thf(binunionT_lem_type,type,
binunionT_lem: $o ).
thf(inIntersectImpInUnion2_type,type,
inIntersectImpInUnion2: $o ).
thf(sk__53_type,type,
sk__53: $i ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(complementTcontraSubset_type,type,
complementTcontraSubset: $o ).
thf(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(doubleComplementEq_type,type,
doubleComplementEq: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(funcextLem_type,type,
funcextLem: $o ).
thf(iftrueorfalse_type,type,
iftrueorfalse: $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(demorgan2b2_type,type,
demorgan2b2: $o ).
thf(breln1compE_type,type,
breln1compE: $o ).
thf(demorgan2b_type,type,
demorgan2b: $o ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(ex1E1_type,type,
ex1E1: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(breln1invprop_type,type,
breln1invprop: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(lam2p_type,type,
lam2p: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(ubforcartprodlem1_type,type,
ubforcartprodlem1: $o ).
thf(binintersectTERcontra_type,type,
binintersectTERcontra: $o ).
thf(theeq_type,type,
theeq: $o ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(theprop_type,type,
theprop: $o ).
thf(complementInPowersetComplementIntersect_type,type,
complementInPowersetComplementIntersect: $o ).
thf(complementTnotintersectT_type,type,
complementTnotintersectT: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(infuncsetfunc_type,type,
infuncsetfunc: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(setextT_type,type,
setextT: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(sk__59_type,type,
sk__59: $i > $i > $i > $i > $i > $i ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(ap2p_type,type,
ap2p: $o ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(ex1I2_type,type,
ex1I2: $o ).
thf(dpsetconstrEL2_type,type,
dpsetconstrEL2: $o ).
thf(woz1_1_type,type,
woz1_1: $o ).
thf(demorgan1_type,type,
demorgan1: $o ).
thf(binintersectTELcontra_type,type,
binintersectTELcontra: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(breln1compI_type,type,
breln1compI: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(doubleComplementSub1_type,type,
doubleComplementSub1: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(setbeta_type,type,
setbeta: $o ).
thf(binunionTE_type,type,
binunionTE: $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(iftrueProp1_type,type,
iftrueProp1: $o ).
thf(powersetTE1_type,type,
powersetTE1: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(app_type,type,
app: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(inComplementUnionImpInComplement1_type,type,
inComplementUnionImpInComplement1: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(lamp_type,type,
lamp: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(ifSingleton_type,type,
ifSingleton: $o ).
thf(iffalse_type,type,
iffalse: $o ).
thf(singletoninpowunion_type,type,
singletoninpowunion: $o ).
thf(inIntersectImpInUnion_type,type,
inIntersectImpInUnion: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(cartprodmempair_type,type,
cartprodmempair: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(cartprodpairsurjEq_type,type,
cartprodpairsurjEq: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(funcext2_type,type,
funcext2: $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(binintersectSubset2_type,type,
binintersectSubset2: $o ).
thf(setunionI_type,type,
setunionI: $o ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(prop2setI_type,type,
prop2setI: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf(setminusER_type,type,
setminusER: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(dpsetconstrEL1_type,type,
dpsetconstrEL1: $o ).
thf(setukpairinjR12_type,type,
setukpairinjR12: $o ).
thf(binunionTILcontra_type,type,
binunionTILcontra: $o ).
thf(complementTI1_type,type,
complementTI1: $o ).
thf(inComplementUnionImpNotIn1_type,type,
inComplementUnionImpNotIn1: $o ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(dpsetconstrER_type,type,
dpsetconstrER: $o ).
thf(subbreln1_type,type,
subbreln1: $o ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(upairequniteq_type,type,
upairequniteq: $o ).
thf(woz1_4_type,type,
woz1_4: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(kpairp_type,type,
kpairp: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(eta1_type,type,
eta1: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(contrasubsetT1_type,type,
contrasubsetT1: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(eta2_type,type,
eta2: $o ).
thf(contrasubsetT3_type,type,
contrasubsetT3: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(setunionsingleton1_type,type,
setunionsingleton1: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(setminusT_lem_type,type,
setminusT_lem: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(iftrue_type,type,
iftrue: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(doubleComplementSub2_type,type,
doubleComplementSub2: $o ).
thf(woz1_5_type,type,
woz1_5: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $o ).
thf(beta2_type,type,
beta2: $o ).
thf(complementSubsetComplementIntersect_type,type,
complementSubsetComplementIntersect: $o ).
thf(brelnall2_type,type,
brelnall2: $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(ifp_type,type,
ifp: $o ).
thf(setminusLsub_type,type,
setminusLsub: $o ).
thf(woz1_3_type,type,
woz1_3: $o ).
thf(notinsingleton_type,type,
notinsingleton: $o ).
thf(eqimpsubset2_type,type,
eqimpsubset2: $o ).
thf(exuEu_type,type,
exuEu: $o ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(upairsetE_type,type,
upairsetE: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(breln1invI_type,type,
breln1invI: $o ).
thf(complementTE1_type,type,
complementTE1: $o ).
thf(contrasubsetT2_type,type,
contrasubsetT2: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(intersectInPowersetIntersectUnions_type,type,
intersectInPowersetIntersectUnions: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(setOfPairsIsBReln1_type,type,
setOfPairsIsBReln1: $o ).
thf(breln1SetBreln1_type,type,
breln1SetBreln1: $o ).
thf(sk__57_type,type,
sk__57: $i ).
thf(breln1compset_type,type,
breln1compset: $i > $i > $i > $i ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(breln1all2_type,type,
breln1all2: $o ).
thf(woz13rule0_type,type,
woz13rule0: $o ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(contraSubsetComplement_type,type,
contraSubsetComplement: $o ).
thf(woz1_2_type,type,
woz1_2: $o ).
thf(sk__56_type,type,
sk__56: $i ).
thf(binintersectLsub_type,type,
binintersectLsub: $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(symdiffE_type,type,
symdiffE: $o ).
thf(descrp_type,type,
descrp: $o ).
thf(dsetconstr__Cong_type,type,
dsetconstr__Cong: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyI_type,type,
emptyI: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(binintersectEL_type,type,
binintersectEL: $o ).
thf(emptyE1_type,type,
emptyE1: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(demorgan2_type,type,
demorgan2: $o ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(ex1E2_type,type,
ex1E2: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(woz13rule3_type,type,
woz13rule3: $o ).
thf(iffalseProp2_type,type,
iffalseProp2: $o ).
thf(woz13rule2_type,type,
woz13rule2: $o ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(breln1invE_type,type,
breln1invE: $o ).
thf(lam2lamEq_type,type,
lam2lamEq: $o ).
thf(choice2fnsingleton_type,type,
choice2fnsingleton: $o ).
thf(apProp_type,type,
apProp: $o ).
thf(dpsetconstrSub_type,type,
dpsetconstrSub: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(iffalseProp1_type,type,
iffalseProp1: $o ).
thf(demorgan2a2_type,type,
demorgan2a2: $o ).
thf(powersetT_lem_type,type,
powersetT_lem: $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(breln1compprop_type,type,
breln1compprop: $o ).
thf(setminusSubset2_type,type,
setminusSubset2: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(inIntersectImpInIntersectUnions_type,type,
inIntersectImpInIntersectUnions: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(binunionTIRcontra_type,type,
binunionTIRcontra: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(woz13rule4_type,type,
woz13rule4: $o ).
thf(breln1all1_type,type,
breln1all1: $o ).
thf(setunionsingleton2_type,type,
setunionsingleton2: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(eqbreln1_type,type,
eqbreln1: $o ).
thf(woz13rule1_type,type,
woz13rule1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(notdallE_type,type,
notdallE: $o ).
thf(demorgan1a_type,type,
demorgan1a: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(ap2apEq2_type,type,
ap2apEq2: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(sk__58_type,type,
sk__58: $o ).
thf(subbreln_type,type,
subbreln: $o ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(iftrueProp2_type,type,
iftrueProp2: $o ).
thf(cartprodsndin_type,type,
cartprodsndin: $o ).
thf(contrasubsetT_type,type,
contrasubsetT: $o ).
thf(powersetTI1_type,type,
powersetTI1: $o ).
thf(funcext_type,type,
funcext: $o ).
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(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(demorgan2a1_type,type,
demorgan2a1: $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(complementUnionInPowersetComplement_type,type,
complementUnionInPowersetComplement: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(ap2apEq1_type,type,
ap2apEq1: $o ).
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('0',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('1',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('2',plain,
( breln1compprop
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( breln1 @ X4 @ ( breln1compset @ X4 @ X6 @ X8 ) ) ) ) ) ),
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('3',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('4',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('5',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('6',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(breln1,axiom,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
thf('7',plain,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln1]) ).
thf('8',plain,
( breln1
= ( ^ [V_1: $i,V_2: $i] : ( breln @ V_1 @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
thf('9',plain,
( cartprodmempaircEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( kpair @ X8 @ X10 )
= ( kpair @ X8 @ X10 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjR,axiom,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ) ).
thf('10',plain,
( setukpairinjR
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X6 = X10 ) ) ) ),
define([status(thm)]) ).
thf(setukpairinjL,axiom,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ) ).
thf('11',plain,
( setukpairinjL
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) ) ) ),
define([status(thm)]) ).
thf(breln1compEex,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
=> ! [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(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
=> ( 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
=> ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
( ( ( kpair @ X12 @ X14 )
= ( kpair @ X16 @ X18 ) )
=> ( X14 = X18 ) )
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X20 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( kpair @ X24 @ X26 )
= ( kpair @ X24 @ X26 ) ) ) )
=> ( 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
=> ( ! [X28: $i,X30: $i] :
( ( breln @ X28 @ X28 @ X30 )
=> ! [X32: $i > $o] :
( ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ( ( in @ ( kpair @ X34 @ X36 ) @ X30 )
=> ( X32 @ ( kpair @ X34 @ X36 ) ) ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X30 )
=> ( X32 @ X38 ) ) ) )
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( ! [X40: $i,X42: $i] :
( ( breln @ X40 @ X40 @ X42 )
=> ! [X44: $i > $o] :
( ! [X46: $i] :
( ( in @ X46 @ X40 )
=> ! [X48: $i] :
( ( in @ X48 @ X40 )
=> ( ( in @ ( kpair @ X46 @ X48 ) @ X42 )
=> ( X44 @ ( kpair @ X46 @ X48 ) ) ) ) )
=> ! [X50: $i] :
( ( in @ X50 @ X42 )
=> ( X44 @ X50 ) ) ) )
=> ( ! [X52: $i,X54: $i] :
( ( breln @ X52 @ X52 @ X54 )
=> ! [X56: $i] :
( ( breln @ X52 @ X52 @ X56 )
=> ( ! [X58: $i] :
( ( in @ X58 @ X52 )
=> ! [X60: $i] :
( ( in @ X60 @ X52 )
=> ( ( in @ ( kpair @ X58 @ X60 ) @ X54 )
=> ( in @ ( kpair @ X58 @ X60 ) @ X56 ) ) ) )
=> ( subset @ X54 @ X56 ) ) ) )
=> ( ! [X62: $i,X64: $i] :
( ( breln @ X62 @ X62 @ X64 )
=> ! [X66: $i] :
( ( breln @ X62 @ X62 @ X66 )
=> ( ! [X68: $i] :
( ( in @ X68 @ X62 )
=> ! [X70: $i] :
( ( in @ X70 @ X62 )
=> ( ( in @ ( kpair @ X68 @ X70 ) @ X64 )
=> ( in @ ( kpair @ X68 @ X70 ) @ X66 ) ) ) )
=> ( ! [X72: $i] :
( ( in @ X72 @ X62 )
=> ! [X74: $i] :
( ( in @ X74 @ X62 )
=> ( ( in @ ( kpair @ X72 @ X74 ) @ X66 )
=> ( in @ ( kpair @ X72 @ X74 ) @ X64 ) ) ) )
=> ( X64 = X66 ) ) ) ) )
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( ! [X76: $i,X78: $i] :
( ( breln @ X76 @ X76 @ X78 )
=> ! [X80: $i] :
( ( breln @ X76 @ X76 @ X80 )
=> ( breln @ X76 @ X76 @ ( breln1compset @ X76 @ X78 @ X80 ) ) ) )
=> ( ! [X82: $i,X84: $i] :
( ( breln @ X82 @ X82 @ X84 )
=> ! [X86: $i] :
( ( breln @ X82 @ X82 @ X86 )
=> ! [X88: $i] :
( ( in @ X88 @ X82 )
=> ! [X90: $i] :
( ( in @ X90 @ X82 )
=> ! [X92: $i] :
( ( in @ X92 @ X82 )
=> ( ( in @ ( kpair @ X88 @ X92 ) @ X84 )
=> ( ( in @ ( kpair @ X92 @ X90 ) @ X86 )
=> ( in @ ( kpair @ X88 @ X90 ) @ ( breln1compset @ X82 @ X84 @ X86 ) ) ) ) ) ) ) ) )
=> ( ! [X94: $i,X96: $i] :
( ( breln @ X94 @ X94 @ X96 )
=> ! [X98: $i] :
( ( breln @ X94 @ X94 @ X98 )
=> ! [X100: $i] :
( ( in @ X100 @ X94 )
=> ! [X102: $i] :
( ( in @ X102 @ X94 )
=> ( ( in @ ( kpair @ X100 @ X102 ) @ ( breln1compset @ X94 @ X96 @ X98 ) )
=> ? [X104: $i] :
( ( in @ ( kpair @ X104 @ X102 ) @ X98 )
& ( in @ ( kpair @ X100 @ X104 ) @ X96 )
& ( in @ X104 @ X94 ) ) ) ) ) ) )
=> ! [X106: $i,X108: $i] :
( ( breln @ X106 @ X106 @ X108 )
=> ! [X110: $i] :
( ( breln @ X106 @ X106 @ X110 )
=> ! [X112: $i] :
( ( in @ X112 @ X106 )
=> ! [X114: $i] :
( ( in @ X114 @ X106 )
=> ( ( in @ ( kpair @ X112 @ X114 ) @ ( breln1compset @ X106 @ X108 @ X110 ) )
=> ! [X116: $o] :
( ! [X118: $i] :
( ( in @ X118 @ X106 )
=> ( ( in @ ( kpair @ X112 @ X118 ) @ X108 )
=> ( ( in @ ( kpair @ X118 @ X114 ) @ X110 )
=> X116 ) ) )
=> X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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
=> ( 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
=> ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X4 = X8 ) )
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
( ( ( kpair @ X12 @ X14 )
= ( kpair @ X16 @ X18 ) )
=> ( X14 = X18 ) )
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( ! [X20: $i,X22: $i,X24: $i] :
( ( in @ X24 @ X20 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( kpair @ X24 @ X26 )
= ( kpair @ X24 @ X26 ) ) ) )
=> ( 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
=> ( ! [X28: $i,X30: $i] :
( ( breln @ X28 @ X28 @ X30 )
=> ! [X32: $i > $o] :
( ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ( ( in @ ( kpair @ X34 @ X36 ) @ X30 )
=> ( X32 @ ( kpair @ X34 @ X36 ) ) ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X30 )
=> ( X32 @ X38 ) ) ) )
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( ! [X40: $i,X42: $i] :
( ( breln @ X40 @ X40 @ X42 )
=> ! [X44: $i > $o] :
( ! [X46: $i] :
( ( in @ X46 @ X40 )
=> ! [X48: $i] :
( ( in @ X48 @ X40 )
=> ( ( in @ ( kpair @ X46 @ X48 ) @ X42 )
=> ( X44 @ ( kpair @ X46 @ X48 ) ) ) ) )
=> ! [X50: $i] :
( ( in @ X50 @ X42 )
=> ( X44 @ X50 ) ) ) )
=> ( ! [X52: $i,X54: $i] :
( ( breln @ X52 @ X52 @ X54 )
=> ! [X56: $i] :
( ( breln @ X52 @ X52 @ X56 )
=> ( ! [X58: $i] :
( ( in @ X58 @ X52 )
=> ! [X60: $i] :
( ( in @ X60 @ X52 )
=> ( ( in @ ( kpair @ X58 @ X60 ) @ X54 )
=> ( in @ ( kpair @ X58 @ X60 ) @ X56 ) ) ) )
=> ( subset @ X54 @ X56 ) ) ) )
=> ( ! [X62: $i,X64: $i] :
( ( breln @ X62 @ X62 @ X64 )
=> ! [X66: $i] :
( ( breln @ X62 @ X62 @ X66 )
=> ( ! [X68: $i] :
( ( in @ X68 @ X62 )
=> ! [X70: $i] :
( ( in @ X70 @ X62 )
=> ( ( in @ ( kpair @ X68 @ X70 ) @ X64 )
=> ( in @ ( kpair @ X68 @ X70 ) @ X66 ) ) ) )
=> ( ! [X72: $i] :
( ( in @ X72 @ X62 )
=> ! [X74: $i] :
( ( in @ X74 @ X62 )
=> ( ( in @ ( kpair @ X72 @ X74 ) @ X66 )
=> ( in @ ( kpair @ X72 @ X74 ) @ X64 ) ) ) )
=> ( X64 = X66 ) ) ) ) )
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( ! [X76: $i,X78: $i] :
( ( breln @ X76 @ X76 @ X78 )
=> ! [X80: $i] :
( ( breln @ X76 @ X76 @ X80 )
=> ( breln @ X76 @ X76 @ ( breln1compset @ X76 @ X78 @ X80 ) ) ) )
=> ( ! [X82: $i,X84: $i] :
( ( breln @ X82 @ X82 @ X84 )
=> ! [X86: $i] :
( ( breln @ X82 @ X82 @ X86 )
=> ! [X88: $i] :
( ( in @ X88 @ X82 )
=> ! [X90: $i] :
( ( in @ X90 @ X82 )
=> ! [X92: $i] :
( ( in @ X92 @ X82 )
=> ( ( in @ ( kpair @ X88 @ X92 ) @ X84 )
=> ( ( in @ ( kpair @ X92 @ X90 ) @ X86 )
=> ( in @ ( kpair @ X88 @ X90 ) @ ( breln1compset @ X82 @ X84 @ X86 ) ) ) ) ) ) ) ) )
=> ( ! [X94: $i,X96: $i] :
( ( breln @ X94 @ X94 @ X96 )
=> ! [X98: $i] :
( ( breln @ X94 @ X94 @ X98 )
=> ! [X100: $i] :
( ( in @ X100 @ X94 )
=> ! [X102: $i] :
( ( in @ X102 @ X94 )
=> ( ( in @ ( kpair @ X100 @ X102 ) @ ( breln1compset @ X94 @ X96 @ X98 ) )
=> ? [X104: $i] :
( ( in @ ( kpair @ X104 @ X102 ) @ X98 )
& ( in @ ( kpair @ X100 @ X104 ) @ X96 )
& ( in @ X104 @ X94 ) ) ) ) ) ) )
=> ! [X106: $i,X108: $i] :
( ( breln @ X106 @ X106 @ X108 )
=> ! [X110: $i] :
( ( breln @ X106 @ X106 @ X110 )
=> ! [X112: $i] :
( ( in @ X112 @ X106 )
=> ! [X114: $i] :
( ( in @ X114 @ X106 )
=> ( ( in @ ( kpair @ X112 @ X114 ) @ ( breln1compset @ X106 @ X108 @ X110 ) )
=> ! [X116: $o] :
( ! [X118: $i] :
( ( in @ X118 @ X106 )
=> ( ( in @ ( kpair @ X112 @ X118 ) @ X108 )
=> ( ( in @ ( kpair @ X118 @ X114 ) @ X110 )
=> X116 ) ) )
=> X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl177,plain,
in @ sk__56 @ sk__53,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl173,plain,
in @ sk__57 @ sk__53,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl178,plain,
breln @ sk__53 @ sk__53 @ sk__54,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl172,plain,
breln @ sk__53 @ sk__53 @ sk__55,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl176,plain,
in @ ( kpair @ sk__56 @ sk__57 ) @ ( breln1compset @ sk__53 @ sk__54 @ sk__55 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl171,plain,
! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ~ ( breln @ X22 @ X22 @ X23 )
| ~ ( in @ X24 @ X22 )
| ( in @ ( sk__59 @ X24 @ X25 @ X23 @ X26 @ X22 ) @ X22 )
| ~ ( in @ ( kpair @ X25 @ X24 ) @ ( breln1compset @ X22 @ X26 @ X23 ) )
| ~ ( in @ X25 @ X22 )
| ~ ( breln @ X22 @ X22 @ X26 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl170,plain,
! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ~ ( breln @ X22 @ X22 @ X23 )
| ~ ( in @ X24 @ X22 )
| ( in @ ( kpair @ X25 @ ( sk__59 @ X24 @ X25 @ X23 @ X26 @ X22 ) ) @ X26 )
| ~ ( in @ ( kpair @ X25 @ X24 ) @ ( breln1compset @ X22 @ X26 @ X23 ) )
| ~ ( in @ X25 @ X22 )
| ~ ( breln @ X22 @ X22 @ X26 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl169,plain,
! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ~ ( breln @ X22 @ X22 @ X23 )
| ~ ( in @ X24 @ X22 )
| ( in @ ( kpair @ ( sk__59 @ X24 @ X25 @ X23 @ X26 @ X22 ) @ X24 ) @ X23 )
| ~ ( in @ ( kpair @ X25 @ X24 ) @ ( breln1compset @ X22 @ X26 @ X23 ) )
| ~ ( in @ X25 @ X22 )
| ~ ( breln @ X22 @ X22 @ X26 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl174,plain,
~ sk__58,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl175,plain,
! [X27: $i] :
( sk__58
| ~ ( in @ X27 @ sk__53 )
| ~ ( in @ ( kpair @ X27 @ sk__57 ) @ sk__55 )
| ~ ( in @ ( kpair @ sk__56 @ X27 ) @ sk__54 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8112,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl177,zip_derived_cl173,zip_derived_cl178,zip_derived_cl172,zip_derived_cl176,zip_derived_cl171,zip_derived_cl170,zip_derived_cl169,zip_derived_cl174,zip_derived_cl175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU781^1 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hjryeDVtnX true
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:39:01 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.20/0.66 % Total configuration time : 828
% 0.20/0.66 % Estimated wc time : 1656
% 0.20/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.34/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.34/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 177.26/23.65 % Solved by lams/40_c_ic.sh.
% 177.26/23.65 % done 843 iterations in 22.800s
% 177.26/23.65 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 177.26/23.65 % SZS output start Refutation
% See solution above
% 177.26/23.66
% 177.26/23.66
% 177.26/23.66 % Terminating...
% 177.26/23.85 % Runner terminated.
% 177.26/23.85 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------